Vortex and Droplet Engineering in Holographic Superconductors

TL;DR

This paper constructs and analyzes vortex and droplet solutions in a holographic superconductor model, revealing insights into the phase diagram using numerical and analytical methods.

Contribution

It introduces new localized vortex and droplet solutions in a holographic superconductor model with magnetic fields, advancing understanding of the phase diagram.

Findings

Existence of vortex solutions with conserved winding number

Identification of condensate droplet solutions

Insights into the (B,T) phase diagram of holographic superconductors

Abstract

We give a detailed account of the construction of non--trivial localized solutions in a 2+1 dimensional model of superconductors using a 3+1 dimensional gravitational dual theory of a black hole coupled to a scalar field. The solutions are found in the presence of a background magnetic field. We use numerical and analytic techniques to solve the full Maxwell--scalar equations of motion in the background geometry, finding condensate droplet solutions, and vortex solutions possessing a conserved winding number. These solutions and their properties, which we uncover, help shed light on key features of the (B,T) phase diagram.