Holographic methods for the theory of High-Tc Superconductors

自1911年Kamerlingh Onnes首次观察到超导性以来，高温超导（HTSC）材料一直是科学家的梦想。1986年，在Bednorz和Mueller的开创性工作之后，很快发现一些铜钙钛矿陶瓷材料的临界温度Tc高于90开尔文（183摄氏度）。这些高温超导体的改进和潜在的室温超导性的前景重新引起了人们的兴趣。高温超导体不仅在电子学、高功率磁体和高精度探测器方面有着明显的潜在应用，而且在科学上也很复杂。尽管经过了25年的深入研究，高温超导材料的起源以及这些材料中出现的各种热力学相仍然不清楚。最重要的是，所有这些系统的特点是强电子相关，在凝聚态物理学中使用的传统方法是不起作用的。正如最近已经清楚的那样，这些材料的不寻常性质是由零温度下量子临界点的存在所决定的（S.Sachdev 2008，D. M. Broun 2008）。拟议研究的目的是应用新的理论方法来描述这种强关联的电子系统：HTSC以及二维电子气和重费米子化合物。这项研究是跨学科的：它需要凝聚态理论方法、量子场论和弦理论的知识。这些新的方法通常被称为全息术“（J.Maldacena 1997，A.Polyakov 1998，E.维滕1998）：这些方法是由弦理论激发的，适用于量子临界点附近的相图区域。全息方法能够在高维时空中根据引力理论描述材料的不寻常性质，其中量子临界点的对称性是几何实现的。全息方法可以通过考虑黑洞的引力解扩展到非零温度;并且可以计算材料的许多实时动力学性质，例如传导性和热传输。因此，存在一个迷人的和以前意想不到的机会，将超导体与黑洞物理学联系起来。全息框架最近在弦理论家中非常流行，但这些模型与基础晶格物理学的联系还没有在微观水平上建立起来。研究这种联系并建立已知微观晶格模型和全息模型之间的明确关系是研究的中心目标。这有望为描述高温超导体和其他具有奇异特性的材料提供一个全新的框架。它甚至可能导致对物质新相的预测。

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.