Inhomogeneous magnetic field in AdS/CFT superconductor

TL;DR

This work addresses holographic modeling of a $(2+1)$-dimensional superconductor under an inhomogeneous magnetic field. A GL-like matter sector is placed on a fixed AdS background with spatially varying fields to realize both type I and type II superconductivity and to observe a novel type-changing behavior near Tc. The analysis yields reduced equations coupling the order parameter to the inhomogeneous field, controlled by parameters defined from the boundary value ψ1, and shows that a temperature dependence drives a transition between type I and type II as Tc is approached. The work discusses back-reaction effects, showing partial corrections to the metric, and outlines limitations of the probe-field approach while highlighting potential for fully back-reacted or string-theoretic realizations as future directions.

Abstract

We study the holographically dual description of superconductor in (2+1)-dimensions in the presence of inhomogeneous magnetic field and observe that there exists type I and type II superconductor. A new feature of type changing is observed for type I superconductor near critical temperature.

Figures (1)

• Figure 1: To the left, a vortex forms in a type II superconductor where order parameter drops to zero at the center. To the right is the plot of magnetic field $H/\kappa$ (solid curve) and order parameter $s$ (dotted curve) near the vortex center. It shows that magnetic flux penetrates through the center of vortex.