Graphene in periodically alternating magnetic field: unusual quantization of the anomalous Hall effect

TL;DR

This paper investigates how a periodic magnetic field affects graphene's electronic structure, revealing unusual quantization of the anomalous Hall effect linked to topological properties of minibands.

Contribution

It provides an analytical and numerical study of miniband formation and topological effects in graphene under a zero-average periodic magnetic field, highlighting novel quantization phenomena.

Findings

Formation of minibands with gaps controllable by external field

Calculation of Berry phase and Chern numbers for energy bands

Unusual fractional quantization of the anomalous Hall effect

Abstract

We study the energy spectrum and electronic properties of graphene in a periodic magnetic field of zero average with a symmetry of triangular lattice. The periodic field leads to formation of a set of minibands separated by gaps, which can be manipulated by external field. The Berry phase, related to the motion of electrons in $k$ space, and the corresponding Chern numbers characterizing topology of the energy bands are calculated analytically and numerically. In this connection, we discuss the anomalous Hall effect in the insulating state, when the Fermi level is located in the minigap. The results of calculations show that in the model of gapless Dirac spectrum of graphene the anomalous Hall effect can be treated as a sum of fractional quantum numbers, related to the nonequivalent Dirac points.