Half-integer contributions to the quantum Hall conductivity from single Dirac cones

TL;DR

This paper demonstrates that individual Dirac cones contribute half-integer quantized values to the quantum Hall conductivity, confirming the theoretical prediction of half-integer contributions in graphene-like systems.

Contribution

It introduces a lattice model with shifted Dirac points and explicitly calculates the topological number to reveal half-integer contributions from each Dirac cone.

Findings

Each Dirac cone contributes half-integer quantized Hall conductivity.

The half-integer contributions are confirmed through bulk-edge correspondence.

The model demonstrates the half-integer series in Landau levels.

Abstract

While the quantum Hall effect in graphene has been regarded as a realization of the anomaly associated with the massless Dirac particle carrying half the usual topological integer, this is hidden due to the doubling of the Dirac cones. In order to confirm the half-integer contribution from each Dirac cone, here we theoretically consider a lattice model in which the relative energy between the two Dirac points is systematically shifted. With an explicit calculation of the topological (Chern) number, we have demonstrated that each Dirac cone does indeed contribute to the Hall conductivity as the half odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) when the Fermi energy traverses the (shifted sets of) Landau levels. The picture is also endorsed, via the bulk-edge correspondence, from the edge mode spectrum for the present model.