Numerical cookbook for electronic quantum transport at finite frequency

TL;DR

This paper introduces a systematic method to compute finite frequency quantum transport properties using Green's functions, extending existing DC codes to analyze AC conductance, quantum capacitance, and related phenomena.

Contribution

It develops a unified framework within Keldysh formalism to calculate finite frequency observables from stationary Green's functions, linking with scattering approaches.

Findings

Validated the method with quantum point contact AC conductance

Analyzed quantum Hall interferometer response at finite frequency

Extended numerical capabilities to new quantum transport observables

Abstract

Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function of the system, i.e. the natural output of most DC numerical codes. Our framework allows to extend the simulations capabilities of existing codes to a large class of observables including, for instance, AC conductance, quantum capacitance, quantum pumping, spin pumping or photo-assisted shot noise. The theory is developed within the framework of Keldysh formalism and we provide explicit links with the alternative (and equivalent) scattering approach. We illustrate the formalism with a study of the AC conductance in a quantum point contact and an electronic Mach-Zehnder interferometer in the quantum Hall regime.