Electron screening and excitonic condensation in double-layer graphene systems

TL;DR

This paper theoretically examines excitonic condensation in double-layer graphene systems, accounting for screening effects, and finds that the transition temperature is extremely low, making experimental observation unlikely.

Contribution

It introduces a comprehensive screening model in double-layer graphene, showing that excitonic condensation is highly suppressed due to weak Coulomb interactions and disorder effects.

Findings

Maximum transition temperature is below 1 mK.

Screening significantly weakens interlayer Coulomb attraction.

Disorder suppresses excitonic condensation at realistic conditions.

Abstract

We theoretically investigate the possibility of excitonic condensation in a system of two graphene monolayers separated by an insulator, in which electrons and holes in the layers are induced by external gates. In contrast to the recent studies of this system, we take into account the screening of the interlayer Coulomb interaction by the carriers in the layers, and this drastically changes the result. Due to a large number of electron species in the system (two projections of spin, two valleys, and two layers) and to the suppression of backscattering in graphene, the maximum possible strength of the screened Coulomb interaction appears to be quite small making the weak-coupling treatment applicable. We calculate the mean-field transition temperature for a clean system and demonstrate that its highest possible value $T_c^\text{max}\sim 10^{-7}\epsilon_F\lesssim 1 \text{mK}$ is extremely small ($\epsilon_F$ is the Fermi energy). In addition, any sufficiently short-range disorder with the scattering time $\tau \lesssim \hbar /T_c^\text{max}$ would suppress the condensate completely. Our findings renders experimental observation of excitonic condensation in the above setup improbable even at very low temperatures.