Computational implementation of the Kubo formula for the static conductance: application to two-dimensional quantum dots

TL;DR

This paper presents a computational method to calculate the static conductance of two-dimensional quantum dots using the Kubo formula, accounting for disorder, magnetic fields, and system geometry.

Contribution

It introduces a general computational implementation of the Kubo formula for disordered 2D clusters with customizable parameters and geometries.

Findings

Conductance can be computed for various disorder realizations.

Method accommodates magnetic fields and fluxes.

Applicable to rectangular clusters with ideal leads.

Abstract

Kubo formula is used to get the d.c conductance of a statistical ensemble of two-dimensional clusters of the square lattice in the presence of standard diagonal disorder, a uniform magnetic field and random magnetic fluxes. Working within a one-band tight-binding approach the calculation is quite general. The shape of the cluster is rectangular with ideal leads attached to opposite corners. Both geometrical characteristics and physical parameters can be easily selected. The output is just the conductance of a system of given parameters or a statistical ensemble of conductances measured for different disorder realizations.