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Quantum Tunnelling
Quantum tunnelling is a quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. Friedrich Hund first used quantum tunnelling to explain molecular spectra in 1927. George Gamow first applied it to calculate alpha decay in 1928. Max Born recognized it as a general result of quantum mechanics. Important applications include scanning tunneling microscopes, tunnel diodes, and the Josephson effect in superconductors. Recent research has explored tunnelling in other systems and potential uses in quantum computing.
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Quantum Tunnelling
- 1. TUNNELLING IN QUANTUMMECHANICAL SYSTEM Department of Chemistry School of Chemical Sciences and Pharmacy CENTRAL UNIVERSITY OF RAJASTHAN Bandar Sindri, Ajmer- 305801 Submitted to: Dr. Jony Saha Assistant Professor Central University of Rajasthan Presentation by: Soham Thakur Integrated M.Sc. B.Ed. Chemistry 2018IMSBCH014
- 2. INTRODUCTION Quantum Tunnelling Quantummechanical phenomenon Observed in microscopic particles such as electron A subatomic particle’s probability disappears from one side of a potential barrier and appears on the other side without any probability current appearing inside the well. Occurs in all quantum systems. Crucial for nucleosynthesis in stars. Fig: Representation of Tunnelling in a generalised way Merzbacher, E., Physics Today, 2002, 55(8), 44–49.
- 3. HISTORY Friedrich Hund GeorgeGamow 1927 1928 First to use quantum mechanical barrier penetration in discussing the theory of molecular spectra Fig 1: Double Potential well by Hund showing that Levels 2 and 3 are characteristically quantal and occupy both wells, with tunnelling through the barrier First application of the effect by mathematical calculation of the alpha decay Fig 2: 1D potential used by George Gamow to illustrate the tunnelling of alpha particles F. Hund, Z. Phys., 1927 40, 742 G. Gamow, Z. Phys., 1928, 51, 204.
- 4. Max Born 1929 Contd. Tunnelling, not restricted tonuclear physics but, a general result of quantum mechanics that applies to many different systems. Recognizes the generality of tunnelling. Nobel Prize for Tunnelling 1973 Leo Esaki Ivar GiaeverBrian Josephson www.nobleprize.org
- 5. Mathematical Discussion 0 32 V 1 Lx E (Particleenergy) Fig: Representation of a 1D potential barrier which will be penetrated by the particle (Barrier Potential) Schrödinger equation yields two different differential equations depending on the region: Region 1 & 3: Region 2: The general solutions can be written as: :Region 1 :Region 2 :Region 3 Griffiths, David J. Introduction to Quantum Mechanics. Second Edition. Pearson: Upper Saddle River, NJ, 2006
- 6. Contd. Transmission coefficient forthe particle tunnelling across, is calculated using the solution of the Schrödinger eqation and is given as: Fig: These graphs shows a localized wavefunction tunnelling through the one-dimensional barrier by evolving the time- dependent Schrödinger equation Griffiths, David J. Introduction to Quantum Mechanics. Second Edition. Pearson: Upper Saddle River, NJ, 2006
- 7. APPLICATIONS Scanning Tunnelling Microscope •Extremely sharp tip of only a single-atom-thick runs over the surface of the material, with the tip at a higher voltage than the material. • Voltage allows tunnelling current to flow from electrons that tunnel from the surface of the material, through the potential barrier represented by the air, to the tip of the microscope, completing a circuit. • Basis of detection is amount of current. Griffiths, David J. Introduction to Quantum Mechanics. Second Edition. Pearson: Upper Saddle River, NJ, 2006
- 8. Tunnel Diode Contd. • Anapplied voltage can make electrons from the n-type semiconductor tunnel through the depletion region, causing a unidirectional current towards the p-type semiconductor at low voltages. • As voltage increases, the current drops as the depletion region widens and then increases again at high voltages to function as a normal diode. • The ability of tunnel diodes to direct current at low voltages due to tunnelling allows them to operate at very high AC frequencies. Fig: Characteristics of Tunnel Diode Griffiths, David J. Introduction to Quantum Mechanics. Second Edition. Pearson: Upper Saddle River, NJ, 2006
- 9. Josephson effect • Insuperconductors, at certain temperature ranges a current can flow indefinitely without resistive heating occurring. • In Josephson junctions, two superconducting semiconductors are separated by a thin insulating barrier. • In the Josephson effect, superconducting pairs of electrons tunnel through this barrier to carry the superconducting current through the junction. Contd. Fig: Characteristics of Josephson Effect Griffiths, David J. Introduction to Quantum Mechanics. Second Edition. Pearson: Upper Saddle River, NJ, 2006
- 10. ADVANCEMENT Substrate imprinted universalsensors and sensors having nano-tunnelling effect Quantum Tunnelling of water Tunneling effect in the heterogeneously- catalyzed formic acid dehydrogenation Self-aligned tunnelling field effect transistors Tunnel field-effect transistor with reduced trap- assisted tunnelling leakage Kolesnikov, Alexander I.; et. al, Physical Review Letters.. 2016, 116 (16): 167802 Zhou, Y., US Patent, US10495637B2, 2020 Vasen, T., et. al., US20200006542A1, 2020 Song Y., et. al., US20200119168A1, 2019 Mori, K., et. al., Nature Comm., 2019, 10(4094)
- 11. CONCLUSION The phenomenon oftunnelling, which has no counterpart in classical physics, is an important consequence of quantum mechanics. It has enormous number of applications in the phenomenonal science as well as in instruments like Diode, Transistor, etc. Efforts need to improvise quantum computing, and innovation of a quantum computer of which tunnelling effect will be a huge landmark.
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