Phases of Holographic Superconductors in an External Magnetic Field

TL;DR

This paper investigates the phase diagram of holographic superconductors under external magnetic fields using a gravitational dual model, revealing localized condensate solutions like droplets and vortices through numerical and analytical methods.

Contribution

It introduces a detailed analysis of the (B,T) phase diagram of holographic superconductors, identifying localized condensate solutions and their properties.

Findings

Existence of condensate droplets and vortices in the phase diagram

Characterization of the (B,T) phase boundary

Numerical and analytical solutions of Maxwell-scalar equations

Abstract

We study a 2+1 dimensional model of superconductors using a 3+1 dimensional gravitational dual theory of a black hole coupled to a scalar field, with negative cosmological constant. In the presence of finite temperature T and a background magnetic field B, we use numerical and analytic techniques to solve the full Maxwell-scalar equations of motion in the background geometry, finding non-trivial localized solutions that correspond to condensate droplets, and to vortices. The properties of these solutions enable us to deduce several key features of the (B,T) phase diagram.