Transmission through rectangular potentials in semimetals featuring quadratic dispersion

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.