Holographic Superconductivity in the Presence of Dark Matter: Basic Issues

Abstract

The holographic approach to study strongly coupled superconductors in the presence of dark matter is reviewed. We discuss the influence of dark matter on the superconducting transition temperature of both s-wave and p-wave holographic superconductors. The upper critical field, coherence length, penetration depth of holographic superconductors as well as the metal-insulator transitions have also been analysed. Issues related to the validity of AdS/CFT correspondence for the description of superconductors studied in the laboratory and possible experiments directed towards the detection of dark matter are discussed. In doing so we shall compare our assumptions and assertions with those generally accepted in the elementary particle experiments aimed at the detection of dark matter particles. The superconductivity is a macroscopic quantum phenomenon 1 appearing in many condensed matter systems and characterized by the expulsion of the magnetic field and zero resistance state at sufficiently low temperature. The superconducting rings show quantization of magnetic flux. This is also true for vortices in the type two superconductors. A number of other quantum effects appear if the superconductor is in contact with normal metal (Andreev reflection) or other superconductors (Josephson effect). All these properties and phenomena are at the heart of numerous applications of superconductors. Zero resistivity state allows the construction and operation of powerful superconducting electromagnets for important scientific and medical applications. The superconducting quantum interference devices (SQUIDs) are the most sensitive magnetometers. SQUIDs allow for the precise measurements of the flux quantum � = h/2e, where e is the electron charge and h the Planck constant. These devices have been proposed and used in the search for the magnetic monopole; the elementary particle postulated 2 by Dirac in 1931. The search 3 for this elusive particle continues 4 , with the hope that it might address an important question of composition of dark matter 5 . According to standard theory of gravity based on Newtonian dynamics the explanation of many astrophysical observations require the existence of large amount of matter that cannot be seen with telescopes, and is thus termed dark matter. The Planck satellite mission reveals that dark matter constitutes 26.8% of the total mass of the Universe, while ordinary matter makes only 4.9% of it. The rest 6 is the mysterious dark energy, 68.3%.