A knitting algorithm for calculating Green functions in quantum systems

TL;DR

This paper introduces a fast recursive Green function algorithm for calculating various local and transport properties in complex mesoscopic quantum systems, applicable to multiterminal devices with arbitrary geometries.

Contribution

The authors develop a generalized recursive Green function method within the non-equilibrium formalism, enabling analysis of multiterminal quantum devices with arbitrary shapes.

Findings

Analyzed an electronic Mach-Zehnder interferometer in 2D gas.

Studied a graphene nanoribbon Hall bar in quantum Hall regime.

Found Landau edge state dilution with increasing carrier density.

Abstract

We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state or local currents in mesoscopic quantum systems. Within the non equilibrium 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 2D gas and a Hall bar made of graphene nanoribbons in 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.