  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.
