Dirac electrons in the presence of matrix potential barrier: application to graphene and topological insulators

TL;DR

This paper analyzes how Dirac electrons scatter off matrix potential barriers in 2D systems like graphene and topological insulators, revealing conditions for Klein tunneling, waveguiding modes, and edge/bulk state spectra.

Contribution

It introduces a formalism using spinor transfer matrices to study Dirac electron scattering on matrix barriers, including effects of Zeeman interaction and edge/bulk state properties.

Findings

Klein tunneling can occur at oblique incidence without a mass term.

Edge states form finite bands with massless excitations.

Bulk state spectra can be finite or infinite, with massive or massless excitations.

Abstract

Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not necessarily suppressed but occurs at oblique incidence. The formalism is applied to studying waveguiding modes of the barrier, which are supported by the edge and bulk states. The condition of existence of the uni-directionality property is found. We show that the band of edge states is always finite with massless excitations, while the spectrum of the bulk states, depending on parameters of the barrier, may consist of the infinite or finite band with both, massive and massless, low-energy excitations. The effect of the Zeeman term is considered and the condition of appearance of two distinct energy dependent directions corresponding to the Klein tunneling is found.