Scanning the Parameter Space of Holographic Superconductors

TL;DR

This paper investigates how physical properties of holographic s-wave superconductors depend on the scaling dimensions of dual condensates, revealing their sensitivity and the conditions under which they exhibit type I or II behavior.

Contribution

It systematically analyzes the influence of scaling dimensions on holographic superconductor properties, connecting these effects to the Ginzburg-Landau theory and superconductor classification.

Findings

Physical quantities are sensitive to the scaling dimensions of condensates.

Characteristic lengths diverge at the critical temperature, consistent with Ginzburg-Landau theory.

Superconductors can be type I or II depending on charge and scaling dimensions.

Abstract

We study various physical quantities associated with holographic s-wave superconductors as functions of the scaling dimensions of the dual condensates. A bulk scalar field with negative mass squared $m^2$, satisfying the Breitenlohner-Freedman stability bound and the unitarity bound, and allowed to vary in $0.5$ unit intervals, were considered. We observe that all the physical quantities investigated are sensitive to the scaling dimensions of the dual condensates. For all the $m^2$, the characteristic lengths diverge at the critical temperature in agreement with the Ginzburg-Landau theory. The Ginzburg-Landau parameter, obtained from these length scales indicates that the holographic superconductors can be type I or type II depending on the charge and the scaling dimensions of the dual condensates. For a fixed charge, there exists a critical scaling dimension, above which a holographic superconductor is type I, below which it becomes a type II.