Band-structure and electronic transport calculations in cylindrical wires: the issue of bound states in transfer-matrix calculations

Research output: Contribution to journalArticle

1 Downloads (Pure)

Abstract

The transfer-matrix methodology is used to solve linear systems of differential equations, such as those thatarise when solving Schr ̈odinger’s equation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization in three dimensions of methods usedto obtain scattering solutions in one dimension. Using the layer-addition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, whichis an update of an article originally published in Physical and Chemical News 16, 46-53 (2004), provides apedagogical presentation of this technique. It describes in details how the band structure associated with aninfinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit.The method is applied to the calculation of the transmission and band structure of electrons subject to cosinepotentials in a cylindrical wire. The simulations show that bound states must be considered because of theirimpact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of the representation
Original languageEnglish
Article number1907.06940
Number of pages13
JournalArXiv pre-print
Publication statusPublished - 16 Jul 2019

Fingerprint

wire
news
completeness
linear systems
electronics
repetition
discontinuity
energy spectra
differential equations
methodology
scattering
electrons
simulation

Keywords

  • electronic transport
  • transfert matrix methodology
  • S matrices
  • band structure calculation
  • bound states
  • quantum wires

Cite this

@article{d8675c118f1e42b4a545d00393fc5b63,
title = "Band-structure and electronic transport calculations in cylindrical wires: the issue of bound states in transfer-matrix calculations",
abstract = "The transfer-matrix methodology is used to solve linear systems of differential equations, such as those thatarise when solving Schr ̈odinger’s equation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization in three dimensions of methods usedto obtain scattering solutions in one dimension. Using the layer-addition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, whichis an update of an article originally published in Physical and Chemical News 16, 46-53 (2004), provides apedagogical presentation of this technique. It describes in details how the band structure associated with aninfinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit.The method is applied to the calculation of the transmission and band structure of electrons subject to cosinepotentials in a cylindrical wire. The simulations show that bound states must be considered because of theirimpact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of the representation",
keywords = "transfer matrix, bound states, band structure, electronic transport, electronic transport, transfert matrix methodology, S matrices, band structure calculation, bound states, quantum wires",
author = "Alexandre Mayer",
year = "2019",
month = "7",
day = "16",
language = "English",
journal = "ArXiv pre-print",

}

TY - JOUR

T1 - Band-structure and electronic transport calculations in cylindrical wires

T2 - the issue of bound states in transfer-matrix calculations

AU - Mayer, Alexandre

PY - 2019/7/16

Y1 - 2019/7/16

N2 - The transfer-matrix methodology is used to solve linear systems of differential equations, such as those thatarise when solving Schr ̈odinger’s equation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization in three dimensions of methods usedto obtain scattering solutions in one dimension. Using the layer-addition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, whichis an update of an article originally published in Physical and Chemical News 16, 46-53 (2004), provides apedagogical presentation of this technique. It describes in details how the band structure associated with aninfinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit.The method is applied to the calculation of the transmission and band structure of electrons subject to cosinepotentials in a cylindrical wire. The simulations show that bound states must be considered because of theirimpact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of the representation

AB - The transfer-matrix methodology is used to solve linear systems of differential equations, such as those thatarise when solving Schr ̈odinger’s equation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization in three dimensions of methods usedto obtain scattering solutions in one dimension. Using the layer-addition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, whichis an update of an article originally published in Physical and Chemical News 16, 46-53 (2004), provides apedagogical presentation of this technique. It describes in details how the band structure associated with aninfinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit.The method is applied to the calculation of the transmission and band structure of electrons subject to cosinepotentials in a cylindrical wire. The simulations show that bound states must be considered because of theirimpact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of the representation

KW - transfer matrix

KW - bound states

KW - band structure

KW - electronic transport

KW - electronic transport

KW - transfert matrix methodology

KW - S matrices

KW - band structure calculation

KW - bound states

KW - quantum wires

M3 - Article

JO - ArXiv pre-print

JF - ArXiv pre-print

M1 - 1907.06940

ER -