The Emergence of Superconducting Systems in Anti-de Sitter Space

TL;DR

This paper explores the mathematical connection between a gravity model in Anti-de Sitter space and a superconducting system on its boundary, showing that Ginzburg-Landau equations can be derived from Einstein's theory.

Contribution

It introduces a flexible interaction potential in the holographic superconductor model, linking gravitational equations to superconducting phenomena near transition temperature.

Findings

Ginzburg-Landau equations derived from Einstein's gravity.

Interaction potential enhances model flexibility.

Demonstrates holographic correspondence between gravity and superconductivity.

Abstract

In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space $\rm AdS_4$, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of $\rm AdS_4$ (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field ${\bf H}$. An interaction potential $V(r,\psi) = \alpha(T)|\psi|^2/r^2+\chi|\psi|^2/L^2+\beta|\psi|^4/(2 r^k )$ is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature $T_c$. Overall, our result demonstrates that the two Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.