Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2008-06-17
J. Comput. Phys. 228, 8548 (2009)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
28 pages, 14 figures; submitted to Journal of Computational Physics
Scientific paper
10.1016/j.jcp.2009.08.001
Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms requires 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 arbitrary 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.
Richter Klaus
Wimmer Michael
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