Transmission coefficient through a saddle-point electrostatic potential for graphene in the quantum Hall regime

TL;DR

This paper analytically derives the transmission coefficient for electrons in graphene under high magnetic fields through a saddle-point potential, revealing half-quantized conductance steps and symmetry-breaking effects.

Contribution

It provides a new analytical model for electron transmission in graphene in the quantum Hall regime considering a saddle-point electrostatic potential.

Findings

Half-quantized conductance steps observed.

Backscattering amplitude linked to potential curvature.

Particle-hole symmetry breaking in asymmetric potentials.

Abstract

From the scattering of semicoherent-state wavepackets at high magnetic field, we derive analytically the transmission coefficient of electrons in graphene in the quantum Hall regime through a smooth constriction described by a quadratic saddle-point electrostatic potential. We find anomalous half-quantized conductance steps that are rounded by a backscattering amplitude related to the curvature of the potential. Furthermore, the conductance in graphene breaks particle-hole symmetry in cases where the saddle-point potential is itself asymmetric in space. These results have implications both for the interpretation of split-gate transport experiments, and for the derivation of quantum percolation models for graphene.