Coherent-scatterer enhancement and Klein-tunneling suppression by potential barriers in gapped graphene with chirality-time-reversal symmetry

TL;DR

This study numerically investigates electron tunneling in gapped graphene with various potential barriers, demonstrating how spatial modulation, bias fields, and impurities influence Klein tunneling suppression and electron conductance.

Contribution

It introduces a detailed finite-difference analysis of tunneling in gapped graphene with non-square barriers, revealing enhanced control over Klein tunneling suppression and conductance modulation.

Findings

Spatially modulated barriers significantly enhance Klein tunneling suppression.

Bias fields enable control of electron flow at normal incidence.

Impurities cause conductance peaks and broadening depending on barrier shape.

Abstract

We have utilized the finite-difference approach to explore electron-tunneling properties in gapped graphene through various electrostatic-potential barriers changing from Gaussian to a triangular envelope function in comparison with a square potential barrier. Transmission coefficient is calculated numerically for each case and applied to corresponding tunneling conductance. It is well known that Klein tunneling in graphene will be greatly reduced in a gapped graphene. Our results further demonstrate that such a decrease of transmission can be significantly enhanced for spatially-modulated potential barriers. Moreover, we investigate the effect from a bias field applied to those barrier profiles, from which we show that it enables the control of electron flow under normal incidence. Meanwhile, the suppression of Klein tunneling is found more severe for a non-square barrier and exhibits a strong dependence on bias-field polarity for all kinds of barriers. Finally, roles of a point impurity on electron transmission and conductance are analyzed with a sharp peak appearing in electron conductance as the impurity atom is placed at the middle of a square barrier. For narrow triangular and Gaussian barriers, however, the conductance peaks become significantly broadened, associated with an enhancement in tunneling conductance.