Cooper pairing near charged black holes

TL;DR

This paper demonstrates that charged fermions near a charged black hole can form Cooper pairs, leading to superconductivity, with the critical temperature depending on fermion charge and interactions in a holographic framework.

Contribution

It introduces a mechanism for superconductivity via fermion pairing in a holographic black hole background, analyzing the critical temperature and Fermi surface properties.

Findings

Superconducting instability occurs at high fermion charges.

Critical temperature decreases to zero near a marginal Fermi liquid.

Fermion pairing is driven by a quartic contact interaction.

Abstract

We show that a quartic contact interaction between charged fermions can lead to Cooper pairing and a superconducting instability in the background of a charged asymptotically Anti-de Sitter black hole. For a massless fermion we obtain the zero mode analytically and compute the dependence of the critical temperature T_c on the charge of the fermion. The instability we find occurs at charges above a critical value, where the fermion dispersion relation near the Fermi surface is linear. The critical temperature goes to zero as the marginal Fermi liquid is approached, together with the density of states at the Fermi surface. Besides the charge, the critical temperature is controlled by a four point function of a fermionic operator in the dual strongly coupled field theory.