# Quantum transport in graphene Hall bars: Effects of side gates

## TL;DR

This study explores how side gates in graphene Hall bars influence quantum electron transport, revealing new propagating states and quantized resistance plateaus, with analytical predictions matching numerical simulations.

## Contribution

It introduces a detailed analysis of side-gate effects on Landau levels and resistance quantization, providing analytical and numerical insights into electron guiding in graphene.

## Key findings

- New propagating snake states due to side gates
- Appearance of additional quantized resistance plateaus
- Analytical predictions align with numerical results

## Abstract

Quantum electron transport in side-gated graphene Hall bars is investigated in the presence of quantizing external magnetic fields. The asymmetric potential of four side-gates distorts the otherwise flat bands of the relativistic Landau levels, and creates new propagating states in the Landau spectrum (i.e. snake states). The existence of these new states leads to an interesting modification of the bend and Hall resistances, with new quantizing plateaus appearing in close proximity of the Landau levels. The electron guiding in this system can be understood by studying the current density profiles of the incoming and outgoing modes. From the fact that guided electrons fully transmit without any backscattering (similarly to edge states), we are able to analytically predict the values of quantized resistances, and they match the resistance data we obtain with our numerical (tight-binding) method. These insights in the electron guiding will be useful in predicting the resistances for other side-gate configurations, and possibly in other system geometries, as long as there is no backscattering of the guided states.