Disorder-induced tail states in a gapped bilayer graphene

TL;DR

This paper uses an instanton approach to analyze in-gap fluctuation states in biased bilayer graphene, revealing how impurity concentration affects the tail states' energy distribution and density of states.

Contribution

It introduces a novel application of the instanton method to describe tail states in bilayer graphene, linking tail energy to impurity concentration and system parameters.

Findings

Density of states decays as exp(-|ε/ε_t|^{3/2}) in the tail region.

Tail energy ε_t scales with impurity concentration as n_i^{2/3}.

Tail states extend down to the mid-gap, influenced by bias and tunneling parameters.

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.