Tunneling for Dirac Fermions in Constant Magnetic Field

TL;DR

This paper investigates the tunneling behavior of two-dimensional Dirac fermions in graphene under a constant magnetic field, analyzing reflection, transmission, and resonant tunneling phenomena in different system configurations.

Contribution

It introduces a detailed analysis of Dirac fermion tunneling in magnetic fields, including the effects of energy gaps and Lorentz potentials, with practical illustrations for barriers and diodes.

Findings

Total transmission possible with Lorentz potential

Transmission depends on energy ratio and energy gap t'

Resonant tunneling occurs under specific conditions

Abstract

The tunneling effect of two-dimensional Dirac fermions in a constant magnetic field is studied. This can be done by using the continuity equation at some points to determine the corresponding reflexion and transmission coefficients. For this, we consider a system made of graphene as superposition of two different regions where the second is characterized by an energy gap t'. In fact, we treat concrete systems to practically give two illustrations: barrier and diode. For each case, we discuss the transmission in terms of the ratio of the energy conservation and t'. Moreover, we analyze the resonant tunneling by introducing a scalar Lorentz potential where it is shown that a total transmission is possible.