General accounts of Topological Insulators have been presented. A holistic idea of the basic theories related to topological insulators and material properties were presented. Furthermore, there were discussions on the 2D-Two dimensional and 3D-three dimensional topological insulators. The Dirac fermion material science and subsequent quantum oscillations were discussed in this paper.
This document analyzes wave packet propagation in weakly nonlinear acoustic metamaterials through spectro-spatial analysis. Spectro-spatial analysis uses full-scale transient analysis and signal processing techniques to reveal dispersion curves and localized solitary wave properties. The analysis finds an unusual frequency shift phenomenon in the middle-wavelength region of the optical wave branch that causes it to behave like a band gap for transient waves. This frequency shift is then used to design a direction-biased waveguide with high efficiency, as shown through numerical simulations.
Vitality of Physics In Nanoscience and NanotechnologyIOSR Journals
This document discusses the vital role of physics in nanoscience and nanotechnology. It explains that at the nanoscale, physics is different due to quantum effects and a high surface area to volume ratio. Properties like band structure and optical properties can be altered at the nanoscale. The document also discusses manufacturing approaches like top-down and bottom-up methods and how they apply physics principles to create nanomaterials. Finally, it notes that nanomaterials can have significantly different properties than bulk materials of the same composition due to their small size and large surface area.
FERROMAGNETIC-FERROELECTRIC COMPOSITE 1D NANOSTRUCTURE IN THE PURSUIT OF MAGN...ijrap
Nanocomposites of linear chain of ferroelectric-ferromagnetic crystal structure is considered. It is analyzed
theoretically in the motion equation method on the pursuit of magnonic excitations,lattice vibration
excitations and their interactions leading to a new collective mode of excitations,the electormagnons. In
this particular work, it is observed that the magnetizations and polarizations are tunable in a given temperature ranges for some specific values of the coupling order parameter.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
This document discusses magnetized plasma with ferromagnetic grains (MPFG) as a potential negative refractive index medium. It is shown that:
1) MPFG has permittivity and permeability tensors that are controlled by the magnetized plasma and ferromagnetic grains.
2) For extraordinary waves propagating parallel to an external magnetic field, the refractive index of MPFG can be negative, indicating left-handed behavior, in certain frequency domains near resonance.
3) Numerical calculations demonstrate that both the effective permittivity and permeability of MPFG can be simultaneously negative for some frequencies, allowing for negative refractive index and transparent propagation of electromagnetic waves.
This document summarizes the fundamentals of nonlinear optical materials. It discusses how nonlinear optical materials play a major role in nonlinear optics and their impact on information technology and applications. Nonlinear optical effects can be represented by Maxwell's equations, with the total polarization consisting of a linear and nonlinear component. Second-order effects like second harmonic generation depend on the material's nonlinear susceptibility χ(2) and require the material to be non-centrosymmetric. Third-order effects dominate in centrosymmetric materials and include third harmonic generation and the optical Kerr effect. Parametric processes also allow frequency conversion through phase matching of waves. Nonlinear optical materials are crucial for applications like optical switching and communication.
This document describes a theoretical study of graphene membrane rupture under strong electric fields using molecular dynamics simulations. The study examined pristine and defective graphene membranes of various sizes under electric fields of varying strengths, both with and without ion bombardment, to determine the cause of experimental membrane ruptures. The simulations found that electric fields alone did not rupture membranes. Ion bombardment was shown to be able to rupture membranes if ions possessed kinetic energies of approximately 0.7 electronvolts upon impact. Sequential ion bombardment, mimicking experimental conditions, was also found to potentially rupture membranes through accumulated damage.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document analyzes wave packet propagation in weakly nonlinear acoustic metamaterials through spectro-spatial analysis. Spectro-spatial analysis uses full-scale transient analysis and signal processing techniques to reveal dispersion curves and localized solitary wave properties. The analysis finds an unusual frequency shift phenomenon in the middle-wavelength region of the optical wave branch that causes it to behave like a band gap for transient waves. This frequency shift is then used to design a direction-biased waveguide with high efficiency, as shown through numerical simulations.
Vitality of Physics In Nanoscience and NanotechnologyIOSR Journals
This document discusses the vital role of physics in nanoscience and nanotechnology. It explains that at the nanoscale, physics is different due to quantum effects and a high surface area to volume ratio. Properties like band structure and optical properties can be altered at the nanoscale. The document also discusses manufacturing approaches like top-down and bottom-up methods and how they apply physics principles to create nanomaterials. Finally, it notes that nanomaterials can have significantly different properties than bulk materials of the same composition due to their small size and large surface area.
FERROMAGNETIC-FERROELECTRIC COMPOSITE 1D NANOSTRUCTURE IN THE PURSUIT OF MAGN...ijrap
Nanocomposites of linear chain of ferroelectric-ferromagnetic crystal structure is considered. It is analyzed
theoretically in the motion equation method on the pursuit of magnonic excitations,lattice vibration
excitations and their interactions leading to a new collective mode of excitations,the electormagnons. In
this particular work, it is observed that the magnetizations and polarizations are tunable in a given temperature ranges for some specific values of the coupling order parameter.
MAGNETIZED PLASMA WITH FERROMAGNETIC GRAINS AS A VIABLE NEGATIVE REFRACTIVE I...ijrap
This document discusses magnetized plasma with ferromagnetic grains (MPFG) as a potential negative refractive index medium. It is shown that:
1) MPFG has permittivity and permeability tensors that are controlled by the magnetized plasma and ferromagnetic grains.
2) For extraordinary waves propagating parallel to an external magnetic field, the refractive index of MPFG can be negative, indicating left-handed behavior, in certain frequency domains near resonance.
3) Numerical calculations demonstrate that both the effective permittivity and permeability of MPFG can be simultaneously negative for some frequencies, allowing for negative refractive index and transparent propagation of electromagnetic waves.
This document summarizes the fundamentals of nonlinear optical materials. It discusses how nonlinear optical materials play a major role in nonlinear optics and their impact on information technology and applications. Nonlinear optical effects can be represented by Maxwell's equations, with the total polarization consisting of a linear and nonlinear component. Second-order effects like second harmonic generation depend on the material's nonlinear susceptibility χ(2) and require the material to be non-centrosymmetric. Third-order effects dominate in centrosymmetric materials and include third harmonic generation and the optical Kerr effect. Parametric processes also allow frequency conversion through phase matching of waves. Nonlinear optical materials are crucial for applications like optical switching and communication.
This document describes a theoretical study of graphene membrane rupture under strong electric fields using molecular dynamics simulations. The study examined pristine and defective graphene membranes of various sizes under electric fields of varying strengths, both with and without ion bombardment, to determine the cause of experimental membrane ruptures. The simulations found that electric fields alone did not rupture membranes. Ion bombardment was shown to be able to rupture membranes if ions possessed kinetic energies of approximately 0.7 electronvolts upon impact. Sequential ion bombardment, mimicking experimental conditions, was also found to potentially rupture membranes through accumulated damage.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Electron transport in one dimensional nanosystemsVorname Nachname
This document provides an overview of electron transport theory in one-dimensional nanoscale systems. It begins with an introduction to Landauer theory and asymmetric potential barriers. It then examines tight binding models of perfect and defective wires to understand electron transmission. Applications to scanning tunneling microscopes are discussed, modeling the tip-surface junction as a tight binding wire. Vibrational effects on conduction are also considered.
This document discusses heat conduction at the nanoscale and how it differs from macroscale heat transfer. At the nanoscale, the characteristic lengths of phonons (the main heat carriers in dielectrics and semiconductors) become comparable to nanostructure sizes. This invalidates the Fourier law of heat conduction, which assumes local thermal equilibrium. The document outlines different heat transfer regimes depending on relative sizes and discusses implications for thermal conductivity and applications like thermoelectrics where nanoscale effects could improve performance. Size effects are most dramatic in superlattices and thin films, while studies of heat transfer in nanowires and nanoparticles are still emerging. Understanding nanoscale heat transfer is important for optimizing nano-enabled technologies.
This document summarizes a study on quantum phase transitions in small spinless fermion systems and their comparison to infinitely large systems. The study evaluates a one-dimensional model of spinless fermions with nearest neighbor interactions. For small system sizes, certain evolutionary behaviors were observed as the number of sites increased, though no direct phase transitions could be analyzed due to limitations of computer capabilities. The document outlines the model, methodology using Hamiltonian matrices, and presents some initial results on systems with interaction strength U=0.
This document discusses numerical modeling of the mechanical properties of polymer nanocomposites reinforced with carbon nanotube (CNT) bundles and ropes. The key points are:
1) Finite element models are developed using representative volume elements (RVEs) containing CNT bundles or ropes to determine the effective properties.
2) Models are made with bundles and ropes containing various numbers of CNTs (5, 7, 9, 13) to study the effect of rope geometry.
3) Elasticity theory for anisotropic materials is used to extract the composite properties from the RVE simulations.
4) The results indicate the longitudinal modulus of the nanocomposite decreases as the number of CNTs in
This document summarizes research on the superconducting behavior of carbon nanotubes (CNTs). It first discusses how the transition temperature (Tc) determines a material's superconductivity and how electron-phonon interactions can induce superconductivity in CNTs due to their curvature. The document then presents a theoretical model for CNT resistivity incorporating relaxation time, Fermi velocity, and coulomb interaction. Experimental results showing superconductivity in CNT ropes/bundles at temperatures up to 15K are discussed. The conclusion is that managing electron-electron interaction to increase Fermi velocity can decrease resistivity and lead to superconductivity at low temperatures.
This document discusses superdiffusion of waves in random media. It describes how Lévy walks, which involve random walks with heavy-tailed step lengths, can lead to superdiffusion described by fractional diffusion equations. This results in anomalous transport properties like superdiffusive propagation. The document also discusses how interference effects between multiply scattered waves can occur and be observed through phenomena like coherent backscattering in such disordered media exhibiting superdiffusion.
Quantum tunneling sensors can be used for force sensing and biomolecule detection. Force-based quantum tunneling sensors utilize the principle that tunneling current increases exponentially as the width of the tunneling barrier decreases with applied force. This phenomenon is exploited in quantum tunneling composites which contain conductive nanoparticles in a flexible polymer and can be used to create sensitive touch screens and force sensors. Biomolecule sensing uses quantum tunneling to detect different molecules by how much they alter the tunnel current when introduced into a steady-state tunnel junction. These techniques open applications in healthcare diagnostics, smart skins and other high-precision force sensing areas.
This curriculum vitae is for Amal Sarkar of IIT Bombay. It provides details of his education including a Ph.D in experimental particle physics from IIT Bombay, as well as his work experience including research associate positions at IIT Bombay and RHIC. It also lists his research focusing on measuring moments of net kaon distributions to search for the QCD critical point and studying D meson production.
Dresden 2014 A tour of some fractional models and the physics behind themNick Watkins
This document provides a summary of fractional models and the physics they seek to describe. It begins with an overview of classical Brownian motion and diffusion models, highlighting the central limit theorem, Wiener process, Langevin equation, and fluctuation-dissipation theorem. It then discusses two approaches to generalizing these models: fractional kinetics via continuous time random walks, which modifies diffusion through time subordination; and fractional motions like fractional Brownian motion, which derive from non-Markovian generalizations of the Langevin equation. The document aims to build intuition about these fractional models and their relationships to underlying physical phenomena.
This document numerically analyzes the wave function of atoms under the combined effects of an optical lattice trapping potential and a harmonic oscillator potential, as used in Bose-Einstein condensation experiments. It employs the Crank-Nicolson scheme to solve the Gross-Pitaevskii equation. The results show that the wave function distribution responds to parameters like the trapping frequencies ratio, optical lattice intensity, chemical potential, and energy. Careful adjustment of the time step and grid spacing is needed to satisfy conservation of norms and energy as required by the physical system. Distributions of the overlapping potentials for different q-factors are presented.
This document summarizes a study investigating compositional modulations in AlxGa1-xAs thin films using solid-state NMR and DFT calculations. The researchers were able to identify all possible As coordination sites in AlxGa1-xAs using 75As NMR experiments. Spectral deconvolution complied with an absence of long-range ordering, but an unconstrained fit showed a deviation from the imposed ordering parameter. NMR and DFT showed that the electric field gradients experienced by arsenic sites are distributed due to compositional variation in the higher coordination spheres of Al and Ga atoms. DFT calculations reproduced the experimentally observed electric field gradient distributions and showed NMR is sensitive to compositional modulations up to the 7th coordination shell
Seminário proferido pelo pesquisador Thiago Burgo (Unicamp) em 26 de agosto de 2015 para cerca de 20 estudantes e professores, na seção UCS (Caxias do Sul, RS) do Instituto Nacional de Engenharia de Superfícies.
The document discusses transparent electronics and transparent conducting materials. It explains that transparent conductors are neither 100% optically transparent nor metallically conductive due to the contradictory nature of these properties from a band structure perspective. Transparent conducting oxides (TCOs) are commonly used by degenerately doping the material to displace the Fermi level into the conduction band, providing high carrier mobility and low optical absorption. The document also discusses applications of transparent amorphous oxide semiconductors (TAOSs) in displays and chemical detection.
This document discusses transparent electronics and various technologies related to it. It describes how transparent electronics uses wide band-gap semiconductors to create invisible circuits. It also discusses the challenges of creating materials that are both electrically conductive and optically transparent, as well as various technologies like transparent thin-film transistors, resistors, capacitors and inductors that are components of transparent electronics.
Ultracold atoms in superlattices as quantum simulators for a spin ordering mo...Alexander Decker
This document discusses using ultracold fermionic atoms in optical lattices to simulate spin ordering models. It begins by describing how atoms can be trapped in optical lattices using laser light. It then proposes how a spin ordering Hamiltonian could be used to achieve superexchange interaction in a double well system. Finally, it suggests going beyond double wells to study resonating valence bond states in a kagome lattice, which could provide insights into phenomena like high-temperature superconductivity.
The document provides an overview of dielectric materials and their importance in modern technology. It discusses the early history and development of the field including key contributions from Faraday, Clausius, Mossotti, Debye and others. Debye developed a theory to explain the dielectric properties of polar materials by accounting for their permanent dipole moments and molecular relaxation processes. The theory was successful for polar liquids but broke down for solids due to interactions between dipoles. Modern applications of dielectric materials continue to demand new materials with tailored properties.
This document provides an introduction to dielectric materials and their importance in modern technology. It discusses the early history and development of the field, including Faraday's discovery of dielectric polarization and Debye's theory relating molecular dipole moments to macroscopic dielectric properties. Modern applications demand materials with specific dielectric properties tailored for uses like integrated circuits, wireless communication technologies, and microwave devices. The document outlines the classical theory of dielectrics, including the different polarization mechanisms (electronic, atomic/ionic, dipolar/orientational, space charge) that contribute to a material's overall dielectric constant and frequency-dependent behavior.
Temperature, acceptor concentration and donor concentration dependency of ele...IJAMSE Journal
This document discusses the calculation of low-field electron mobility in bulk GaN and GaP semiconductors. It examines the dependency of mobility on temperature, acceptor concentration, and donor concentration. Five scattering mechanisms are considered: ionized impurity scattering, neutral impurity scattering, acoustic deformation potential scattering, piezoelectric scattering, and optical deformation potential scattering. Graphs show how the total electronic mobility decreases with increasing temperature and is mostly independent of acceptor/donor concentration for both materials. The document provides equations and parameters used to model each scattering mechanism and calculate the total mobility.
An introduction to the fundamental physics of transparent conducting oxides including a review of the electrical and optical properties of common materials.
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...Lewis Larsen
“Spatial coherence and stability in a disordered organic polariton condensate”
K. Daskalakis et al. Physical Review Letters 115 pp. 035301 - 06 (2015)
Inside a laser-pumped microcavity, they demonstrated the formation of spatially localized, entangled plasmon condensates in 100 nm layer of organic TDAF molecules at room temperature in a disordered system. Created plasmon condensates have spatial dimensions that seem to max-out at diameters of ~100 μ; beyond this critical size limit they destabilize. First-order temporal coherence of condensates = 0.8 picoseconds (ps); this is in reasonable agreement with coherence decay time estimate of 1 ps which is calculated from the observed emission linewidth.
According to Widom-Larsen theory of LENRs, many-body collective quantum and electromagnetic effects are crucial and enabling to the operation of electroweak nuclear catalysis at ambient temperatures; quantum entanglement amongst protons and plasmons at LENR sites is inferred; 1 ps lifetime of plasmon condensate is very ample time for LENRs. In 2006 EPJC paper (Widom & Larsen) we originally estimated the size of many-body coherence domains in LENR sites on metallic hydride surfaces to be ~ 1 - 10 μ. As discussed in this document, in 2009 Larsen extended Widom-Larsen theory to cover occurrence of LENRs on organic aromatic molecules; at that time, maximum size of W-L coherence domains was re-estimated and increased up to ~ 100 μ. It is not known whether this striking similarity to Daskalakis et al.’s apparent size limit of 100 μ is coincidental. W-L active site functions like a microcavity; thus seems reasonable to speculate that the surface plasmons in LENR-active sites form condensates similar to what Daskalakis et al. observed.
Electron transport in one dimensional nanosystemsVorname Nachname
This document provides an overview of electron transport theory in one-dimensional nanoscale systems. It begins with an introduction to Landauer theory and asymmetric potential barriers. It then examines tight binding models of perfect and defective wires to understand electron transmission. Applications to scanning tunneling microscopes are discussed, modeling the tip-surface junction as a tight binding wire. Vibrational effects on conduction are also considered.
This document discusses heat conduction at the nanoscale and how it differs from macroscale heat transfer. At the nanoscale, the characteristic lengths of phonons (the main heat carriers in dielectrics and semiconductors) become comparable to nanostructure sizes. This invalidates the Fourier law of heat conduction, which assumes local thermal equilibrium. The document outlines different heat transfer regimes depending on relative sizes and discusses implications for thermal conductivity and applications like thermoelectrics where nanoscale effects could improve performance. Size effects are most dramatic in superlattices and thin films, while studies of heat transfer in nanowires and nanoparticles are still emerging. Understanding nanoscale heat transfer is important for optimizing nano-enabled technologies.
This document summarizes a study on quantum phase transitions in small spinless fermion systems and their comparison to infinitely large systems. The study evaluates a one-dimensional model of spinless fermions with nearest neighbor interactions. For small system sizes, certain evolutionary behaviors were observed as the number of sites increased, though no direct phase transitions could be analyzed due to limitations of computer capabilities. The document outlines the model, methodology using Hamiltonian matrices, and presents some initial results on systems with interaction strength U=0.
This document discusses numerical modeling of the mechanical properties of polymer nanocomposites reinforced with carbon nanotube (CNT) bundles and ropes. The key points are:
1) Finite element models are developed using representative volume elements (RVEs) containing CNT bundles or ropes to determine the effective properties.
2) Models are made with bundles and ropes containing various numbers of CNTs (5, 7, 9, 13) to study the effect of rope geometry.
3) Elasticity theory for anisotropic materials is used to extract the composite properties from the RVE simulations.
4) The results indicate the longitudinal modulus of the nanocomposite decreases as the number of CNTs in
This document summarizes research on the superconducting behavior of carbon nanotubes (CNTs). It first discusses how the transition temperature (Tc) determines a material's superconductivity and how electron-phonon interactions can induce superconductivity in CNTs due to their curvature. The document then presents a theoretical model for CNT resistivity incorporating relaxation time, Fermi velocity, and coulomb interaction. Experimental results showing superconductivity in CNT ropes/bundles at temperatures up to 15K are discussed. The conclusion is that managing electron-electron interaction to increase Fermi velocity can decrease resistivity and lead to superconductivity at low temperatures.
This document discusses superdiffusion of waves in random media. It describes how Lévy walks, which involve random walks with heavy-tailed step lengths, can lead to superdiffusion described by fractional diffusion equations. This results in anomalous transport properties like superdiffusive propagation. The document also discusses how interference effects between multiply scattered waves can occur and be observed through phenomena like coherent backscattering in such disordered media exhibiting superdiffusion.
Quantum tunneling sensors can be used for force sensing and biomolecule detection. Force-based quantum tunneling sensors utilize the principle that tunneling current increases exponentially as the width of the tunneling barrier decreases with applied force. This phenomenon is exploited in quantum tunneling composites which contain conductive nanoparticles in a flexible polymer and can be used to create sensitive touch screens and force sensors. Biomolecule sensing uses quantum tunneling to detect different molecules by how much they alter the tunnel current when introduced into a steady-state tunnel junction. These techniques open applications in healthcare diagnostics, smart skins and other high-precision force sensing areas.
This curriculum vitae is for Amal Sarkar of IIT Bombay. It provides details of his education including a Ph.D in experimental particle physics from IIT Bombay, as well as his work experience including research associate positions at IIT Bombay and RHIC. It also lists his research focusing on measuring moments of net kaon distributions to search for the QCD critical point and studying D meson production.
Dresden 2014 A tour of some fractional models and the physics behind themNick Watkins
This document provides a summary of fractional models and the physics they seek to describe. It begins with an overview of classical Brownian motion and diffusion models, highlighting the central limit theorem, Wiener process, Langevin equation, and fluctuation-dissipation theorem. It then discusses two approaches to generalizing these models: fractional kinetics via continuous time random walks, which modifies diffusion through time subordination; and fractional motions like fractional Brownian motion, which derive from non-Markovian generalizations of the Langevin equation. The document aims to build intuition about these fractional models and their relationships to underlying physical phenomena.
This document numerically analyzes the wave function of atoms under the combined effects of an optical lattice trapping potential and a harmonic oscillator potential, as used in Bose-Einstein condensation experiments. It employs the Crank-Nicolson scheme to solve the Gross-Pitaevskii equation. The results show that the wave function distribution responds to parameters like the trapping frequencies ratio, optical lattice intensity, chemical potential, and energy. Careful adjustment of the time step and grid spacing is needed to satisfy conservation of norms and energy as required by the physical system. Distributions of the overlapping potentials for different q-factors are presented.
This document summarizes a study investigating compositional modulations in AlxGa1-xAs thin films using solid-state NMR and DFT calculations. The researchers were able to identify all possible As coordination sites in AlxGa1-xAs using 75As NMR experiments. Spectral deconvolution complied with an absence of long-range ordering, but an unconstrained fit showed a deviation from the imposed ordering parameter. NMR and DFT showed that the electric field gradients experienced by arsenic sites are distributed due to compositional variation in the higher coordination spheres of Al and Ga atoms. DFT calculations reproduced the experimentally observed electric field gradient distributions and showed NMR is sensitive to compositional modulations up to the 7th coordination shell
Seminário proferido pelo pesquisador Thiago Burgo (Unicamp) em 26 de agosto de 2015 para cerca de 20 estudantes e professores, na seção UCS (Caxias do Sul, RS) do Instituto Nacional de Engenharia de Superfícies.
The document discusses transparent electronics and transparent conducting materials. It explains that transparent conductors are neither 100% optically transparent nor metallically conductive due to the contradictory nature of these properties from a band structure perspective. Transparent conducting oxides (TCOs) are commonly used by degenerately doping the material to displace the Fermi level into the conduction band, providing high carrier mobility and low optical absorption. The document also discusses applications of transparent amorphous oxide semiconductors (TAOSs) in displays and chemical detection.
This document discusses transparent electronics and various technologies related to it. It describes how transparent electronics uses wide band-gap semiconductors to create invisible circuits. It also discusses the challenges of creating materials that are both electrically conductive and optically transparent, as well as various technologies like transparent thin-film transistors, resistors, capacitors and inductors that are components of transparent electronics.
Ultracold atoms in superlattices as quantum simulators for a spin ordering mo...Alexander Decker
This document discusses using ultracold fermionic atoms in optical lattices to simulate spin ordering models. It begins by describing how atoms can be trapped in optical lattices using laser light. It then proposes how a spin ordering Hamiltonian could be used to achieve superexchange interaction in a double well system. Finally, it suggests going beyond double wells to study resonating valence bond states in a kagome lattice, which could provide insights into phenomena like high-temperature superconductivity.
The document provides an overview of dielectric materials and their importance in modern technology. It discusses the early history and development of the field including key contributions from Faraday, Clausius, Mossotti, Debye and others. Debye developed a theory to explain the dielectric properties of polar materials by accounting for their permanent dipole moments and molecular relaxation processes. The theory was successful for polar liquids but broke down for solids due to interactions between dipoles. Modern applications of dielectric materials continue to demand new materials with tailored properties.
This document provides an introduction to dielectric materials and their importance in modern technology. It discusses the early history and development of the field, including Faraday's discovery of dielectric polarization and Debye's theory relating molecular dipole moments to macroscopic dielectric properties. Modern applications demand materials with specific dielectric properties tailored for uses like integrated circuits, wireless communication technologies, and microwave devices. The document outlines the classical theory of dielectrics, including the different polarization mechanisms (electronic, atomic/ionic, dipolar/orientational, space charge) that contribute to a material's overall dielectric constant and frequency-dependent behavior.
Temperature, acceptor concentration and donor concentration dependency of ele...IJAMSE Journal
This document discusses the calculation of low-field electron mobility in bulk GaN and GaP semiconductors. It examines the dependency of mobility on temperature, acceptor concentration, and donor concentration. Five scattering mechanisms are considered: ionized impurity scattering, neutral impurity scattering, acoustic deformation potential scattering, piezoelectric scattering, and optical deformation potential scattering. Graphs show how the total electronic mobility decreases with increasing temperature and is mostly independent of acceptor/donor concentration for both materials. The document provides equations and parameters used to model each scattering mechanism and calculate the total mobility.
An introduction to the fundamental physics of transparent conducting oxides including a review of the electrical and optical properties of common materials.
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...Lewis Larsen
“Spatial coherence and stability in a disordered organic polariton condensate”
K. Daskalakis et al. Physical Review Letters 115 pp. 035301 - 06 (2015)
Inside a laser-pumped microcavity, they demonstrated the formation of spatially localized, entangled plasmon condensates in 100 nm layer of organic TDAF molecules at room temperature in a disordered system. Created plasmon condensates have spatial dimensions that seem to max-out at diameters of ~100 μ; beyond this critical size limit they destabilize. First-order temporal coherence of condensates = 0.8 picoseconds (ps); this is in reasonable agreement with coherence decay time estimate of 1 ps which is calculated from the observed emission linewidth.
According to Widom-Larsen theory of LENRs, many-body collective quantum and electromagnetic effects are crucial and enabling to the operation of electroweak nuclear catalysis at ambient temperatures; quantum entanglement amongst protons and plasmons at LENR sites is inferred; 1 ps lifetime of plasmon condensate is very ample time for LENRs. In 2006 EPJC paper (Widom & Larsen) we originally estimated the size of many-body coherence domains in LENR sites on metallic hydride surfaces to be ~ 1 - 10 μ. As discussed in this document, in 2009 Larsen extended Widom-Larsen theory to cover occurrence of LENRs on organic aromatic molecules; at that time, maximum size of W-L coherence domains was re-estimated and increased up to ~ 100 μ. It is not known whether this striking similarity to Daskalakis et al.’s apparent size limit of 100 μ is coincidental. W-L active site functions like a microcavity; thus seems reasonable to speculate that the surface plasmons in LENR-active sites form condensates similar to what Daskalakis et al. observed.
The document describes an experiment where quantum state transfer was realized between atomic and photonic qubits. Efficiencies of 0.04 and 0.03 were measured for the read and write processes respectively. It is estimated that implementing a second node and joint detection of signal photons could realize quantum repeater protocols and distant teleportation of atomic qubits at a rate of around 3 x 10-7 s-1. Improvements to efficiency through increasing optical thickness or eliminating transmission losses could increase the rate by several orders of magnitude. The results also demonstrate the possibility of multiple atomic qubits in a quantum node using multiple light beams.
Analysis of Pseudogap in SuperconductorsIOSR Journals
The document analyzes the effect of the pseudogap on the static magnetic susceptibility of the high-temperature superconductor YBa2Cu3O7-δ. Magnetic susceptibility measurements were taken for various levels of oxygen deficiency δ, corresponding to different hole concentrations p. The data shows anomalous suppression of magnetic susceptibility above the critical temperature Tc in the underdoped region, indicative of the presence of a pseudogap. Analysis of the temperature and doping dependence of the magnetic susceptibility provides information about the pseudogap energy scale and its variation with hole concentration p.
Ab Initio Thermometry For Long-Term Unattended Space Reactor OperationJoe Andelija
This document discusses two potential techniques for long-term, unattended temperature measurement in space nuclear reactors: radiation thermometry and Johnson noise thermometry. Radiation thermometry relies on measuring the variation in light emitted from a surface with temperature changes, while Johnson noise thermometry measures the random voltage fluctuations across a resistor due to atomic vibrations. Both techniques depend on fundamental physical phenomena and are therefore not susceptible to drift over time. However, both face significant technical challenges to implement in space reactors, such as developing radiation-tolerant electronics and distinguishing the small Johnson noise signal from other noise sources. The document provides an overview of the operating principles and considerations for applying these ab initio thermometry techniques to space nuclear power reactors.
The document summarizes a study investigating the dielectric susceptibility of magnetoelectric thin films containing magnetic vortex-antivortex pairs. The study models the magnetic subsystem using the XY model and incorporates a magnetoelectric coupling term. Magnetic vortices acquire electric charges proportional to their topological charge. Vortex-antivortex pairs form electric dipoles that contribute to the dielectric susceptibility. In the approximation of non-interacting dipole pairs, the susceptibility diverges as temperature approaches the Berezinskii-Kosterlitz-Thouless transition temperature. At low temperatures, the susceptibility takes an exponential form reflecting the thermal activation of vortex pairs.
Effect of Poling Field and Non-linearity in Quantum Breathers in FerroelectricsIOSR Journals
Abstract : Lithium tantalate is technologically one of the most important ferroelectric materials with a low poling field that has several applications in the field of photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the polarization behavior of such ferroelectrics can be well-modeled by Klein-Gordon (K-G) equation. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition. The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite tantalum defects in the system, i.e. a point of easier switching within the limited amount of data on poling field.
This document reports on a project to measure the dielectric properties of materials at microwave frequencies. It discusses key concepts such as dielectric constant, permittivity, permeability, Maxwell's equations and how they relate to a material's ability to store and transmit electromagnetic energy. It describes measurement techniques using resonant cavities and waveguides to characterize a material's dielectric constant and loss factor. Sample preparation and ensuring uniform temperature and moisture conditions are important. Both resonant cavity and transmission line methods are covered, with cavity methods noted as providing higher accuracy for loss measurements.
Annette bussmann holder, hugo keller high tc superconductors and related tran...Edward Flores
This document provides an introduction to the scientific career and contributions of K. Alex Müller, honoring his 80th birthday. It summarizes that while he is best known for his work discovering high-temperature superconductivity, over half of his research career focused on other areas including phase transitions, critical phenomena, electron paramagnetic resonance, and ferroelectricity. The document outlines some of his seminal contributions in these fields, including establishing a theory of phase transitions involving soft modes and elastic instabilities. It also discusses his work on the nature and dynamics of structural phase transitions and ferroelectricity in perovskite oxides.
Dielectric Dilemma 1901.10805 v2 feb 4 2019Bob Eisenberg
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the epolarization of the vacuumf ..0 .......... Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws reliably describe circuits that switch in nanoseconds.
This document discusses radiation hardness assurance (RHA) for electronics used in space systems. It notes that the space radiation environment can degrade electronics over time and discusses the need for RHA activities to ensure components perform as designed after radiation exposure. Some key points made:
- RHA consists of all steps to ensure components work as intended after radiation exposure, including environment definition, part selection/testing, layout, and mitigation techniques.
- Traditional particle accelerators may not accurately simulate the natural space radiation environment. High power lasers are a promising alternative for testing due to their similar exponential energy distributions.
- The document revisits the definition of RHA and notes it goes beyond just individual components to consider things like the radiation
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TOPLOGICAL INSULATORS REVIEW PAPER
1. NAME: STEPHEN UDOCHUKWU CHUKWUEMEKA
I.D NO: 14210334
LECTURER: Prof. Patrick McNally
MODULE: EE559 FUNDAMENTALS OF NANOELECTRONICS TECHNOLOGY
PAPER TITLE: Topological Insulators
I hereby declare that the attached submission is all my own work, that it has not previously been
submitted for assessment, and that I have not knowingly allowed it to be used by another student.
I understand that deceiving or attempting to deceive examiners by passing off the work of
another as one's own is not permitted. I also understand that using another's student’s work or
knowingly allowing another student to use my work is against the University regulations and that
doing so will result in loss of marks and possible disciplinary proceedings.
Signed: STEPHEN
Date: 2nd
December, 2015
2. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 1
Abstract — Topological Insulators are electronic
devices which possess bulk band gap like an ordinary
insulator in its interior but whose edge or surface
contains protected conducting states.
These states are conceivable because of the merger of
spin-orbit connections and time-inversion symmetry.
This review paper presents a general account of
Topological Insulators with an emphasis on basic
theory and material properties. Topological
Insulators like 2D – two dimensional is known as a
quantum spin Hall insulator which is related to
integer quantum Hall State, while the 3D – three
dimensional topological insulators encourages
innovative spin-polarized 2D Dirac fermions on its
surface. Adequate examination of the distinctive
properties of topological insulators will be observed
in this paper. Specifically, the Dirac fermion material
science and the subsequent unconventional quantum
oscillation examples are talked about in point of
interest. It is underlined that appropriate
examinations of quantum motions make it
conceivable to unambiguously recognize surface
Dirac fermions through transport estimations.
Keywords – topological insulator, quantum oscillation,
Dirac fermions
1. INTRODUCTION
The advancement in consolidated matter material
science is regularly determined by innovations of new
materials. In such manner, materials introducing one of a
kind quantum-mechanical property are of specific
significance. Topological Insulators (TIs) are a class of
such materials and they are presently making a surge of
survey activities.1–3)
Because TIs concern a subjectively
new part of quantum mechanics, that is, the topology of
the Hilbert space, they opened another window for
understanding the complex workings of nature. TIs are
called "topological" in light of the fact that the wave
capacities depicting their electronic states compass a
Hilbert space that has a nontrivial topology. Keep in
mind, quantum-mechanical wave capacities are depicted
by linear blends of orthonormal vectors shaping a
premise set, and the theoretical space spread over by this
orthonormal premise is called Hilbert space. In
crystalline solids, where the wave vector k turns into a
decent quantum number, the wave capacity can be seen
as a mapping from the k-space to a complex in the
Hilbert space (or in its projection), and subsequently the
topology gets to be important to electronic states in
solids. Subject to the way the Hilbert-space topology
gets to be nontrivial, there can be different various types
of TIs.4)
A vital result of a nontrivial topology related with the
wave elements of an insulator is that a gapless interface
state essentially shows up when the insulator is
physically terminated and meets an ordinary insulator
(including the vacuum). This is on the grounds that the
nontrivial topology is a discrete characteristic for gapped
energy states, and in as much as the energy gap stays
open, the topology can't change; thus, all together for the
topology to change over the interface into a trifling one,
the gap must close at the interface. Along these lines,
three-dimensional (3D) TIs are continuously connected
with gapless surface states, likewise two-dimensional
(2D) TIs with gapless edge states. This rule for the
fundamental event of gapless interface states is called
bulk-boundary correspondence in topological stages. 6]
Topological Insulators
Stephen Chukwuemeka, School of Electronic Engineering, Dublin City University, Glasnevin, Dublin 9, Ireland.
stephen.chukwuemeka2@mail.dcu.ie
3. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 2
Figure 1; Edge and surface states of topological
insulators with Dirac dispersions. (a) Schematic real-
space picture of the 1D helical edge state of a 2D TI. (b)
Energy dispersion of the spin non-degenerate edge state
of a 2D TI forming a 1D Dirac cone. (c) Schematic real-
space picture of the 2D helical surface state of a 3D TI.
(d) Energy dispersion of the spin non-degenerate surface
state of a 3D TI forming a 2D Dirac cone; due to the
helical spin polarization, back scattering from k to -k is
prohibited 6]
(Yiochi Ando, 2013)
A huge section of the distinct quantum-mechanical
properties of TIs originate from the curious attributes of
the edge/ surface states. Presently, the TI exploration is
engaged for the most part on time-reversal (TR)
invariant systems, where the nontrivial topology is
ensured by time-inversion symmetry (TRS).1–3)
In those
systems, the edge/surface states present Dirac scatterings
(Fig. 1), and subsequently the material science of
relativistic Dirac fermions gets to be significant.
Moreover, spin degeneracy is lifted in the Dirac
fermions dwelling in the edge/surface conditions of TR-
invariant TIs and their sin is bolted to the force (Fig. 1).
Such a spin state is said to have ''helical spin
polarization'' and it gives a chance to acknowledge
Majorana fermions 5)
in the vicinity of proximity-
induced superconductivity, 6)
also its undeniable
consequences for spintronics applications.
A vital target of the trial investigations of TIs has been
to explain the presence and the technique of such
helically turn spellbound Dirac fermions in the
topological surface state.
This review paper is expected to give an informative
prologue to the field of topological insulators, laying
emphasis on the essential hypothesis and materials
properties. It likewise expounds on the fundamentals of
the portrayals of TI materials utilizing transport
estimations.
2. HISTORY
With the intention of comprehending the historical
background of TIs, we have to appreciate the
significance of TIs in condensed matter physics. In this
segment, I will shortly discuss the important topics that
paved way to the discovery of TIs as well as a
description on the advancement of the researches that
were carried out based on TIs in its earlier days.
2.1 Integer Quantum Hall Effect
In the year 1980, von Klitzing et al. found the quantum
Hall effect in a high-versatility 2D semiconductor under
high attractive fields.7)
The event of this impact is more
often constrained to low temperatures, where
localization of electrons and Landau quantization of their
energy range lead to vanishing longitudinal conductivity
𝜎xx together with quantization of the Hall conductivity
𝜎xy to integer number products of 𝑒2
/h when the
synthetic potential is situated in the middle Landau
levels. Such a quantization of transport coefficients
clearly indicated a perceptible quantum phenomenon, as
was clarified by Laughlin's gauge argument.8)
It is
reasonable to specify that this quantization phenomenon
was hypothetically foreseen already in 1974.9)
In 1982,
it was perceived by Thouless, Kohmoto, Nightingale,
and den Nijs (TKNN)10)
that this phenomenon not only
is quantum mechanical but it is also topological; to be
specific, TKNN showed10)
that in the quantum Hall
system the k-space is mapped to a topologically-
nontrivial Hilbert space, whose topology can be
determined by a whole number topological invariant
called TKNN invariant 𝑣, and that 𝜎xy becomes equal to
𝑣 times 𝑒2
/h. The TKNN invariant is also called the first
Chern number or the winding number, and it is
4. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 3
equivalent to the Berry phase of the Bloch wave function
calculated around the Brillouin zone (BZ) limit separated
by 2𝜋 (genuine computations are presented in the
subsequent section). 6]
In knowledge of the past, the quantum Hall system could
be accepted as the first topological insulator that became
known to physicists, in light of the fact that when the
quantization is occurring, the energy range is gapped
because of the Landau quantization furthermore, the
chemical potential is situated inside of the crevice, which
is a situation akin to an insulator. For this situation, the
nontrivial topology indicated by the TKNN invariant is
trademark of a 2D system with broken TRS. Likewise,
as it was indicated by Halperin,11)
the integer quantum
Hall effect is dependably joined by chiral edge states,
and those gapless states living at the interface to the
vacuum can be comprehended to be an aftereffect of the
bulk-boundary correspondence because of the
topological 2D "bulk" state.
It is judicious to say that the integer quantum Hall effect
was just the beginning. The fractional quantum Hall
(FQH) effect found in 1982 by Tsui, Stormer, and
Gossard12)
ended up containing wealthier material
science, on the grounds that electron relationships
assume fundamental parts in the FQH effect and also,
they prompt the presence of partially charged
quasiparticles.13)
As regards topology, nevertheless,
FQH states try not to have much pertinence to
topological insulators, since the previous present
ground-state decline and their topological character is
portrayed by a significant conceptual idea of topological
order.14)
2.2 Quantum spin Hall effect and Z2 topology
On an alternate front in consolidated matter material
science, generation and control of spin currents have
been drawing in a great deal of enthusiasm, since they
will have a significant sway on future spintronics.15)
In
such manner, the spin Hall effect, the presence of
transverse spin current accordingly to longitudinal
electric field, has been talked about hypothetically since
1970s, 16–20)
however its trial affirmation by Kato
et al. 21)
in 2004 gave a major help to the examination of
this phenomenon. It was soon perceived that the spin
Hall effect in nonmagnetic systems is on a very basic
level identified with the anomalous Hall effect in
ferromagnets,22)
and likewise to the last effect, there are
both intrinsic and extrinsic starting points of the spin
Hall effect. The intrinsic system of the spin Hall effect
originates from the Berry bend of the valence band
Bloch wave capacities incorporated over the Brillouin
zone.19, 20)
Since such an integral can get to be limited
even in an insulator, Murakami, Nagaosa, and Zhang
went ahead to propose the thought of spin Hall insulator,
23)
which is a gapped insulator with zero charge
conductivity yet has a limited spin Hall conductivity
because of a limited Berry phase of the involved states.
Later it was shown 24)
that the proposed spin Hall
insulators can't actually produce spin currents without
any electrons at the Fermi level, however this thought
activated consequent proposition of its quantized
version, the quantum spin Hall (QSH) insulator, by Kane
and Mele, 25,26)
trailed by an autonomous proposition by
Bernevig and Zhang. 27)
The QSH insulators are
basically two duplicates of the quantum Hall system, in
which the chiral edge state is spin polarized,
furthermore, the two states form a time-switched pair to
regain the general TRS. At the point when current
streams utilizing the edge conditions of a QSH protector,
a quantized adaptation of the twist Hall impact, the QSH
impact, is anticipated to be watched. Since the
anticipated marvel depends on the quantum Hall impact,
it just exists in 2D. While it is not clear from the onset
on how one can accomplish such a state with quantized
edge states in zero magnetic field, the clever proposition
by Kane and Mele gave a solid model to understand the
QSH insulator.25)
Their model is basically a graphene
model with spin–orbit coupling (SOC).
In graphene, the band structure close to the Fermi level
comprises of two linearly scattering cones situated at 𝐾
and 𝐾’ focuses in the BZ; 28)
since the low-energy
material science on these cones is portrayed by utilizing
the Dirac equation with the rest mass set to zero, 29)
this
scattering is called Dirac cone and the electrons are said
5. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 4
to carry on as massless Dirac fermions. Kane and Mele
showed 25)
that a limited SOC prompts an opening of a
hole at the intersection purpose of the cone (called Dirac
point) and, moreover, that a time-switched pair of spin-
polarized one-dimensional (1D) states in reality appear
at the edge in some parameter range; in this model, the
preferred spin polarization of the edge state is
accomplished because of the SOC which has a
characteristic inclination to adjust spins in connection to
the momentum path. This curious spin- non-degenerate
state [Figs. 1(a) and 1(b)] is regularly said to have
helical spin polarization or spin-momentum locking.
Intriguingly, those electrons in the gapless edge state act
as 1D massless Dirac fermions inside of the hole opened
in the 2D Dirac cone. For this situation, the 2D "bulk"
electrons can be seen as huge Dirac fermions in view of
the limited energy gap at the Dirac point.
In particular, Kane and Mele perceived that the
electronic conditions of their QSH insulator is described
by a novel topology indicated by a Z2 index, 26)
which
communicates whether the amount of times the 1D edge
state crosses the Fermi level somewhere around 0 and
𝜋/𝑎 is even or odd (𝑎 is the lattice constant). Keep in
mind, in arithmetic the group of integer numbers is
called Z and its quotient set sorting even and odd
numbers is called Z2; henceforth, a Z2 list for the most
part gives a topological arrangement in view of equality.
(A definite portrayal of the Z2 record for TR-invariant
TIs is given in the following segment.) The hypothetical
innovation of the Z2 topology in insulators was a major
stride in our comprehension of topological stages of
matter, on the grounds that it demonstrated that
nontrivial topology can be inserted in the band structure
of a normal insulator and that breaking of TRS by use of
magnetic fields is not obligatory for figuring it out a
topological stage.
Shockingly, the SOC in graphene is exceptionally weak,
and consequently it is hard to experimentally detect the
QSH effect expected in the Kane–Mele model. Be that
as it may, another hypothetical increase was soon made
by Bernevig, Hughes, and Zhang (BHZ),30)
who
developed a 2D model to deliver a Z2 topological stage
taking into account the band structure of HgTe; taking
into account their model, BHZ anticipated that a
CdTe/HgTe/CdTe quantum well ought to offer rise to
the QSH effect. This forecast was confirmed in 2007 by
Konig et al., 31)
who watched 𝜎xx to be quantized to
2𝑒2
/h in zero magnetic field when the chemical potential
is tuned into the bulk band gap(Fig. 2), giving proof for
the gapless edge states in the offending administration.
This was the first test affirmation of the TR-invariant TI
described by the Z2 topology.
Figure 2; Longitudinal four-terminal resistance of
various CdTe/HgTe/CdTe quantum-well structures as a
function of the gate voltage measured in zero magnetic
field at 30 mK. Devices with the size of 1 × 1 µ𝑚2 or
less in the band-inverted regime (III and IV) show
quantized conductance of 2𝑒2
/h, giving evidence for the
2D TR-invariant TI phase. (Yiochi Ando, 2013)
Figure 3; Spin-resolved surface band structure of
Bi1-x Sbx (x=0.12- 0.13) on the (111) cleaved surface. Its
surface BZ and the momentum direction of the data are
shown in the inset. Dispersions shown by symbols are
6. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 5
determined from the peak positions of the spin-resolved
energy dispersion curves and they are plotted on top of
the spin-integrated ARPES data shown in grey scale.
There are three Fermi-level crossings of the surface
states, which signify the Z2-nontrivial nature of this
system. (Yiochi Ando, 2013)
Without sitting tight for test check of the Z2 topology in
2D, scholars saw that this topological grouping of
insulators can be reached out to 3D systems, where there
are four Z2 invariants to completely describe the
topology.32–34)
actually, the term ''topological insulator''
was created by Moore and Balents in their paper to
propose the presence of TIs in 3D systems.32)
For 3D
TIs, Fu and Kane made a solid forecast in 2006 that the
Bi1-xSbx alloy in the insulating structure ought to be a
TI, and they further recommended that the nontrivial
topology can be checked by taking a glance at the
surface states utilizing the angle-resolved photoemission
spectroscopy (ARPES) and calculating the amount of
times the surface states cross the Fermi energy between
two TR-invariant momenta.35)
The proposed test was
directed by Hsieh et al. who reported in 2008 that
Bi1-xSbx is without a doubt a 3D TI.36)
The experimental
distinguishing proof of Bi1-x Sbx as a TR-invariant TI
opened a great deal of new experimental opportunities to
address a topological stage of matter. For instance, the
first transport investigation of Bi1-xSbx to recognize
topological 2D transport channels was accounted for by
Taskin and Ando,37)
and the first scanning tunneling
spectroscopy (STS) study that tended to the exceptional
spin polarization was accounted for by Roushan et al.,38)
both in 2009. Direct awareness of the helical spin
polarization of the surface states in Bi1-x Sbx utilizing
spin resolved ARPES was first mostly done by Hsieh et
al.39)
and after that completely refined by Nishide et al.
(Fig. 3).40)
2.3 Topological Field Theory
While the idea of topological insulators got to be
prevalent when the disclosure of the Z2 topology by
Kane and Mele, 26)
there had been hypothetical
endeavors to imagine topological conditions of matter
past the extent of the quantum Hall system. With regards
to this, an imperative advancement was made in 2001 by
Zhang and Hu, who summed up the 2D quantum Hall
state to a four-dimensional (4D) TR-invariant state
having a whole number topological invariant.41)
The
compelling field theory for this 4D topological system
was developed by Bernevig et al.42)
After the Z2
topology was found for TR-invariant systems in 2D and
3D, 26, 32–34)
it was portrayed by Qi, Hughes, and Zhang
43)
that the framework of topological field hypothesis is
valuable for portraying those systems too, and they
further showed that the Z2 TIs in 2D and 3D can really
be reasoned from the 4D compelling field theory by
utilizing the dimensional reduction. From a functional
perspective, the topological field hypothesis is suitable
for depicting the electromagnetic reaction of TIs what's
more, has been utilized for anticipating novel topological
magneto electric effects.43
2.4 Dirac Materials
It is intriguing to take note of that the initial 3D TI
material Bi1-x Sbx whose topological surface state
comprises of 2D massless Dirac fermions, has long been
known not impossible to miss band structure to offer
ascent to 3D monstrous Dirac fermions in the bulk.44]
This circumstance is like the Kane– Mele model where
1D massless Dirac fermions rise out of 2D enormous
Dirac fermions. Since Dirac fermions play essential parts
in TIs, it is helpful to specify the history of Dirac
material science in consolidated matter.
The semimetal Bi has been an essential testing ground of
quantum material science since the time that the
Shubnikov–de Haas (SdH) and de Haas–van Alphen
(dHvA) motions were found in Bi in 1930.45]
This is
basically on the grounds that the great degree low carrier
density ~10−5
per atom) and the precise long mean free
path (reaching ~1 mm) effortlessly put the framework in
''quantum limit” at generally low magnetic fields.46]
In
the mid-twentieth century, one of the long-standing
riddles in Bi was its extensive diamagnetism, which
opposes the regular intelligence for attraction in metals
including Pauli para-magnetism what's more, Landau
diamagnetism.47]
Intriguingly, in Bi1-x Sbx at low Sb
concentration, the carrier density turns out to be even
lower than in Bi, while the diamagnetic susceptibility
7. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 6
rises, which is likewise inverse to the desire from
Landau diamagnetism.47]
To address the bizarre electronic properties of Bi, a
compelling two-band model was developed by Cohen
and Blount in 1960.48]
In 1964, Wolff perceived that this
two-band model can be changed into the four-part
enormous Dirac Hamiltonian, and he introduced a rich
investigation of the choice principles utilizing the Dirac
theory.44]
This was the start of the idea of Dirac fermions
in strong states, albeit a portion of the impossible to miss
material science of massless Dirac fermions were
perceived in as right on time as 1956 by McClure in the
setting of graphite.
Talking about graphite, the mapping of the k ∙ p
Hamiltonian of its 2D sheet (i.e., graphene) 50]
to the
massless Dirac Hamiltonian was initially utilized by
Semenoff in 1984. 51]
With the test acknowledgment of
graphene, 28]
this framework has turned into a
prototypical Dirac material. One of the recognizing
properties of massless Dirac fermions is the Berry period
of 𝜋; an imperative outcome of the 𝜋 Berry stage in the
dense matter setting is the truancy of backscattering,
which was pointed out first by Ando, Nakanishi, and
Saito in 1998. 52]
An imperative part of the Dirac material science is that
magnetic fields essentially cause collaborations in the
middle of upper and lower Dirac cones. Indeed, the
Dirac formalism permits one to normally incorporate
such ''interband effects'' of magnetic fields into
computations. 6]
In 1970, Fukuyama and Kubo showed,
by expressly performing the assessments, that the
extensive diamagnetism in Bi and Bi1-x Sbx is actually a
result of their Dirac nature. 47]
Intriguingly, because of
such interband effects of magnetic fields, the Hall
coefficient does not deviate but rather gets to be zero
when the carrier density vanishes at the Dirac point, 53]
which is surely seen in a topological insulator. 54]
3 FUNDAMENTALS OF THE TOPOLOGY IN
TOPOLOGICAL INSULATORS
3.1 TKNN Invariant
The topological invariant characterized for the whole
integer quantum Hall system, the TKNN invariant, 10)
is
firmly identified with the Berry stage. To see this, we
determine the TKNN invariant by computing the Hall
conductivity of a 2D electron arrangement of size L × L
in opposite magnetic fields, where the electric field E
and the magnetic field B are connected along the y-and
z-axes, separately. By treating the effect of the electric
field E as an irritation potential V = -eEy, one may
utilize the irritation theory 6]
to estimate the distressed
eigen state |𝑛> E as
|𝑛> E = |𝑛> + ∑
⟨ 𝑚|(−𝑒𝐸𝑦)|𝑛⟩
𝐸𝑛−𝐸𝑚
|𝑚𝑚(≠𝑛) > + ... (1)
In order to use this distressed eigenstate, the expectation
value of the current density along the x-axis is
obtainable, jx, in the existence of the E field along the y-
axis as
(𝑗𝑥)E = ∑ 𝑓(𝐸𝑛 n)⟨𝑛|𝐸(
𝑒𝑣 𝑥
𝐿2 |𝑛⟩ 𝐸
= (𝑗𝑥)E= 0 +
1
𝐿2
∑ 𝑓(𝐸𝑛 𝑛)
× ∑ (
⟨𝑛|(𝑒𝑣 𝑥)|𝑚⟩ ⟨𝑚|(−𝑒𝐸𝑦|𝑛⟩
𝐸𝑛 − 𝐸𝑚
𝑚(≠𝑛)
+
⟨ 𝑛|(−𝑒𝐸𝑦| 𝑚⟩⟨ 𝑚|−𝑒𝐸𝑦| 𝑛⟩
𝐸𝑛−𝐸𝑚
), (2)
where vx is the electron velocity along the x-direction
and 𝑓(𝐸𝑛) is the Fermi distribution function. The
Heisenberg equation of motion
𝑑
𝑑𝑡
𝑦 = 𝑣 𝑦 =
1
𝑖ħ
[y, H]
leads to
⟨𝑚|𝑣 𝑦|𝑛⟩ =
1
𝑖ħ
(𝐸𝑛 − 𝐸𝑚)⟨𝑚|𝑦|𝑛⟩, (3)
which allows one to evaluate
𝜎 𝑥𝑦 =
〈𝑗𝑥〉𝐸
𝐸
= -
𝑖ħ𝑒2
𝐿2
∑ 𝑓(𝐸 𝑛)𝑛≠𝑚
8. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 7
⟨ 𝑛| 𝑣 𝑥| 𝑚⟩⟨ 𝑚| 𝑣 𝑦| 𝑛⟩−⟨ 𝑛| 𝑣 𝑦| 𝑚⟩⟨ 𝑚| 𝑣 𝑥| 𝑛⟩
(𝐸𝑛−𝐸𝑚)2 (4)
The identity of the system considered in a periodic
potential and its blocks are as follows:
⟨𝑢 𝑚𝑘′|𝑣𝜇|𝜇 𝑛𝑘⟩ =
1
ħ
(𝐸 𝑛𝑘 − 𝐸 𝑚𝑘′) ⟨𝑢 𝑚𝑘′|
𝜕
𝜕 𝑘𝜇
|𝑢 𝑛𝑘⟩ (5)
Rewrite equation (4) into the form
𝜎 𝑥𝑦 = −
𝑖𝑒2
ħ𝐿2
∑ ∑ 𝑓(𝐸 𝑛𝑘)
𝑛≠𝑚𝑘
× (
𝜕
𝜕𝑘 𝑥
⟨𝑢 𝑛𝑘|
𝜕
𝜕𝑘 𝑦
𝑢 𝑛𝑘⟩ −
𝜕
𝜕𝑘 𝑦
⟨𝑢 𝑛𝑘|
𝜕
𝜕𝑘 𝑥
𝑢 𝑛𝑘⟩) (6)
Berry connection equation written for Bloch states:
𝑎 𝑛(𝑘) = −𝑖⟨𝑢 𝑛𝑘|∇ 𝑘|𝑢 𝑛𝑘⟩ = −𝑖 ⟨𝑢 𝑛𝑘|
𝜕
𝜕𝑘 𝑥
|𝑢 𝑛𝑘⟩ (7)
The Hall conductivity reduces to
𝜎 𝑥𝑦 = 𝑣
𝑒2
ℎ
(8)
With
𝑣 = ∑ ∫
𝑑2 𝑘
2𝜋𝐵𝑍𝑛 (
𝜕𝑎 𝑛,𝑦
𝜕𝑘 𝑥
−
𝜕𝑎 𝑛,𝑥
𝜕𝑘 𝑦
) (9)
This 𝑣 can be expressed as 𝑣 = ∑ 𝑣 𝑛𝑛 with 𝑣 𝑛 the
contribution from the nth band, and one can easily see
that 𝑣 𝑛 is related to the Berry period, namely
𝑣 𝑛 = ∫
𝑑2 𝑘
2𝜋𝐵𝑍
(
𝜕𝑎 𝑛,𝑦
𝜕𝑘 𝑥
−
𝜕𝑎 𝑛,𝑥
𝜕𝑘 𝑦
)
=
1
2𝜋
∮ 𝑑𝒌. 𝑎 𝑛(𝒌)𝜕𝐵𝑍
= -
1
2𝜋
𝑦𝑛 [𝜕𝐵𝑍]. (10)
Due to the nature of the single valued wave function,
changes in the period factor as soon as it’s done with the
encircling the Brillouin zone boundary [𝜕𝐵𝑍] 𝑐𝑎𝑛 only
be an integer multiple of 2𝜋, which means
𝑦𝑛 [𝜕𝐵𝑍] = 2𝜋𝑚 (𝑚 𝜖 𝑍). (11)
Therefore, 𝑣 𝑛 can only take an integer value, and hence
𝜎 𝑥𝑦 is quantized to integer multiples of
𝑒2
ℎ
. The integer 𝑣
is called TKNN invariant, and it plays the role of the
topological invariant of the quantum Hall system, which
is a TRS breaking TI. It is clear from Equation (10) that
the TKNN invariant becomes nonzero (i.e., the system
becomes topological) when the Berry connection
𝒂 𝑛(𝒌) is not a single-valued function 6]
3.2 Extension to 3D systems
Taking into account a general homotopy contention,
Moore and Balents showed 32)
that there are four Z2
invariants for 3D systems. While the development of the
homotopy was included, the physical birthplace of the
four invariants can be effectively caught on. For
effortlessness, consider a cubic system furthermore, take
the cross section steady a = 1. In the 3D BZ of this
system, there are eight TRIMs meant as ʌ0,0,0, ʌ 𝜋,0,0,
ʌ0,𝜋,0, ʌ0,0,𝜋, ʌ 𝜋,0,𝜋, ʌ0,𝜋,𝜋, ʌ 𝜋,𝜋,0, and ʌ 𝜋,𝜋,𝜋, [see Fig.
5(c)]. At these focuses in the BZ, the Bloch Hamiltonian
gets to be TR symmetric, i.e., 𝛩𝐻(ʌ𝑖)𝛩−1
= 𝐻(ʌ𝑖), and
every Kramers pair of groups get to be deteriorate.
Notice that the six planes in the 3D BZ, x = 0, x = ±𝜋,
y = 0, y =±𝜋, z = 0, and z = ±𝜋 have the symmetries
of the 2D BZ, and subsequently they each have a Z2
invariant. The six invariants may be meant as x0, x1, y0,
y1, z0, and z1, be that as it may, those six invariants are
not all independent. 32)
This is since the items x0x1, y0y1,
and z0z1 are excess, which comes from the way that
those three items include Pf[w(ʌ𝑖)]/√det[𝑤(ʌ𝑖)] from
each of the eight TRIMs and henceforth are the same.
This implies there are two compelling relations x0x1 =
y0y1 = z0z1, which directs that just four invariants can be
autonomously decided in a 3D system.
The solid development of the four Z2 invariants was
given by Fu and Kane. 33)
For each TRIM ʌ𝑖 we define
𝛿(ʌ𝑖) ≡
Pf[𝑤(ʌ 𝑖)]
√det[𝑤(ʌ 𝑖)]
(12)
Using this 𝛿(ʌ𝑖), the four Z2 invariants V0, V1, V2, V3
are defined as
9. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 8
(−1) 𝑣0
= ∏ 𝛿(ʌ 𝑛1,𝑛2,𝑛3),
𝑛𝑗=0,𝜋
(13)
(−1) 𝑣1
= ∏ 𝛿(Ʌ 𝑛1,𝑛2,𝑛3),
𝑛≠𝑖=0,𝜋;𝑛𝑖=𝜋
(𝑖 = 1,2,3) (14)
The invariant V0 is given by a product of all eight
𝛿(ʌ𝑖)′s, so it is unique to a 3D system. Alternatively,
other Vi’s are a product of four 𝛿(ʌ𝑖)′s and is similar to
the Z2 invariant in the 2D case. For example,
(−1) 𝑣3
= 𝛿(ʌ0,0,𝜋) 𝛿(ʌ 𝜋,0,𝜋)𝛿(ʌ0,𝜋,𝜋)𝛿(ʌ 𝜋𝜋,,𝜋) (15)
corresponds to the Z2 invariant on the Z = 𝜋 plane, which
can be seen by considering the TR polarization defined
on this plane, 𝑃𝜃(𝑦 = 0) 𝑍=𝜋 =
1
𝑖𝜋
log[𝛿(ʌ0,0,𝜋)𝛿(ʌ 𝜋,0,𝜋)]
and
𝑃𝜃(𝑦 = 0) 𝑍=𝜋 =
1
𝑖𝜋
log[𝛿(ʌ0,𝜋,𝜋)𝛿(ʌ 𝜋,𝜋,𝜋)]. When the
TR polarization changes between y = 0 and y = 𝜋 [i.e.,
Figure 6. Schematic pictures of the surface states
between two surface TRIMs, ʌ 𝑎
𝑠
and ʌ 𝑏
𝑠
, for (a)
topologically trivial and (b) topologically nontrivial
cases. In the latter, the ‘‘switch-partner’’ characteristic is
a reflection of the change in the TR polarization (see
text). The shaded regions represent the bulk continuum
states. To enhance the visibility of the Kramers
degeneracy, surface state dispersions are shown
from −ʌ 𝑎
𝑠
to −ʌ 𝑏
𝑠
through ʌ 𝑎
𝑠
.
𝑃𝜃(𝑦 = 0) 𝑍=𝜋 and 𝑃𝜃(𝑦 = 𝜋) 𝑍=𝜋 are different, then the
Z2 topology is nontrivial and V3 becomes 1.
The physical outcome of a nontrivial Z2 invariant is the
presence of topologically-ensured surface states. This is
graphically appeared in Fig. 6, in which topologically
trifling and nontrivial surface states are analysed. In the
nontrivial case, the Kramers sets in the surface state
''switch accomplices'', and subsequently, the surface state
is ensured to cross any Fermi energy inside the bulk gap.
This switch-accomplice trademark is an impression of
the change in the TR polarization talked about above. It
is standard to compose the blend of the four invariants in
the structure (V0; V1, V2, V3), in light of the fact that (V1,
V2, V3), can be translated as Miller files to indicate the
bearing of vector ʌi in the proportional space.
A 3D TI is called "solid" at the point when V0 = 1, while
it is called "frail" when V= 0 and Vi = 1 for some i
=1,2,3.
4. TWO-DIMENSIONAL TI’S
The primary material that was tentatively distinguished
as a TR-invariant TI was CdTe/HgTe/CdTe quantum
well, 31)
in particular, a slim layer of HgTe sandwiched
by CdTe. This is a 2D framework where the level of
opportunity for the opposite bearing is extinguished
because of the quantum imprisonment of the electronic
states in the HgTe unit and the subsequent subband
development. Both HgTe and CdTe solidify in
zincblende structure, and their superlattices have been
effectively concentrated on in light of their application to
infrared indicators.
In this way, the fundamental innovation to blend the
required quantum well was at that point created before
the expectation of its TI nature, despite the fact that it
includes an exceptionally specific sub-atomic shaft
epitaxy (MBE) strategy to manage mercury.31)
As we
have found in the examination of the BHZ model in the
past area, the reversal in the middle of p-and s-orbital
groups is vital for the framework to acquire the TI
nature. Mass HgTe acknowledges such a band reversal,
while CdTe does not.
Along these lines, HgTe is a decent beginning material
for considering a TI stage; on the other hand, there is an
issue in the band structure of mass HgTe, that is, a
precious stone symmetry-ensured decadence at the point
makes the framework to be naturally a zero-crevice
semiconductor,30)
which implies that there is no band
crevice between the p-and s-orbital groups and the
framework is not qualified as a cover. On the other hand,
by sandwiching HgTe by CdTe, which has marginally
bigger cross section steady, the epitaxial strain applied
on HgTe breaks the cubic cross section symmetry and
10. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 9
prompts a hole opening, and thus the framework can turn
into a honest to goodness separator. It was anticipated by
BHZ that over a certain basic thickness the strained
HgTe unit holds the band reversal and ought to be a
TI.30)
This forecast was affirmed by a gathering at the
College of Wu¨rzburg drove by Molenkamp by means of
transport examination of small scale manufactured
samples.31)
They found that, at the point when the
thickness of the HgTe unit is over the basic thickness dc
of 6.3 nm, their examples demonstrate a ''negative
energy gap” (i.e., band is upset) and quantization of the
conductance to 2e2
/h in zero attractive field was watched
at the point when the synthetic potential is tuned into the
hole (Fig. 2). In contrast, when the thickness is beneath
dc, the band reversal is lost and they watched separating
resistivity.
The Wu¨rzburg gather later reported the perception of
nonlocal transport, 55)
which gave further backing to the
presence of an edge state. They additionally
demonstrated that the 1D edge state in charge of the
quantized transport in the 2D TI stage is prone to be
helically turn spellbound, by manufacturing an intricate
gadget structure which depends on the routine twist Hall
impact that happens in metallic (doped) HgTe.56)
The CdTe/HgTe/CdTe quantum well can be made
extremely clean with the transporter versatility of up to
~105
cm2
V-1
s-1
, which makes it conceivable to study
quantum transport properties. Then again, the downside
of this framework is that the mass band hole that opens
because of the epitaxial strain is small (up to ~10 meV,
contingent upon the thickness 57]
, which makes the
recognition of the TI stage to be conceivable just at low
temperature. Additionally, since the combination of
CdTe/HgTe/CdTe quantum wells requires devoted MBE
machines, the wellsprings of tests for fundamental
material science investigations are at present extremely
constrained, which has made the advancement of test
investigations of 2D TIs (QSH encasings) moderately
moderate.
As of late, another 2D TI framework,
AlSb/InAs/GaSb/AlSb quantum well, was hypothetically
predicted58]
and tentatively
confirmed.59–61]
The vital workings of this system are the
accompanying: The valence-band top of GaSb lies above
the conduction-band base of InAs. Consequently, when
InAs what's more, GaSb are in direct contact and they
are both quantum limited (by the external units of AlSb
which has an extensive band hole and acts as a
boundary), the subsequent gap subband in GaSb may lie
over the electron subband in InAs, and in this way the
band request of this quantum well is transformed. The
band hole in this quantum well emerges from hostile to
crossing of the two subbands at limited force and thus is
exceptionally little (~ 4 meV), which mentions clean
objective fact of the helical edge state exceptionally
difficult.59,62)
Reasonably persuading proof for the TI
stage was gotten by means of perception of the 2e2
/h
quantization of the zero-predisposition Andreev
reflection conductance through Nb point contacts,60)
yet
all the more as of late, direct perception of the
conductance quantization to 2e2
/h has been
accomplished by acquainting issue with the InAs/GaSb
interface by Si doping to confine the undesirable mass
carriers.
5. THREE-DIMENSIONAL TI’S
As specified in Sect. 2, the initial 3D TI material that
was tentatively distinguished was Bi1-x Sbx,36)
taking
after the particular expectation by Fu and Kane.35)
This
material is a combination of Bi and Sb and it normally
has the two vital elements, (i) band reversal at an odd
number of TRIMs and (ii) opening of a mass band hole,
in the Sb focus scope of 0.09 to 0.23.63]
The 3D Z2
invariant has been recognized as (1;111).
Sadly, it worked out that this framework is not extremely
suitable for definite investigations of the topological
surface state because of the convoluted surface-state
structure,36,40)
as can be found in Fig. 3. This is on the
grounds that its guardian material, Bi, as of now
harbours noticeable twist non-ruffian surface states
because of the solid Rashba impact on the surface of this
material.64]
In Bi1-x Sbx, such non-topological,
Rashbasplit surface states are in charge of 2 or 4 Fermi-
level intersections of the surface states (contingent upon
the compound potential), 36,40)
and the topological one
contributes only one extra Fermi-level intersection.
11. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 10
To start with guideline counts of the surface conditions
of Bi1-x Sbx have been reported, 65,66]
however the
anticipated surface-state structure does not by any means
concur with the test results. Such a fragmented
comprehension of the way of the surface state is mostly
in charge of disarrays every so often found in
understandings of exploratory information.
For instance, in the STS work which tended to the
security from backscattering in the surface condition of
Bi1-x Sbx,38)
the examination considered the turn
polarizations of just those surface expresses that are
additionally present in topologically insignificant Bi,87)
but then, it was inferred that the outcome gives proof for
topological assurance. By the by, Bi1-x Sbx is interesting
among known 3D TI materials in that it has a
characteristically high 2D transporter versatility of ~104
cm2
V-1
s-1
(regardless of the fact that it is an alloy),
which makes it simple to study novel 2D quantum
transport.37,67]
Also, it is generally simple for this framework to
decrease the mass bearer thickness to ~1016
cm-3
in high
caliber single gems, making it conceivable, for instance,
to perform Landau level spectroscopy of the surface
states through magnetooptics. 68]
The mass band hole of
Bi1-x Sbx is not substantial (up to ~30 meV relying upon
x), 63]
yet it is sufficiently substantial to distinguish the
2D transport properties at 4K. Alongside Bi1-x Sbx, Fu
and Kane predicted 35)
that HgTe, -period of Sn (called
''dim tin''), and Pb-1
xSnxTe would gotten to be 3D TIs
under uniaxial strain to break the cubic grid symmetry.
They additionally proposed that Bi2Te3 would be an
applicant, yet they didn't perform band estimations to
explain the equality eigenvalues. Such computations
were done by Zhang et al., 69]
who concocted a solid
expectation that Bi2Se3, Bi2Te3, and Sb2Te3 ought to be
3D TIs be that as it may, Sb2Se3 is not; moreover, Zhang
et al. proposed a low energy viable model to portray the
mass band structure of this class of materials.
This model, with a few amendments made later, 70]
has
turned into a famous model for hypothetically examining
the properties of a 3D TI. Tentatively, presence of a
solitary Dirac-cone surface state was accounted for in
2009 for Bi2Se3 by Xia et al.71]
and for Bi2Te3 by Chen et
al.72]
furthermore by Hsieh et al., 73]
Sb2Te3 was
measured by Hsieh et al.73]
alongside Bi2Te3, yet the
presence of the topological surface state was left
unsubstantiated because of the vigorously p-sort nature
of the deliberate specimens. The topological nature of
Sb2Te3 was affirmed just as of late in meagre film tests
utilizing STS.74]
Bi2Se3, Bi2Te3, and Sb2Te3 all take shape in tetra-dymite
structure, which comprises of covalently fortified
quintuple layers (e.g., Se–Bi–Se–Bi–Se) that are stacked
in –A–B–C– A–B–C– way and are pitifully
collaborating with van der Waals power (Fig. 7); thusly,
those materials separate effectively between quintuple
layers (QLs). Since each QL is around 1 nm thick, the
cross section consistent along the c-hub is around 3 nm.
The 3D Z2 invariant of these tetra-dymite frameworks is
(1;000), which implies that topological Dirac-cone
surface state is focused at the ¬ purpose of the surface
BZ (Figure 8).
This openness of the topological surface state and the
nonappearance of non-topological surface states make
those materials appropriate for tentatively tending to the
properties of the topological surface state. Additionally,
single crystal development of those materials is
generally straightforward, which made it simple for
some experimentalists to begin dealing with them.
Moreover, the mass band crevice of Bi2Se3 is generally
substantial, 0.3 eV, and along these lines one can see
mechanical pertinence that topological properties of this
material may conceivably be abused at room
temperature. Every one of those components made a
difference start a surge of examination exercises on 3D
TIs.
The surface-state structure of Bi2Se3 is moderately
straightforward what's more, shows a practically
admired Dirac cone with just slight ebb and flow, as
demonstrated schematically in Figure. 8(a).
Interestingly, the surface condition of Bi2Te3 is more
convoluted [see Figure. 8(b)] and the Dirac point is
situated underneath the highest point of the valence
band, which makes it hard to test the surface transport
properties close to the Dirac point without being
bothered by mass transporters in Bi2Te3.
12. Stephen Chukwuemeka [14210334] EE559 Fundamentals of Nanoelectronics Technology Review Paper 11
Fig. 7. Crystal structure of tetra-dymite chalcogenides, Taken
(Yiochi Ando, 2013)
Fig, 8. Schematic bulk and surface band structures of
(a) Bi2Se3 and (b) Bi2Te3.
CONCLUSION
In this paper, general accounts of Topological Insulators
have been presented. A holistic idea of the basic theories
related to topological insulators and material properties
were presented. Furthermore, there were discussions on
the 2D-Two dimensional and 3D- three dimensional
topological insulators. The Dirac fermion material
science as well as the examples of subsequent quantum
oscillations was discussed in this paper.
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