Edge magnetotransport in graphene: A combined analytical and numerical study

TL;DR

This study combines analytical and numerical methods to explore edge magnetotransport in graphene, revealing how boundary conditions and magnetic fields influence resistance oscillations and edge current behavior.

Contribution

It provides a unified analytical and numerical analysis of edge magnetotransport in graphene, explaining resistance oscillations and boundary effects with a simplified Dirac model.

Findings

Hall resistance exhibits equidistant peaks due to cyclotron motion

Anomalous resistance oscillations occur at higher magnetic fields

Boundary geometry significantly influences local current flow

Abstract

The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account.