Disorder-induced tail states in gapped bilayer graphene

The instanton approach to the in-gap fluctuation states is applied to the spectrum of biased bilayer graphene. It is shown that the density of states falls off with energy measured from the band edge as nu(epsilon)proportional to exp(-parallel to epsilon/epsilon(t)parallel to(3/2)), where the characteristic tail energy, epsilon(t), scales with the concentration of impurities, n(i), as n(i)(2/3). While the bare energy spectrum is characterized by two energies: the bias-induced gap, V, and interlayer tunneling, t(perpendicular to), the tail, epsilon(t), contains a single combination V(1/3)t(perpendicular to)(2/3). We show that the above expression for nu(epsilon) in the tail actually applies all the way down to the midgap.