On a method to calculate conductance by means of the Wigner function: two critical tests

TL;DR

This paper critically evaluates a Wigner function-based method for calculating electron conductance in nanosystems, revealing its fundamental limitations in accurately describing quantum transport.

Contribution

It provides a detailed analysis showing that the method's failure is due to boundary condition implementation issues, which cannot be easily fixed.

Findings

The method fails to accurately predict zero-bias conductance.

Boundary condition imposition is identified as the main source of failure.

The failure persists even with electron correlations considered.

Abstract

We have implemented the linear response approximation of a method proposed to compute the electron transport through correlated molecules based on the time-independent Wigner function [P. Delaney and J. C. Greer, \prl {\bf 93}, 36805 (2004)]. The results thus obtained for the zero-bias conductance through quantum dot both without and with correlations demonstrate that this method is either quantitatively nor qualitatively able to provide a correct physical escription of the electric transport through nanosystems. We present an analysis indicating that the failure is due to the manner of imposing the boundary conditions, and that it cannot be simply remedied.