Klein Tunneling in the presence of random impurities

TL;DR

This study investigates how random impurities affect Klein tunneling in graphene by simulating relativistic wavepacket propagation, revealing impurity-induced conductivity loss and deriving a general loss expression.

Contribution

It introduces a relativistic quantum lattice Boltzmann simulation to analyze impurity effects on Klein tunneling and provides a new formula for conductivity loss.

Findings

Conductivity decreases more for massive particles with impurities.

Derived a general expression for conductivity loss due to impurities.

Compared conductivity loss with classical fluid dynamics law.

Abstract

In this paper, we study Klein tunneling in random media. To this purpose, we simulate the propagation of a relativistic Gaussian wavepacket through a graphene sample with randomly distributed potential barriers (impurities). The simulations, based on a relativistic quantum lattice Boltzmann method, permit to compute the transmission coefficient across the sample, thereby providing an estimate for the conductivity as a function of impurity concentration and strength of the potentials. It is found that the conductivity loss due to impurities is significantly higher for wave-packets of massive particles, as compared to massless ones. A general expression for the loss of conductivity as a function of the impurity percentage is presented and successfully compared with the Kozeny-Carman law for disordered media in classical fluid dynamics.