Dirac electrons in a Kronig-Penney potential: dispersion relation and transmission periodic in the strength of the barriers

TL;DR

This paper investigates how transmission, conductance, and dispersion relations of Dirac electrons in a Kronig-Penney superlattice are periodic functions of barrier strength, revealing effects like collimation and Dirac line formation.

Contribution

It demonstrates the periodic dependence of transmission, conductance, and dispersion on barrier strength in Dirac electron systems, including novel phenomena like collimation and Dirac lines.

Findings

Transmission and conductance are periodic in barrier strength P.

Electron beam collimation occurs at P = 2 pi n.

Dirac points evolve into Dirac lines at P = (n + 1/2) pi.

Abstract

The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the delta-function barrier V(x,y) / hbar v_F = P delta(x). The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of P and causes collimation of an incident electron beam for P = 2 pi n and n integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = (n + 1/2) pi.