The Holographic Superconductor Vortex

TL;DR

The paper demonstrates that holographic superconductors with a probe gravity dual support Abrikosov-like vortices in an external magnetic field. By solving the coupled PDEs for the vortex Ansatz in an AdS-Schwarzschild background, it computes the on-shell free energy, magnetization, and superconducting density, and identifies a mixed Shubnikov phase bounded by $B_{c1}$ and $B_{c2}$. The results confirm vortex energetics and flux-quantization in a strongly coupled 3D system, providing quantitative predictions for vortex penetration and the penetration length within a holographic framework.

Abstract

A gravity dual of a superconductor at finite temperature has been recently proposed. We present the vortex configuration of this model and study its properties. In particular, we calculate the free energy as a function of an external magnetic field, the magnetization and the superconducting density. We also find the two critical magnetic fields that define the region in which the vortex configurations are energetically favorable.

Figures (3)

• Figure 1: Order parameter $\langle {\cal O}_\Delta \rangle$ for the $n=1$ (solid) and $n=2$ (dashed) vortex configuration. The lower (upper) curves correspond to the case $m^2=0\ (-2)$. Presented in units of $\sqrt{\rho}=1$.
• Figure 2: Free energy for the $m^2=0$ case as a function of the external magnetic field for the $n=0$ (solid), $n=1$ (dashed) and $n=2$ (dotted) vortex configuration. Presented in units of $\sqrt{\rho}=1$.
• Figure 3: Superconducting density $n_s(r)$ for the $n=1$ (solid) and $n=2$ (dashed) vortex configuration. The lower (upper) curves correspond to the case $m^2=0\ (-2)$. Presented in units of $\sqrt{\rho}=1$.