Integer quantum Hall effect in AAA-stacked trilayer graphene

TL;DR

This paper derives an analytical expression for the Hall conductivity in AAA-stacked trilayer graphene, revealing unusual quantization behavior dependent on chemical potential and magnetic field, linked to its Landau level spectrum.

Contribution

It provides the first analytical formula for Hall conductivity in AAA-stacked TLG and explains its unique quantization features due to Landau levels.

Findings

Hall conductivity quantization depends on chemical potential and magnetic field.

Unusual quantization is linked to the Landau level spectrum.

Characteristic behavior is specific to AAA-stacked multilayer graphene.

Abstract

We obtain an analytical expression for the Hall conductivity in AAA-stacked trilayer graphene (TLG) within the linear response Kubo formalism. Interestingly, we find that the quantization of the Hall conductivity is severely dependent on the value of the chemical potential and the magnetic field. The origin of this unusual quantization, attributed to the Landau level spectrum of AAA-stacked TLG, is explained in detail. We show that is a characteristic of the multilayer graphene structures with AA stacking order.