The gapped state of a carbon mono-layer in periodic magnetic and electric fields

TL;DR

Applying smooth, periodic magnetic and electric fields to graphene creates a gapped state that exhibits a quantized Hall effect without magnetic flux, offering a more experimentally feasible realization of topological phenomena.

Contribution

The paper analytically studies a gapped state in graphene under smooth periodic fields, revealing a Hall effect without magnetic flux and providing a simpler physical explanation compared to previous models.

Findings

Induces a band gap in graphene with periodic fields

Demonstrates a quantized Hall current without magnetic flux

Simplifies experimental realization of topological effects

Abstract

When smooth, zero-on-average, periodic magnetic and electric fields are applied to a carbon mono-layer (graphene), a gap between the valence and conduction band is introduced. Here this gapped state is studied analytically. It is found that it does not correspond to a band insulator: a constant electric field induces a quantized Hall current even though the magnetic flux through the sample is zero and there are no Landau levels. The phenomenon is of the same type as that discovered by Haldane for a graphene sample in a periodic magnetic field that is not smooth, i.e. varies rapidly on the scale of the graphene lattice constant. The effect can be explained in terms of the topological theory of Thouless, Kohmoto, Nightingale and den Nijs. For the system studied in this paper, an explanation in terms of simple physical principles is also presented. Thus some of the mystery is taken out of the apparently strange phenomenon of a Hall effect without magnetic flux. Furthermore, Haldane's model requires control over external magnetic fields on length scales less than an angstrom and is therefore hard to realize experimentally. For the model studied here, control over external fields on length scales that are larger by two orders of magnitude or more is sufficient. The model is therefore more amenable to experimental realization.