Berry Phase and Pseudospin Winding Number in Bilayer Graphene

TL;DR

This paper clarifies that the observed quantum Hall effects in bilayer graphene are due to the pseudospin winding number rather than a non-trivial Berry phase, challenging previous interpretations of experimental data.

Contribution

It demonstrates that the Berry phase in bilayer graphene is equivalent to that of a conventional 2D electron gas and highlights the importance of pseudospin winding number in quantum Hall measurements.

Findings

Berry phase in bilayer graphene is effectively zero modulo 2pi.

Quantum Hall effects are governed by pseudospin winding number, not the Berry phase.

Reinterpretation of experimental data on bilayer graphene's quantum Hall effect.

Abstract

Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2pi [K. S. Novoselov et al., "Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene", Nature Phys. 2, 177 (2006)], it has been widely accepted that the low-energy electronic wavefunction in this system is described by a non-trivial Berry phase of 2pi, different from the zero phase of a conventional two-dimensional electron gas. Here, we show that (i) the relevant Berry phase for bilayer graphene is not different from that for a conventional two-dimensional electron gas (as expected, given that Berry phase is only meaningful modulo 2pi) and that (ii) what is actually observed in the quantum Hall measurements is not the absolute value of the Berry phase but the pseudospin winding number.