Disorder induced superconductivity in quasi 1-D strongly correlated systems

摘要：对超导材料的长期研究直到最近才取得成功，因为引入无序可以提高超导材料的相变温度。直到最近，准一维材料中无序的受控结合的进展证明了这种材料的存在。新材料的发现，其中超导配对被无序增强开辟了一条路径，以控制（提高）转变温度。这样的系统不能用相变的标准平均场理论来描述。我们将开发一种新的准一维强相关无序超导体的量子场论，以理解新的超导态的性质。电子之间的吸引力导致超导体的形成。无序定位了电子，因此抑制了它们的传输，导致形成具有无限电阻的“对极”状态，即绝缘体。这两种机制之间的竞争通常被表述为无序诱导的超导性抑制。这个事实已经知道了几十年，主要的开放问题是“过渡到超导状态的温度究竟是如何被无序抑制的”。出乎意料的是，最近在不同材料上进行的实验表明，转变温度有所增加，即所谓的“临界温度增强”。这些材料原来是一维链，它们之间的耦合非常弱。在一维中不可能存在真正的超导性，任何无序都会使电子局域化。然而，一维链之间的弱耦合似乎创造了一种具有超导行为的新状态，这种状态因无序而增强。目前还没有理论能够解释所观察到的行为。这个项目的重点是发展这样一个理论；目的是了解无序诱导相变温度增强的本质，为控制超导性能开辟道路，并指导寻找新的高温超导体。目的为了理解无序诱导超导产生和增强的本质，我们将对新型准一维材料中发生的相变进行详尽的理论研究。研究目标是：1。描述具有超导对的一维耦合电子液体无序系统的有效场论。2. 准一维耦合电子液体系统中多电子波函数多重分形性质的理论分析。3. 相变温度的提高与不同网络结构和材料中支持波函数的拓扑结构有关这一假设的理论检验。方法描述低维系统（其中几乎所有的相互作用都导致非微扰效应）中的相变需要以适合处理凝聚态问题的形式应用量子场论。用玻色子化技术处理一维电子液体。为了描述一组耦合的一维电子液体，我们必须建立相应的场理论模型，该模型推广玻色子化方法，并包括无序和超导性。无序的存在将需要使用基于keldysh或副本的方法进行统计平均。为了分析导致新状态形成的不同机制，我们将使用重整化群分析。为了分析具有非平凡拓扑的晶格（Bethe晶格和无标度网络）中的超导性，我们将使用非线性sigma模型和空腔方法的结合。

AbstractThe long-lasting search for superconducting materials where the phase transition temperature can be increased by the introduction of disorder has been unsuccessful until recently. Only recently, advances in controlled incorporation of disorder in quasi-one-dimensional materials proved the existence of such materials. The discovery of new materials where superconducting pairing is enhanced by disorder opens a path to controlling (increasing) the transition temperature. Such systems are not described by standard mean-field theories of phase transitions. We will develop a new quantum field theory for quasi-one-dimensional strongly correlated disordered superconductors required to understand the nature of the new superconducting state.ContextAttraction between electrons leads to the formation of a superconductor. Disorder localises electrons and, therefore, suppresses their transport, leading to the formation of an 'antipode' state with infinite resistance, insulator. The competition between these two mechanisms is usually formulated as disorder-induced suppression of superconductivity. This fact has been known for decades and the main open question which was "how exactly the temperature of the transition into a superconducting state is suppressed by the disorder". Unexpectedly, recent experiments on different materials demonstrated an increase in the transition temperature, so-called 'critical temperature enhancement'. These materials turned out to be one-dimensional chains with extremely weak couplings between them. In one dimension there can be no true superconductivity and any disorder localises electrons. Nevertheless, it seems that a weak coupling between one-dimensional chains creates a new state with superconducting behaviour which is enhanced by the disorder. There is no theory at the moment capable of explaining the observed behaviour. This project is focused on developing such a theory; the aim is to understand the nature of disorder-induced enhancement of phase transition temperature, open the path to controlling the superconducting properties, and to guide the search for novel high-temperature superconductors.ObjectivesTo understand the nature of disorder-induced emergence and enhancement of superconductivity, we will implement an exhaustive theoretical study of phase transitions taking place in novel quasi-one-dimensional materials. The research objectives are: 1. Formulation of the effective field theory describing disordered system of coupled one-dimensional electron liquids with superconducting pairing. 2. Theoretical analysis of the multi-fractal nature of many-electron wavefunctions in quasi-one-dimensional systems of coupled electron liquids. 3. Theoretical test of the hypothesis that enhancement of phase transition temperature is related to the topology of the wavefunctions support in different network-like structures and materials. MethodA description of phase transitions in low-dimensional systems (where almost all interactions lead to non-perturbative effects) requires application of quantum field theory in a form suitable to dealing with condensed matter problems. A one-dimensional electron liquid is treated by the bosonisation technique. To describe a set of coupled one-dimensional electron liquids we will have to build corresponding field-theoretic model that generalizes bosonisation approach and includes disorder and superconductivity. The presence of disorder will require statistical averaging that will be performed with the use of the Keldysh-based or replica approach. To analyse different mechanisms leading to formation of a new state, we will use renormalisation group analysis. For the analysis of superconductivity onset in lattices with non-trivial topology (Bethe lattice and scale-free networks) we will use a combination of non-linear sigma model and the cavity method.