Holographic Meissner Effect

TL;DR

This paper demonstrates the presence of the Meissner effect in holographic superconductors by making the boundary Maxwell field dynamical, revealing differences from traditional Ginzburg-Landau theory and analyzing the bulk dual theory.

Contribution

It analytically shows the Meissner effect in holographic superconductors by imposing boundary Maxwell equations, and derives the dual Ginzburg-Landau theory in the bulk.

Findings

The Meissner effect is analytically demonstrated in holographic superconductors.

The extreme Type I limit cannot be achieved even at infinite coupling.

The bulk Ginzburg-Landau parameter and theory are derived for a specific scaling dimension.

Abstract

The holographic superconductor is the holographic dual of superconductivity, but there is no Meissner effect in the standard holographic superconductor. This is because the boundary Maxwell field is added as an external source and is not dynamical. We show the Meissner effect analytically by imposing the semiclassical Maxwell equation on the AdS boundary. Unlike in the Ginzburg-Landau (GL) theory, the extreme Type I limit cannot be reached even in the $e\to\infty$ limit where $e$ is the $U(1)$ coupling of the boundary Maxwell field. This is due to the bound current which is present even in the pure bulk Maxwell theory. In the bulk 5-dimensional case, the GL parameter and the dual GL theory are obtained analytically for the order parameter of scaling dimension 2.