Holographic Multi-Band Superconductor

TL;DR

This paper develops a holographic model for multi-band superconductors with a unified symmetry, reproducing key features of real 2-band superconductors like MgB2, including phase diagrams and conductivity behaviors.

Contribution

It introduces a gravity dual with a global SO(3) symmetry for multi-band carriers, providing a novel holographic framework for studying multi-band superconductivity.

Findings

Phase diagram qualitatively matches real 2-band superconductors

Holographic conductivity exhibits mean field behavior

Bulk fields correspond to electromagnetic currents

Abstract

We propose a gravity dual for the holographic superconductor with multi-band carriers. Moreover, the currents of these carriers are unified under a global flavored SO(3) symmetry, which is dual to the bulk SO(3) gauge symmetry. We study the phase diagram of our model, and find it qualitatively agrees with the one for the realistic 2-band superconductor, such as $MgB_2$. We also identify the bulk field dual to the electromagnetic $U(1)_{EM}$ current, which should be invariant under the global flavored SO(3) rotation. We then evaluate the corresponding holographic conductivity and find the expected mean field like behaviors.