Holographic methods for the theory of High-Tc Superconductors

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.

The development of room-temperature superconducting compounds would significantly and widely impact the quality of life and cause a technical revolution. Obvious obstacles in using superconducting devices in everyday life (the need for expensive cryogenic devices) would be removed: there would be levitating trains, compact ion accelerators (which may be used for electric rocket engines), super-fast and energy-efficient electronics based on superconducting circuits and Josephson junctions, and indeed, decreased power consumption might even solve the climate change problem. These techniques would in the near future influence security (terahertz scanners based on Josephson junctions), health (tomography), information technology and exploration of the cosmos. The new generation concepts in computing, transport and electronics would, without doubt, impact on social welfare and national security, influencing governments and policy makers, for example, those investing in capital transport projects across the globe.Unfortunately, to date there is no good theory for high-temperature superconductors that would give answers to all the questions posed. The proposed research applies novel mathematical developments, coming from string theory (a very complicated model with aspirations to be the theory of everything) to the understanding of physical phenomena in superconductors on microscopic level. There are several known materials with exotic properties to which the new concepts can be applied. Thus the proposed research is a first step to be made from mathematics to application. One of the aims is to disseminate the novel ideas coming from string theory among the condensed matter specialists. This new way of thinking about physics would almost certainly lead to new approaches to the development of novel materials. The final stages of proposed research include contact with experimentalists capable of creating such novel materials. Cost-effective methods for industrial manufacturing of superconducting materials could be developed. It is hard to estimate the realistic timescale for room-temperature superconductors, but other useful applications might follow in as little as 5 years. Any aspects from my research that may be directly commercialised will be developed through Loughborough University Enterprises Ltd who will provide help and advice on the exploitation process for any directly applicable IPR.I aim to present my results at cross cutting conferences in applied physics (reaching a broader audience), which may, in turn, lead to contact with non-academic parties, such as industry and government advisors, working groups and other public-facing bodies. I hope that my attendance at high-profile conferences would lead to positions on working in groups with influence on legislation and strategy. I aim to broaden the influence of my work in this way at every opportunity.On the broadest scale, the new theoretical concept of using black holes for describing superconductors might be of interest to the general public. I aim to convey the developments proposed to wider audience, including non-scientists and school children. The Department of Physics at Loughborough has a successful outreach programme that I would be keen to assist.