Manipulation of the Dirac cones and the anomaly in the graphene related quantum Hall effect

TL;DR

This paper investigates how manipulating Dirac cones in graphene-like systems affects the quantum Hall effect, revealing the half-integer contributions of Dirac fermions to Hall conductivity through theoretical models.

Contribution

It introduces two classes of lattice models that manipulate Dirac cones to clarify their role in the quantum Hall effect in graphene.

Findings

Manipulating Dirac cones with different energies affects Hall conductivity.

Theoretical calculations confirm half-integer contributions of Dirac fermions.

Results are consistent with the half-odd integer series in Hall conductivity.

Abstract

The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically consider two classes of lattice models in which we manipulate the Dirac cones with either (a) two Dirac points that have mutually different energies, or (b) multiple Dirac cones having different Fermi velocities. We have shown, with an explicit calculation of the topological (Chern) number for case (a) and with an adiabatic argument for case (b) that the results are consistent with the picture that a single Dirac fermion contributes the half-odd integer series (... -3/2, -1/2, 1/2, 3/2, ...) to the Hall conductivity when the Fermi energy traverses the Landau levels.