Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning t...

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Published inJournal of computational physics Vol. 228; no. 23; pp. 8548 - 8565
Main Authors Wimmer, Michael, Richter, Klaus
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Inc 10.12.2009
Elsevier
Subjects
Online AccessGet full text
ISSN0021-9991
1090-2716
DOI10.1016/j.jcp.2009.08.001

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Abstract Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.
AbstractList Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green's function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.
Author Richter, Klaus
Wimmer, Michael
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  surname: Richter
  fullname: Richter, Klaus
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Issue 23
Keywords 72.10.Bg
05C78
05C50
Recursive Green’s function algorithm
02.70.−c
Coherent quantum transport
Block-tridiagonal matrices
Matrix reordering
Graph theory
02.10.Ox
Semiconductor materials
Green function
Calculation methods
Algorithms
02.70.-c
Hamiltonians
Recursive Green's function algorithm
Calculation
Tridiagonal matrix
Performance
Mesoscopic systems
Quantum transport
Electron gas
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Snippet Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the...
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SubjectTerms ALGORITHMS
Block-tridiagonal matrices
Blocking
CHARGE TRANSPORT
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Coherent quantum transport
Computational techniques
ELECTRON GAS
Exact sciences and technology
GRAPH THEORY
Graphene
GREEN FUNCTION
HAMILTONIANS
Mathematical analysis
Mathematical methods in physics
MATRICES
Matrix reordering
Optimization
Partitioning
Physics
QUANTUM DECOHERENCE
Recursive Green’s function algorithm
SEMICONDUCTOR MATERIALS
Semiconductors
Transport
TRANSPORT THEORY
Title Optimal block-tridiagonalization of matrices for coherent charge transport
URI https://dx.doi.org/10.1016/j.jcp.2009.08.001
https://www.proquest.com/docview/1266744346
https://www.osti.gov/biblio/21333893
Volume 228
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