A study of holographic superconductors

Master Thesis


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University of Cape Town

The proposal that the physics of quantum critical phase transition in strongly coupled condensed matter systems can be described by a gravitational theory within the frame work of gauge/gravity correspondence is investigated more extensively for s-wave superconductors. We consider a gravitational theory with a black hole solution in anti de Sitter spacetime, coupled to an Abelian-Higgs system in (d + 1)-dimensions. A wide range of negative mass squared for the scalar field that satisfied the Brietenlolmer-Freedman stability bound and the unitarity bound are considered in the probe limit. The dependence of the some of the physical quantities on the scaling dimensions of the dual condensates were thoroughly investigated. We observe that the holographic superconductors can be consistently classified into two, based on the scaling dimensions and the charge of the dual condensates. Holographic superconductors of dimension λ- exhibit features of type II superconductors while those of dimension λ+ show features of type 1. The validity of this classification was confirmed by solving the bulk equations of motion perturbatively near the quantum critical point in order to calculate the superconducting characteristic lengths at a fixed charge q. The results show that there is a critical scaling dimension beyond which a holographic superconductor behave as type I and below this value it is a type II. The properties of holographic superconductors presented in this report are in qualitative agreement with the Ginzburg-Landau theory.

Includes bibliographical references (leaves 61-68).