Transmission through rectangular potentials in semimetals featuring quadratic dispersion

TL;DR

This paper corrects previous calculations of quasiparticle transmission through rectangular barriers in quadratic semimetals, providing accurate transmission coefficients and analyzing their impact on conductivity and noise characteristics.

Contribution

It identifies and rectifies missing evanescent wave solutions in earlier work, leading to more accurate transmission and transport property calculations in quadratic semimetals.

Findings

Corrected transmission coefficients for quadratic semimetals.

Analyzed conductivity and Fano factor behavior.

Provided insights into quasiparticle transport in these materials.

Abstract

We revisit the problem of transmission of quasiparticles through a rectangular potential barrier, for semimetals featuring quadratic-in-momentum band-crossings at a nodal point. Although this was considered in Annals of Physics 419 (2020) 168235, the solutions corresponding to evanescent waves were missed, leading to a partial fulfillment of the boundary conditions required to determine the piecewise-continuous wavefunctions. In this paper, our aim is to correct those shortcomings, recompute the transmission coefficients, and show the resulting behaviour of the conductivity and the Fano factor for some representative parameter values.