A brief comparison between two programs that compute the static conductance of a disordered two-dimensional tight-binding system

Abstract

There are two programs in the CPC program library that compute the static conductance of a disordered two-dimensional cluster described by a tight-binding Hamiltonian. The older program uses the Landauer scheme to get the conductance from the transmittance of a cluster attached to two semi-infinite chains that play the role of physical leads. The second program directly uses the Kubo formula to get the conductance of a similar cluster connected to leads of arbitrary width. In both cases, the local Green function should be calculated, but while the first method uses the idea of recursion and implements a set of subroutines to get the desired matrix elements of the resolvent, the second method employs LAPACK subroutines to propagate the self-energy matrix from one side of the cluster to the other. At the end both methods deliver the same numerical answer, with a comparable high precision but at quite different computing speeds. The newer method is typically one order of magnitude quicker thanks to modern methods in linear algebra when just one system is solved, but recursion is advantageous for solving the same systems for several Fermi energies because in this case the slow part of the calculation is done only once.