Cooper pairing near charged black holes

Understand

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.