A Holographic model of Striped Superconductors

One of the most prominent distinguishing features in strongly correlated electron systems, such as the high Tc (critical temperature) cuprates and the most recent iron pnictides, is the presence of "competing orders" that are related to the breaking of the lattice symmetries. Does the ubiquitous presence of such inhomogeneous orders in strongly correlated superconductors have a deep connection to superconductivity? The answer to this question is crucial for identifying the mechanism of superconductivity, at least in the cuprates. Amidst serious difficulties within conventional theoretical framework to deal with strongly interacting degrees of freedom at finite density, "AdS/CFT correspondence" or "gauge/gravity duality" sheds new light into the origin of high Tc superconductivity by mapping the original system into an appropriate weakly coupled one. An example of the ``Holographic principle", according to which, a quantum theory with gravity must be describable by a boundary theory, AdS/CFT duality provides guidelines to model a d dimensional strongly coupled condensed matter system in terms of a suitable gravity theory (as low energy limit of String theory) on a d+1 dimensional anti de-Sitter (AdS) space. In this thesis I will develop a phenomenological holographic model of strongly coupled ``striped" superconductors in two spatial dimensions and study the interplay between charge density waves and superconductivity. It will be shown that charge density waves with large modulation compete with superconducting order, causing the critical temperature to fall off with increasing modulation in various ways depending on free parameters of the theory. For small modulation, the effects of fluctuations dominate, causing an enhancement of critical temperature upon turning on modulation. The highest critical temperature is obtained at an intermediate modulation. Moreover, there exists a region in parameter space of the theory within which the modulation vs Tc phase structures show striking resemblance to doping phase structure of cuprates.