  We investigate the effect that the intrinsic spin-orbit and the inter- and
intra-layer Rashba interactions have on the energy spectrum of either an
unbiased or a biased graphene bilayer. We find that under certain conditions, a
Dirac cone is formed out of a parabolic band and that it is possible to create
a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in
the presence of only an intralayer Rashba interaction, the K (K') point splits
into four distinct ones, contrarily to the case in single-layer graphene, where
the splitting also takes place, but the low-energy dispersion at these points
remains identical.
