Competition and Coexistence of Order Parameters in Holographic Multi-Band Superconductors

TL;DR

This paper develops a holographic multi-band superconductor model revealing five distinct phases with various coexistence patterns of order parameters, influenced by back reaction strength and charge ratios, highlighting gravity's role in facilitating coexistence.

Contribution

It introduces a holographic multi-band superconductor model with back reaction effects, uncovering a rich phase diagram and the conditions favoring coexistence of multiple order parameters.

Findings

Five superconducting phases identified with varying order coexistence.

Back reaction and charge ratio critically influence phase structure.

Gravity-mediated attraction promotes coexistence of multiple orders.

Abstract

We construct a holographic multi-band superconductor model with each complex scalar field in the bulk minimally coupled to a same gauge field. Taking into account the back reaction of matter fields on the background geometry and focusing on the two band case with two scalar order parameters, we find that depending on the strength of the back reaction and the charge ratio of the two bulk scalars, five different superconducting phases exist, and three of five phases exhibit some region where both orders coexist and are thermodynamically favored. The other two superconducting phases have only one scalar order. The model exhibits rich phase structure and we construct the full diagram for the five superconducting phases. Our analysis indicates that the equivalent attractive interaction mediated by gravity between the two order parameters tends to make the coexistence of two orders much more easy rather than more difficult.