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

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.

4 pages, 2 figures Minor modifications as published

References in corpus (5)

• The electronic properties of graphene
• Unconventional Integer Quantum Hall effect in graphene
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• Local density of states in disordered two-dimensional electron gases at high magnetic field
• Electron quantum dynamics in closed and open potentials at high magnetic fields: Quantization and lifetime effects unified by semicoherent states