Cooper pairing of electrons and holes in graphene bilayer: Correlation effects

TL;DR

This paper investigates how electron-hole pairing in graphene bilayers is significantly affected by correlation effects beyond mean-field theory, revealing a sharp transition to a strongly gapped state near a critical coupling strength.

Contribution

It introduces a self-consistent approach to account for correlation effects and vertex corrections, highlighting the importance of these effects near the critical coupling in graphene bilayers.

Findings

A sharp transition to a correlated state with a large gap occurs at a critical coupling.

Correlation effects can double the gap size below the critical coupling.

Vertex corrections have a negligible impact on pairing.

Abstract

Cooper pairing of spatially separated electrons and holes in graphene bilayer is studied beyond the mean-field approximation. Suppression of the screening at large distances, caused by appearance of the gap, is considered self-consistently. A mutual positive feedback between appearance of the gap and enlargement of the interaction leads to a sharp transition to correlated state with greatly increased gap above some critical value of the coupling strength. At coupling strength below the critical, this correlation effect increases the gap approximately by a factor of two. The maximal coupling strength achievable in experiments is close to the critical value. This indicated importance of correlation effects in closely-spaced graphene bilayers at weak substrate dielectric screening. Another effect beyond mean-field approximation considered is an influence of vertex corrections on the pairing, which is shown to be very weak.