Optimal block-tridiagonalization of matrices for coherent charge transport

Journal Article · Thu Dec 10 04:00:00 EST 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.08.001· OSTI ID:21333893

Wimmer, Michael ^[1]; Richter, Klaus ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Regensburg, 93040 Regensburg (Germany)

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.

• OSTI ID: 21333893
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 23 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
CHARGE TRANSPORT
ELECTRON GAS
GRAPH THEORY
GREEN FUNCTION
HAMILTONIANS
MATRICES
QUANTUM DECOHERENCE
SEMICONDUCTOR MATERIALS
TRANSPORT THEORY