Optimal block-tridiagonalization of matrices for coherent charge transport

  • Authors:

  • Michael Wimmer;Klaus Richter

  • Affiliations:

  • Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany;Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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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.