Holographic methods for the theory of High-Tc Superconductors

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High-temperature superconducting (HTSC) materials have been a dream of scientists since 1911, when superconductivity was first observed by Kamerlingh Onnes. In 1986, after the pioneering work of Bednorz and Mueller, it was soon discovered that some cuprate-perovskite ceramic materials have critical temperatures, Tc, above 90 Kelvin (183 degrees C). These high-Tc superconductors renewed interest in the topic because of the prospects for improvement and potential room-temperature superconductivity.HTSCs have attracted great interest not only for their obvious potential applications in electronics, high-power magnets and high-precision detectors, but also for their scientific complexity. Despite 25 years of intensive development, the origin of HTSC and various thermodynamic phases arising in these materials are still not clear. Of fundamental importance is that all these systems are characterised by strong electron correlations, where conventional methods used in Condensed Matter Physics are not functional. As it has become clear recently, the unusual properties of these materials are governed by the presence of a quantum critical point at zero temperature (S.Sachdev 2008, D.M.Broun 2008).The purpose of the proposed research is to apply novel theoretical methods to be able to describe such strongly-correlated electron systems: HTSCs as well as two-dimensional electron gas and heavy-fermion compounds. This research is interdisciplinary: it requires knowledge of both condensed matter theory methods, quantum field theory and string theory.These novel methods are commonly called holography'' (J.Maldacena 1997, A.Polyakov 1998, E.Witten 1998): these are motivated by string theory and are applicable to the region of the phase diagram near the quantum critical point. Holographic methods are capable of describing the unusual properties of materials in terms of gravity theory in higher-dimensional space-time, where symmetries of the quantum critical point are realised geometrically. Holographic methods can be extended to non-zero temperatures by considering gravity solutions with black holes; and many real-time dynamical properties of the material, such as conductivity and heat transport may be computed. Thus, there exists a fascinating and previously unexpected opportunity to connect superconductors with black hole physics. The holographic framework has recently become very popular among string theorists, but the connection of these models with underlying lattice physics has not yet been established on the microscopic level. Studying this connection and establishing explicit relations between known microscopic lattice models and holographic models is the central objective of the research. This is expected to lead to a brand new framework for describing high-temperature superconductors and other materials with exotic properties. It may even lead to the prediction of new phases of matter.