Theory of ballistic quantum transport in presence of localized defects

TL;DR

This paper introduces an efficient numerical method for modeling ballistic quantum transport in systems with localized defects, improving computational speed and memory use, applicable to complex device geometries.

Contribution

The authors develop a novel approach combining wave function matching, Lippmann-Schwinger equation, and scattering matrix formalism to enhance quantum transport simulations with localized defects.

Findings

Reduced matrix elements of Green's function improve computational efficiency.

Method successfully applied to graphene p-n junction and magnetic focusing experiments.

Derived a simple conductance formula for 1D wires with onsite perturbations.

Abstract

We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consumption of the calculations. Our approach can be applied to quantum devices of an arbitrary geometry and any number of degrees of freedom or leads attached. We provide a couple of examples of possible applications of the theory, including current equilibration at the p-n junction in graphene and scanning gate microscopy mapping of electron trajectories in the magnetic focusing experiment on a graphene ribbon. Additionally, we provide a simple toy example of electron transport through 1D wire with added onsite perturbation and obtain a simple formula for conductance showing that Green's function of the device can be obtained from the conductance versus impurity strength characteristics.