Snake states and Klein tunneling in a graphene Hall bar with a pn-junction

TL;DR

This paper investigates how a pn-junction in a graphene Hall bar affects electron transport, revealing distinct behaviors such as Hall plateaus and negative resistance depending on doping regimes, using billiard model simulations.

Contribution

It introduces a detailed analysis of snake states and Klein tunneling effects in a graphene Hall bar with a pn-junction, highlighting new transport phenomena in ballistic regime.

Findings

Hall plateau appears in n-n regime

Negative Hall resistance in n-p regime

Asymmetric bend resistance behavior

Abstract

The Hall (RH) and bend (RB) resistance of a graphene Hall bar structure containing a pn-junction are calculated when in the ballistic regime. The simulations are done using the billiard model. Introducing a pn-junction--dividing the Hall bar geometry in two regions--leads to two distinct regimes exhibiting very different physics: 1) both regions are of n-type and 2) one region is n-type and the other p-type. In regime (1) a 'Hall plateau'--an enhancement of the resistance--appears for RH. On the other hand, in regime (2), we found a negative RH, which approaches zero for large B. The bend resistance is highly asymmetric in regime (2) and the resistance increases with increasing magnetic field B in one direction while it reduces to zero in the other direction.