Strong Coupling BCS Superconductivity and Holography

TL;DR

This paper explores a holographic model of BCS superconductivity using the Sakai-Sugimoto framework, revealing a tachyonic instability linked to Cooper pairing and analyzing its stability and critical temperature dependence.

Contribution

It introduces a holographic description of BCS superconductivity via the Sakai-Sugimoto model, identifying a tachyonic instability as the bulk analog of Cooper pairing.

Findings

Identification of a tachyonic instability as the Cooper pairing analog.

Analysis showing the instability disappears with an electric field.

Numerical and approximate solutions for curved space configurations.

Abstract

We attempt to give a holographic description of the microscopic theory of a BCS superconductor. Exploiting the analogy with chiral symmetry breaking in QCD we use the Sakai-Sugimoto model of two D8 branes in a D4 brane background with finite baryon number. In this case there is a new tachyonic instability which is plausibly the bulk analog of the Cooper pairing instability. We analyze the Yang-Mills approximation to the non-Abelian Born-Infeld action. We give some exact solutions of the non-linear Yang-Mills equations in flat space and also give a stability analysis, showing that the instability disappears in the presence of an electric field. The holograhic picture also suggests a dependence of $T_c$ on the number density which is different from the usual (weak coupling) BCS. The flat space solutions are then generalized to curved space numerically and also, in an approximate way, analytically. This configuration should then correspond to the ground state of the boundary superconducting (superfluid) ground state. We also give some preliminary results on Green functions computations in the Sakai - Sugimoto model without any chemical potential