On the Behavior of Superconductors of High Critical Temperatures Outside Schwarzchild Black Holes in AdS Space

TL;DR

This paper reviews the holographic modeling of high-temperature superconductors using AdS/CFT correspondence, focusing on their behavior outside Schwarzschild black holes and analyzing conductivity and free energy through various Lagrangians.

Contribution

It introduces a detailed holographic framework for high-$T_c$ superconductors in AdS space, including extended Lagrangians and conductivity analysis, advancing understanding of strongly coupled condensed matter systems.

Findings

Conductivity peaks at low frequencies match Drude model predictions.

Extended Lagrangian with higher order Maxwell term improves modeling accuracy.

Behavior of Drude parameters analyzed in different limits.

Abstract

The physical analysis of condensed matter systems can be difficult due to strong coupling, but the mathematical context of the AdS/CFT correspondence enables non-perturbative descriptions in terms of dual weakly coupled systems. This brief review explores the holographic condensed matter applications of AdS/CFT, particularly through the lens of a high-$T_c$ superconductor outside a Schwarzchild black hole in Anti-de Sitter space. A simple two-dimensional electron condensate Lagrangian is examined first, as employed by G. T. Horowitz, later used to calculate a frequency-dependent conductivity and a free energy analysis; the asymptotics of both in this procedure, as examined by P. S\"aterskog, are also reviewed. An extended Lagrangian with a higher order Maxwell term is assessed thereafter, with a conductivity peak obtained at low frequencies described well by the Drude model in certain limits. The behavior of Drude model parameters in these limits is also investigated.