The document summarizes a student's work modeling electron states in silicon for quantum computing applications. The student created a simulation to calculate the wavefunctions of two electrons in quantum dots and determine their interaction strength. The simulation was later modified to focus on calculating the quadrupole interaction between electrons, which is believed to be more robust for quantum information manipulation than exchange interaction. Results from the simulation using realistic parameters agreed with current research, suggesting the quadrupole interaction is viable for quantum computing. The student gained valuable research experience and the project provided insights into pursuing a PhD in related topics.
Study of Radiation Interaction Mechanisms of Different Nuclear DetectorsIJAEMSJORNAL
In this paper, an attempt has been made to describe the radiation interaction mechanisms of nuclear detectors. There are lots of radioactive detectors available in the field of radiation detection and measurements instruments/systems such as Geguier Muller (GM) Tube, Scintillation Counter, High Purity Germanium (HPGe) and so on. Each of these detectors have different and distinct radiation interaction mechanisms and detecting principle for processing each type of radiation measurement (qualititative and quantitative).The interaction mechanisms of these detectors are governed by generation of ions (positive and negative) in case of GM tube; the photo-electric effect, Compton scattering and pair production for Scintillation detector and HPGe along with diode principle. The special feature of this diode is a constant current generator depending on the energy of the photon deposition in the detector. The characteristics of these interaction mechanisms have been presented along with intensity of measurements, efficiency and detector resolution (FWHM).
Effect of Electron - Phonon Interaction on electron Spin Polarization in a q...optljjournal
This paper presents a theoretical model for the effect of electron
-
phonon interaction, temperature and
magnetic field on degree of electron spin polarization in GaAs/InAs quantum dot LED. To describe the
dynamics, quantum Langevin equation for photon numbe
r and carrier number is used. Simulation results
show that degree of electron spin polarization in quantum dot decreases with increase of electron phonon
interaction parameter at constant temperature and constant magnetic field which agrees with experiment
al results in literatures
Study of Radiation Interaction Mechanisms of Different Nuclear DetectorsIJAEMSJORNAL
In this paper, an attempt has been made to describe the radiation interaction mechanisms of nuclear detectors. There are lots of radioactive detectors available in the field of radiation detection and measurements instruments/systems such as Geguier Muller (GM) Tube, Scintillation Counter, High Purity Germanium (HPGe) and so on. Each of these detectors have different and distinct radiation interaction mechanisms and detecting principle for processing each type of radiation measurement (qualititative and quantitative).The interaction mechanisms of these detectors are governed by generation of ions (positive and negative) in case of GM tube; the photo-electric effect, Compton scattering and pair production for Scintillation detector and HPGe along with diode principle. The special feature of this diode is a constant current generator depending on the energy of the photon deposition in the detector. The characteristics of these interaction mechanisms have been presented along with intensity of measurements, efficiency and detector resolution (FWHM).
Effect of Electron - Phonon Interaction on electron Spin Polarization in a q...optljjournal
This paper presents a theoretical model for the effect of electron
-
phonon interaction, temperature and
magnetic field on degree of electron spin polarization in GaAs/InAs quantum dot LED. To describe the
dynamics, quantum Langevin equation for photon numbe
r and carrier number is used. Simulation results
show that degree of electron spin polarization in quantum dot decreases with increase of electron phonon
interaction parameter at constant temperature and constant magnetic field which agrees with experiment
al results in literatures
Spatially adiabatic frequency conversion in opto-electro-mechanical arraysOndrej Cernotik
Optoelectromechanical systems offer a promising route towards frequency conversion between microwaves and light and towards building quantum networks of superconducting circuits. Current theoretical and experimental efforts focus on approaches based on either optomechanically induced transparency or adiabatic passage. The former has the advantage of working with time-independent control but only in a limited bandwidth (typically much smaller than the cavity linewidth); the latter can, in principle, be used to increase the bandwidth but at the expense of working with time-dependent control fields and with strong optomechanical coupling. In my presentation, I will show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that a mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. I will also demonstrate that, remarkably, the bandwidth enhancement per transducer element is largest for small arrays. With these features the scheme is particularly relevant for improving the conversion bandwidth in state-of-the-art experimental setups.
Using spectral radius ratio for node degreeIJCNCJournal
In this paper, we show that the spectral radius ratio for node degree could be used to analyze the variation of node degree during the evolution of complex networks. We focus on three commonly studied models of complex networks: random networks, scale-free networks and small-world networks. The spectral radius ratio for node degree is defined as the ratio of the principal (largest) eigenvalue of the adjacency matrix of a network graph to that of the average node degree. During the evolution of each of the above three categories of networks (using the appropriate evolution model for each category), we observe the spectral radius ratio for node degree to exhibit high-very high positive correlation (0.75 or above) to that of the
coefficient of variation of node degree (ratio of the standard deviation of node degree and average node degree). We show that the spectral radius ratio for node degree could be used as the basis to tune the operating parameters of the evolution models for each of the three categories of complex networks as well as analyze the impact of specific operating parameters for each model.
Design of a Reliable Wireless Sensor Network with Optimized Energy Efficiency...paperpublications3
Abstract: Data gathering in wireless sensor network (WSN) is a crucial field of study and it can be optimized various algorithms like clustering, aggregation, and cryptographic technique in order to reliably transfer data between sensor and sink. But these techniques do not provide an optimized data gathering wireless sensor network because of the fact that they do not leverage the advantages of various techniques. Our problem definition is to create a reliable data gathering wireless sensor network which ensures good energy efficiency and lower delay as compared to existing techniques.
Keywords: Aggregation, Clustering, Data Gathering, Cryptography, Data Compression, Run Length Encoding.
Title: Design of a Reliable Wireless Sensor Network with Optimized Energy Efficiency and Delay
Author: Neelam Ashok Meshram
ISSN 2349-7815
International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
Paper Publications
Measurement of the Lifetime of the 59.5keV excited State of 237Np from the Al...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
A New Transistor Sizing Approach for Digital Integrated Circuits Using Firefl...VLSICS Design
Due to the fact that, the power consumption and speed of a VLSI circuit are dependent on the transistor
sizes, efficient transistor sizing is a new challenge for VLSI circuit designers. However, evolutionary
computation can be successfully used for complex VLSI transistor sizing which reduces the time to market
and enables the designer to find the optimized solutions for a non-linear and complex circuit design
process. In this paper, a new digital integrated circuit design approach is proposed based on the firefly
artificial intelligence optimization algorithm. In order to justify the effectiveness of the proposed algorithm
in the design of VLSI circuits, an inverter (NOT gate) is designed and optimized by the proposed algorithm.
As the simulation results show, the inverter circuit has a very good performance for power and delay
parameters.
Integrating vague association mining with markov modelijsc
The increasing demand of World Wide Web raises the need of predicting the user’s web page request. The
most widely used approach to predict the web pages is the pattern discovery process of Web usage mining.
This process involves inevitability of many techniques like Markov model, association rules and clustering.
Fuzzy theory with different techniques has been introduced for the better results. Our focus is on Markov
models. This paper is introducing the vague Rules with Markov models for more accuracy using the vague
set theory.
World: Zirconium - Market Report. Analysis And Forecast To 2020IndexBox Marketing
IndexBox Marketing has just published its report: "World: Zirconium - Market Report. Analysis And Forecast To 2020". This report has been designed to provide a detailed analysis of the global zirconium market. It covers the most recent data sets of quantitative medium-term projections, as well as developments in production, trade, consumption and prices. The report also includes a comparative analysis of the leading consuming countries, revealing opportunities opened for producers and exporters across the globe. The forecast outlines market prospects to 2020.
Spatially adiabatic frequency conversion in opto-electro-mechanical arraysOndrej Cernotik
Optoelectromechanical systems offer a promising route towards frequency conversion between microwaves and light and towards building quantum networks of superconducting circuits. Current theoretical and experimental efforts focus on approaches based on either optomechanically induced transparency or adiabatic passage. The former has the advantage of working with time-independent control but only in a limited bandwidth (typically much smaller than the cavity linewidth); the latter can, in principle, be used to increase the bandwidth but at the expense of working with time-dependent control fields and with strong optomechanical coupling. In my presentation, I will show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that a mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. I will also demonstrate that, remarkably, the bandwidth enhancement per transducer element is largest for small arrays. With these features the scheme is particularly relevant for improving the conversion bandwidth in state-of-the-art experimental setups.
Using spectral radius ratio for node degreeIJCNCJournal
In this paper, we show that the spectral radius ratio for node degree could be used to analyze the variation of node degree during the evolution of complex networks. We focus on three commonly studied models of complex networks: random networks, scale-free networks and small-world networks. The spectral radius ratio for node degree is defined as the ratio of the principal (largest) eigenvalue of the adjacency matrix of a network graph to that of the average node degree. During the evolution of each of the above three categories of networks (using the appropriate evolution model for each category), we observe the spectral radius ratio for node degree to exhibit high-very high positive correlation (0.75 or above) to that of the
coefficient of variation of node degree (ratio of the standard deviation of node degree and average node degree). We show that the spectral radius ratio for node degree could be used as the basis to tune the operating parameters of the evolution models for each of the three categories of complex networks as well as analyze the impact of specific operating parameters for each model.
Design of a Reliable Wireless Sensor Network with Optimized Energy Efficiency...paperpublications3
Abstract: Data gathering in wireless sensor network (WSN) is a crucial field of study and it can be optimized various algorithms like clustering, aggregation, and cryptographic technique in order to reliably transfer data between sensor and sink. But these techniques do not provide an optimized data gathering wireless sensor network because of the fact that they do not leverage the advantages of various techniques. Our problem definition is to create a reliable data gathering wireless sensor network which ensures good energy efficiency and lower delay as compared to existing techniques.
Keywords: Aggregation, Clustering, Data Gathering, Cryptography, Data Compression, Run Length Encoding.
Title: Design of a Reliable Wireless Sensor Network with Optimized Energy Efficiency and Delay
Author: Neelam Ashok Meshram
ISSN 2349-7815
International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
Paper Publications
Measurement of the Lifetime of the 59.5keV excited State of 237Np from the Al...theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
A New Transistor Sizing Approach for Digital Integrated Circuits Using Firefl...VLSICS Design
Due to the fact that, the power consumption and speed of a VLSI circuit are dependent on the transistor
sizes, efficient transistor sizing is a new challenge for VLSI circuit designers. However, evolutionary
computation can be successfully used for complex VLSI transistor sizing which reduces the time to market
and enables the designer to find the optimized solutions for a non-linear and complex circuit design
process. In this paper, a new digital integrated circuit design approach is proposed based on the firefly
artificial intelligence optimization algorithm. In order to justify the effectiveness of the proposed algorithm
in the design of VLSI circuits, an inverter (NOT gate) is designed and optimized by the proposed algorithm.
As the simulation results show, the inverter circuit has a very good performance for power and delay
parameters.
Integrating vague association mining with markov modelijsc
The increasing demand of World Wide Web raises the need of predicting the user’s web page request. The
most widely used approach to predict the web pages is the pattern discovery process of Web usage mining.
This process involves inevitability of many techniques like Markov model, association rules and clustering.
Fuzzy theory with different techniques has been introduced for the better results. Our focus is on Markov
models. This paper is introducing the vague Rules with Markov models for more accuracy using the vague
set theory.
World: Zirconium - Market Report. Analysis And Forecast To 2020IndexBox Marketing
IndexBox Marketing has just published its report: "World: Zirconium - Market Report. Analysis And Forecast To 2020". This report has been designed to provide a detailed analysis of the global zirconium market. It covers the most recent data sets of quantitative medium-term projections, as well as developments in production, trade, consumption and prices. The report also includes a comparative analysis of the leading consuming countries, revealing opportunities opened for producers and exporters across the globe. The forecast outlines market prospects to 2020.
Computational Chemistry aspects of Molecular Mechanics and Dynamics have been discussed in this presentation. Useful for the Undergraduate and Postgraduate students of Pharmacy, Drug Design and Computational Chemistry
Enhancing the Performance of P3HT/Cdse Solar Cells by Optimal Designing of Ac...IOSRJEEE
The present study examined the influence of different condition like as doping , in active layer, on the performance of P3HT/CdSe Solar cells .In this work, we analyzed the best doping for the configuration of P3HT/ CdSe in order to improve the performance of the solar cell. For this aim, we investigated the current density of electrons, the electric field, the short-circuit current and the open-circuit voltage in different doping . The results indicate that when the doping is increased in P3Ht and is decreased in CdSe, the current density of electrons, the electric field, the short-circuit current, and the open-circuit voltage are increased. Finally, we obtained doping of and for electron and hole donor respectively as the best doping for this configuration
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Ion Channel Simulations for Potassium, Sodium, Calcium, and Chloride Channels...Iowa State University
Computer simulations of realistic ion channel structures have always been challenging and a subject of rigorous study. Simulations based on continuum electrostatics have proven to be computationally cheap and reasonably accurate in predicting a channel's behavior. In this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for KcsA channel and study its steady-state response. SILVACO is a well-established program, typically used by electrical engineers to simulate the process flow and electrical characteristics of solid-state devices. By employing this simulation program, we have presented an alternative computing platform for performing ion channel simulations, besides the known methods of writing codes in programming languages. With the ease of varying the different parameters in the channel's vestibule and the ability of incorporating surface charges, we have shown the wide-ranging possibilities of using a device simulator for ion channel simulations. Our simulated results closely agree with the experimental data, validating our model.
https://www.sciencedirect.com/science/article/abs/pii/S0169260706002276
Computer simulations of realistic ion channel structures have always been challenging and
a subject of rigorous study. Simulations based on continuum electrostatics have proven to
be computationally cheap and reasonably accurate in predicting a channel’s behavior. In
this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for
KcsA channel and study its steady-state response. SILVACO is a well-established program,
typically used by electrical engineers to simulate the process flow and electrical characteristics
of solid-state devices. By employing this simulation program, we have presented an
alternative computing platform for performing ion channel simulations, besides the known
methods of writing codes in programming languages. With the ease of varying the different
parameters in the channel’s vestibule and the ability of incorporating surface charges,
we have shown the wide-ranging possibilities of using a device simulator for ion channel
simulations. Our simulated results closely agree with the experimental data, validating our
model.
Finite Element Method Linear Rectangular Element for Solving Finite Nanowire ...theijes
This paper concerned with the solution of finite nanowire superlattice quantum dot structures with a cylindrical cross-section determine by electronic states in various type of layers in terms of wave functions between structures containing the same number of barriers and wells (asymmetrical) or containing a different number (symmetrical). The solution is considered with the Finite element method with different base linear rectangular element to solve the one electron Ben Daniel-Duke equation. The results of numerical examples are compared for accuracy and efficiency with the finite difference method of this method and finite element method of linear triangular element. This comparison shows that good results of numerical examples.
This paper was published by my former Supervisor and involves partly my calculations and the concepts used during my MSci Thesis at University College London.
1. Modelling Electron States in Silicon-Based Quantum Computers
Ryan Moodie
Dr. Brendon Lovett
University of St. Andrews
August 2015
In experimental research towards quantum computation, planar silicon devices are made comprised of a metal
gate structure over an insulating oxide layer above a silicon substrate. Voltages are applied to the gates to control
the potential in the silicon and create quantum dots to confine electrons, the spin states of which encode quantum
information to form qubits.
Working with Dr. Brendon Lovett’s Theory of Quantum Nanomaterials group, this project involved theoretical work
complementing these experimental developments: a simulation was produced to flexibly model such devices. Using a
self-consistent method based on a Schr¨odinger-Poisson solver, the wavefunctions of two electrons in quantum dots are
solved for and the interaction size between them determined. Results are compared to experimental measurements and
used to gauge viability of exploiting interactions between electrons in specific systems for use in quantum computation.
Original Aims
The project objective was to computationally model elec-
tronic states in silicon, allowing calculation of physical
interaction parameters useful in the implementation of
silicon-based quantum computation. Rrequiring micro-
scopic system analysis, the electron wavefunctions had to
be calculated before determination of coupling parameters.
Initially, it was thought computational modelling would
be best achieved using the simulation package NEMO3D.
It was also considered that the exchange coupling would be
the parameter focussed on as manipulation of silicon-based
quantum data is generally theorised to be performed using
this interaction between qubits.
Python
Before the start of the project, a crude Python program
which solved for the potential from a specified gate struc-
ture then solved for an electronic wavefunction in that re-
gion was shared by collaborators of the research group.
Rather than NEMO3D, this formed the basis of the simu-
lation as it provided greater flexibility in program design.
It also allowed full understanding of program operation,
as opposed to more ‘black box’ packages. While increas-
ing initial difficulty of writing the program, this choice also
aided learning and allowed more low-level control.
This code inspired the final simulation, with sections
being used and rewritten to provide its starting point.
Quantum mechanical calculations were performed using
the Python package Kwant.
Experimental Perspective
While the project concerns theoretical work, the results
of the simulation can be compared to experimental mea-
surements and used to help design systems for particu-
lar applications. To learn more about the implementation
of quantum computation, the project involved a visit to
University College London to meet Prof. John Morton’s
Quantum Spin Dynamics group. This honed simulation
development to be compatible with current devices under
researched and allowed a feel for which system parameters
should be focussed on to generate a realistic model. The
visit also confirmed the theoretical parameters the experi-
mentalists need access to.
Maturing the Simulation
Following this successful start, the simulation was built up
to the point where the wavefunctions of two interacting
electrons in a silicon substrate could be determined in two
dimensions.
The desired gate structure is defined by creating a GDSII
file1
which the simulation reads. All further settings, such
as solving region boundaries, are set in a configuration file.
The voltages applied to gates are set, and the potential
due to this gate structure is solved for in a parallel two-
dimensional electron gas at a set distance below the gate
structure, this being the plane in which the rest of the sim-
ulation works. This initial potential landscape is efficiently
found using an analytical solution of Poisson’s equation.
A square tight-binding lattice is set up in a region where
an electron would experience confinement, generally a po-
tential well artificially introduced by the gate structure po-
tentials to form a quantum dot (see figure 1.). This allows
the Hamiltonian to be found, and thus Schr¨odinger’s Equa-
tion can be solved in this region to find the wavefunction
of the first electron.
This process is repeated in a separate region in the po-
tential landscape to yield the wavefunction of the second
electron, with the difference that this solution includes the
Coulomb repulsion exerted on this electron from the first.
The simulation then returns to the first electron and
solves for its wavefunction under the electrostatic interac-
tion of the second, then repeats this for the second electron
with the new electrostatic interaction of the first electron.
This process forms the second step in an iterative calcula-
tion, which continues to cycle until the eigenvalues of the
systems converge to a set accuracy. The results of this
calculation are the self-consistent wavefunctions of the two
electrons (see figure 2).
Quadrupole Interaction
During the course of the project, ongoing research specu-
lated that a more robust method of qubits interaction to
exploit than exchange interaction was the quadrupole in-
teraction. A post-doc in the group, Giuseppe Pica, was in-
volved in this research. With his collaboration, the project
focus shifted from calculating the exchange coupling to in-
vestigating the quadrupole interaction, EQ, between the
two electrons, given by:
EQ =
1
6
α,β
QαβVαβ
where α and β define system axes, V is an externally ap-
plied electric field gradient and Q is the quadrupole mo-
ment of the system[1].
1A database file format used for data exchange of integrated circuit
layouts in industry.
1
2. Figure 1: Potential landscape at a depth of 50nm from
two square gates of side length 2nm set 100nm apart with
applied voltages of -1V and -2V respectively. This produces
two confinement regions, on which square solving regions
have been centred, with the tight-binding lattices shown.
(a) Region 0 (b) Region 1
Figure 2: Self-consistent probability densities of the two
electrons. The simulation first solves for the wavefunction
of one electron in isolation. Then it solves for the sec-
ond including the Coulomb interaction from the first, and
proceeds to alternate this step between the electrons until
convergence in the eigenenergies is reached.
Exchange energy is a quantum mechanical effect arising
from the requirement of a two electron wavefunction to be
antisymmetric under particle exchange (because electrons
are fermions). As this exchange symmetry concerns the
product of the spatial and spin parts of the wavefunction,
different spatial configurations - with different Coulomb
interactions - and spin states affect it. The exchange cou-
pling therefore depends on the overlap of the wavefunctions
of the two electrons, which are exponentially decaying in
the overlap region and thus the parameter is highly sensi-
tive to changes in potential. The quadrupole interaction,
however, does not depend on wavefunction overlap. Early
research indicates that it should therefore be more robust
as a method of manipulating quantum information through
the interaction of physical qubits. [2]
Finally, the wavefunction results are used to calculate the
quadrupole moment of the system under application of an
electric field gradient, allowing calculation of quadrupole
interaction energy between the electrons.
Results
The results of simulations run at the end of the project us-
ing realistic system parameters correlate with current re-
search into the quadrupole interaction in quantum com-
putation, suggesting as a preliminary outcome that the
quadrupole interaction is viable for use in manipulation
of quantum information. This presents a positive outlook
towards its future use in quantum computation.
Further Research
With the project concluding on this promising result, the
group and collaborators will continue investigation into im-
plementation of silicon-based quantum computers and the
use of quadrupole interaction in quantum computation.
Moreover, the completed simulation will see more use in
this research as a valuable tool for the involved scientific
community.
There is also potential for others to continue this project
with extensions such as expanding the simulation to func-
tion in three dimensions.
Student Experience
My personal experience of the project has been hugely re-
warding and motivating. My initial intent to follow my
undergraduate Master’s degree in Theoretical Physics with
a PhD has blossomed from an interested but uninformed
aim to a passionate and excited purpose.
Having the opportunity to immerse myself in the re-
search of quantum computation, and quantum mechanics
and solid state physics in general, was completely captivat-
ing. Already topics of great interest to me, my knowledge,
understanding and enthusiasm in them has explosively in-
creased, which will be extremely useful for future study as
these will remain core topics. Perhaps most thrillingly, I
worked on and contributed to cutting-edge research in the
forefront of these fields, producing academically useful and
exciting results.
I gained first-hand research experience in both theo-
retical and experimental environments in different lead-
ing UK universities and participated in various meetings
and talks. Furthermore, I worked with some not only bril-
liant, but also exceedingly encouraging and friendly people,
not to mention the outstanding mentorship of Dr. Brendon
Lovett. I have learnt and honed valuable skills while forg-
ing links I can return to, opening up exciting future op-
portunities. The project has given me a fantastic insight
into postgraduate academic life and professional research,
a career path I am eager to embark on.
References
[1] C. P. Slichter, “Electrical Quadrupole Effects” in Prin-
ciples of Magnetic Resonance, vol. 1, Springer Se-
ries in Solid-State Sciences, 3rd Ed. Berlin, Germany:
Springer, 1989, ch. 10, sec. 2, pp. 486-489.
[2] P. A. Mortemousque et al., Quadrupole Shift of
Nuclear Magnetic Resonance of Donors in Sili-
con at Low Magnetic Field, arXiv:1506.04028v1
[cond-mat.mes-hall], Jul 2015.
2