Disorder-induced tail states in a 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 $\nu(\epsilon)\propto \exp(-|\epsilon/\epsilon_t|^{3/2})$,wherethecharacteristictailenergy,$\epsilon_t$,scaleswiththeconcentrationofimpurities,$n_i$,as$n_i^{2/3}$. While the bare energy spectrum is characterized by two energies: the bias-induced gap, $V$, and interlayer tunneling, $t_{\perp }$, the tail, ${ϵ}_t$, contains a {\it single} combination $V^{1\mathrm{/}3}{t}_{\perp }^{2\mathrm{/}3}$. We show that the above expression for $\nu (ϵ)$ in the tail actually applies all the way down to the mid-gap.