Band Collapse and the Quantum Hall Effect in Graphene

TL;DR

This paper investigates how lattice effects influence the quantum Hall conductance in graphene, revealing a band collapse phenomenon that transitions the Hall effect from relativistic to non-relativistic regimes at different magnetic fields.

Contribution

It provides an exact diagonalization analysis of the Landau problem on the hexagonal lattice, highlighting the impact of lattice effects and the band collapse phenomenon on quantum Hall conductance in graphene.

Findings

At very high magnetic fields, lattice effects dominate the Hall conductance.

Band collapse occurs as magnetic field decreases, restoring the relativistic quantum Hall effect.

Graphene exhibits two distinct quantum Hall regimes: odd-integer at low filling and all integers at higher filling.

Abstract

The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice, and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic field, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.