Transmission through Biased Graphene Strip

TL;DR

This paper investigates electron tunneling in biased graphene strips by solving the 2D Dirac equation using numerical and analytical methods, revealing consistent results and insights into quantum transport phenomena.

Contribution

It introduces a combined numerical and analytical approach to study tunneling in biased graphene, reducing the problem to an effective 1D Dirac equation with quantized transverse momentum.

Findings

Numerical Poincare Map results agree with analytical solutions.

Quantized transverse momentum leads to an effective mass in 1D Dirac equation.

Study provides detailed insights into tunneling phenomena in graphene strips.

Abstract

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincare Map approach, based on space discretization of the original Dirac equation, and direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincare Map are in complete agreement with the analytical results.