Disorder-induced tail states in a gapped bilayer graphene

Abstract

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 $\nu (\epsilon )\propto \exp (-|\epsilon /{\epsilon }_t{|}^{3/2})$, 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, $t_{\perp }$, the tail, ${\epsilon }_t$, contains a {\it single} combination $V^{1/3}{t}_{\perp }^{2/3}$. We show that the above expression for $\nu (\epsilon )$ in the tail actually applies all the way down to the mid-gap.

7 pages, 4 figures

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