Knitting algorithm for calculating Green functions in quantum systems

We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state, and local currents in mesoscopic quantum systems. Within the nonequilibrium Green function formalism, we generalize the recursive Green function technique to tackle multiterminal devices with arbitrary geometries. We apply our method to analyze two recent experiments: an electronic Mach-Zehnder interferometer in a two-dimensional gas and a Hall bar made of graphene nanoribbons in a quantum Hall regime. In the latter case, we find that the Landau edge state pinned to the Dirac point gets diluted upon increasing carrier density.