Effect of Inversion Asymmetry on Bilayer Graphene's Superconducting and Exciton Condensates

TL;DR

This paper investigates how inversion asymmetry affects superconductivity and exciton condensation in bilayer graphene, revealing that geometric superfluid stiffness is negligible in superconductors but enhances exciton condensates, influencing transition temperatures.

Contribution

It provides a detailed analysis of the role of inversion symmetry and displacement fields on superfluid properties in bilayer graphene, highlighting the negligible impact on superconductors and the enhancement in exciton condensates.

Findings

Geometric superfluid stiffness is negligible in bilayer graphene superconductors.

Displacement field enhances superfluid stiffness in exciton condensates.

Transition temperature modestly increases due to geometric effects in exciton condensates.

Abstract

Inversion asymmetry in bilayer graphene can be tuned by the displacement field. As a result, the band dispersion in biased bilayer graphene acquires flat band regions near the Dirac points along with a non-trivial band geometry. We analyze the effect of inversion symmetry on the critical temperature and superfluid stiffness of the superconducting state of AB-stacked graphene bilayer and on the exciton condensate in double layers formed by two AB-stacked graphene bilayers. The geometric superfluid stiffness in bilayer graphene superconductors is found to be negligible due to the small superconducting gap. Furthermore, we show that the geometric superfluid stiffness is maximized for a constant order parameter. Therefore, it can be neglected in biased bilayer graphene superconductors with any pairing symmetry. However, the displacement field enhances the geometric superfluid stiffness in exciton condensates. It is most prominent at low densities and high displacement fields. A consequence of the geometric superfluid stiffness is a modest enhancement of the Berezinskii-Kosterlitz-Thouless transition temperature in bilayer graphene's exciton condensate.