A Transfer Matrix Approach to Electron Transport in Graphene through Arbitrary Electric and Magnetic Potential Barriers

TL;DR

This paper introduces a transfer matrix method for analyzing electron transport in graphene under complex electric and magnetic barriers, addressing limitations of previous methods at high energies and low magnetic fields.

Contribution

It presents a novel series expansion technique and compares it with asymptotic methods to improve accuracy in modeling graphene electron scattering.

Findings

Series expansion improves accuracy at high energies

Asymptotic method offers computational advantages

Parabolic cylindrical functions become unreliable at certain conditions

Abstract

A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It is shown that parabolic cylindrical functions, which have previously been used in literature, become inaccurate at high incident energies and low magnetic fields. A series expansion technique is presented to circumvent this problem. An alternate method using asymptotic expressions is also discussed and the relative merits of the two methods are compared.