Berry phase and pseudospin winding number in bilayer graphene

Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2 K. S. Novoselov et al. , Nat. Phys. 2, 177 (2006), it has been widely accepted that the low-energy electronic wave function in this system is described by a nontrivial Berry phase of 2, 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 2), and (ii) what is actually observed in the quantum Hall measurements is not the absolute value of the Berry phase but the pseudospin winding number.