Superconductivity in the presence of strong correlations and spin-orbit interactions

我们对简单金属和半导体的了解大多是基于单粒子的图像。一旦我们确定了一个电子的行为，那么任何宏观电流或反应都是由这个单粒子的行为决定的，并稍加修改以解释许多电子的统计数据。然而，近几十年来，研究人员发现了越来越多支持导电的材料——也就是说，它们表现出金属行为，并被证明具有非常有趣的特性。例如，一类高温铜材料，La2CuO4，不导电，但有迷人的磁性行为。当掺杂时，它们是导体，尽管是较差的导体，但最终，在足够低的温度下，它们会超导。实现这一目标的“低温”比以前发现的任何超导体都要高得多。******超导是高度相关状态的一个例子，不能用单个粒子来理解。此外，在这些材料中，即使是正常状态也不能用单粒子行为来理解。现在有很多种类的材料都出现了这种情况；每个家庭都有足够不同的特征，因此人们对每个家庭中产生相关性的“粘合剂”提供了特定于家庭的解释。在这个提议中，我们想要探索这些材料中一些特殊行为的可能的更普遍的起源。我们的重点将是自旋-轨道耦合，这通常被认为是一个单一的粒子特性，其中一个电子的固有角动量（即它的“自旋”）影响电子的运动，反之亦然。通常的超导理论将自旋和轨道运动分开对待，尽管在过去的15年里，由于某些超导体的结构缺乏反转对称性，使得这种分离不可能实现，已经进行了许多修改。然而，所有超导体都有一定程度的自旋轨道耦合，在本提案中，我们将重新审视具有自旋轨道耦合的超导性的理论公式，特别是在材料表面附近，这正是许多实验探索超导性质的地方。与此同时，我们将探索超导状态的本质，这种超导状态不是由于某种“胶水”而产生的，而是由于量子物质总是膨胀的趋势所驱动的一种更普遍的机制，即通过降低动能。对驱动机制的深入了解将有助于材料科学家开发在更高温度下超导的材料，并最终使超导应用更便宜、更容易获得。

Much of what we understand about simple metals and semiconductors is based on a single-particle picture. Once we determine what one electron does, then any macroscopic current or response is determined by this single-particle behaviour, with slight modifications to account for the statistics of the many electrons. In recent decades, however, researchers have discovered more and more materials that support conduction --- that is, they show metallic behaviour, and turn out to have extremely interesting properties. By way of example, a class of the high temperature cuprate materials, epitomized by La2CuO4, are not conducting, but have fascinating magnetic behaviour. When doped, they are conductors, albeit poor ones, but eventually, at sufficiently low temperatures, they superconduct. The "low temperatures" at which this is achieved turn out to be much higher than in any previously discovered superconductor.******Superconductivity is an example of a highly correlated state that cannot be understood in terms of single particles. Moreover, in these materials, even the normal state cannot be understood in terms of single-particle behaviour. There are now many families of materials where this type of scenario is played out; there are sufficiently different properties from family to family that family-specific explanations have been offered for the "glue" that gives rise to the correlations in each family. In this proposal we want to explore possible more universal origins of some of the peculiar behaviour in these materials. Our focus will be spin-orbit coupling, which is normally thought of as a single particle property, one in which the intrinsic angular momentum of an electron (i.e. its "spin") affects the motion of the electron and vice-versa. The usual theory of superconductivity treats spin and orbital motion separately, although many modifications have been made in the last 15 years because certain superconductors that consist of structures that lack inversion symmetry make this separation impossible. All superconductors, however, have some degree of spin-orbit coupling, and in this proposal we will revisit the theoretical formulation of superconductivity with spin-orbit coupling, particularly near the surface of the material, which is precisely where many experiments probe for superconducting properties. At the same time we will explore the nature of the superconducting state that arises not because of some "glue", but because of a more generic mechanism driven by quantum matter's tendency to always expand, i.e. through kinetic energy lowering. A deeper understanding of the driving mechanism will aid material scientists in their quest to develop materials that superconduct at higher temperatures, and ultimately make superconducting applications cheaper and more accessible.