Influence of Disorder on Electron-Hole Pair Condensation in Graphene Bilayers

Graphene bilayers can condense into a state with spontaneous interlayer phase coherence that supports dissipationless counterflow supercurrents. Here, we address the influence of disorder on the graphene bilayer mean field and Kosterlitz-Thouless critical temperatures and report on a simple criteria for the survival of pair condensation.

Figure 1

KT temperature vs disorder strength. Disorder is parameterized by $\alpha =1/2{\tau }_S{T}_{c0}=\delta /T_{c0}$. The solid line in this figure corresponds to the clean system and the broken lines correspond to (top to bottom) $\alpha =0.1$, 0.5, 0.8. In graphene bilayers, ${ϵ}_F/T_{c0}\sim 10k_{F}d$ in the strongly interacting regime.