Magnetic edge states in graphene in nonuniform magnetic fields

TL;DR

This paper theoretically investigates magnetic edge states in graphene under nonuniform magnetic fields, revealing their dependence on field orientation and Zeeman splitting, with implications for experimental detection via Aharonov-Bohm interferometry.

Contribution

It provides a detailed analysis of magnetic edge states in graphene with nonuniform magnetic fields, highlighting their unique dispersion and splitting behaviors based on field orientation and Zeeman effects.

Findings

Magnetic edge states from n=0 Landau levels are dispersionless when B0 is parallel to B1 without Zeeman splitting.

In the antiparallel case, n=0 edge states split into electron-like and hole-like states.

Zeeman splitting or step potential can open energy gaps between these states.

Abstract

We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 \hat{z}$ in one domain and $B = B_1 \hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether $B_0$ is parallel or antiparallel to $B_1$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels, contrary to those from the $n \ne 0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electron-like and hole-like current-carrying states. The energy gap between the electron-like and hole-like states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudo-spin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov-Bohm interferometry setup in a graphene ribbon for experimental study of the magnetic edge states.