The second order nonlinear conductance of a two-dimensional mesoscopic conductor

TL;DR

This paper explores the weakly non-linear quantum transport in 2D mesoscopic conductors, introducing a general numerical scheme to analyze second order nonlinear conductance and its spatial characteristics.

Contribution

Develops a versatile numerical method to compute second order nonlinear conductance in 2D quantum conductors, revealing spatial structures and symmetry effects.

Findings

Spatial structure of nonlinear conductance quantities

Crossover behavior from symmetric to asymmetric geometries

Discussion on gauge invariance issues

Abstract

We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The nonlinear conductance is computed by explicitly evaluating the various partial density of states, the sensitivity and the characteristic potential. Interesting spatial structure of these quantities are revealed. We present detailed results concerning the crossover behavior of the second order nonlinear conductance when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of interests such as the gauge invariance are also discussed.