Controlling unconventional properties of correlated materials by Fermi surface topological transitions and deformations.

在过去的几十年里，广泛使用的电子技术是通过完善对电子在材料中的响应的控制来实现的，在材料中，电子之间的相互作用基本上很弱。例如，在简单的金属和半导体中，现在可以通过调节费米面和有效电子质量来可靠地实现这一点。然而，由于这类材料表现出的电子性质范围基本上有限，这项技术已经达到了其潜力的极限。如果人们对系统中的集体电子行为建立可靠的控制，就可以实现戏剧性的突破，在这些系统中，电子之间的强烈相互作用会引起有趣的宏观量子现象。多铁性、自旋电子材料中的巨磁电阻、聚合物体系中的电子关联和高温超导只是具有巨大应用潜力的几个例子。由于缺乏可靠的可控物质基础，预计将给现代世界带来革命性变化、并在原则上设想良好的量子计算机仍无法实现。原因很大程度上是因为电子关联物理的先验准确的理论基础，这将允许随意设计所需的电子性质，一直是一个挑战，目前还缺乏。鉴于相关系统新的精确数值工具的最新发展，现在使用新的方法来解决某些具有巨大技术潜力的相关材料的性质是非常及时的，这些材料目前处于广泛的实验研究的重点。在这个项目中，尖端的数值和先进的分析技术将使我们能够对相关电子系统中与量子相变相关的关键效应和机制进行明确和定量的理论描述，从而能够对相应的材料性质进行先验控制。具体地说，我们提出了一个全面的理论研究，通过改变外部参数，以及由此产生的具有非常规物理行为的新相的出现，来研究相关区域中费米面的形变效应。我们的主要目标是：(I)定量地了解关联电子模型系统中费米面重构和Lifshitz拓扑相变的机制和结果，特别是那些具有自旋轨道耦合的系统，以及它们与不稳定性的关系，在化学成分或磁场或外加压力的变化下；(Ii)准确预测具有重大技术意义的特定基准材料的性质，这些材料表现出与费米面变化相关的有趣行为，也是当前实验的焦点，如锶、锶和铁酸锶超导体。(Iii)对这些材料提出具体的实验建议，以检验新的理论；(Iv)最终实现对这类相关材料的性能的可靠控制。这是与技术发展直接相关的基础研究，因为我们选择的基准材料涵盖了广泛的潜在应用。超导SrRu2O4有望拥有Majorana束缚态，使其成为实现量子比特拓扑量子计算机的候选材料。铱酸锶具有自旋-轨道耦合和莫特物理之间的微妙相互作用，这可能导致新一代自旋电子器件，而对超导体在压力下的性质的控制，将为超导行业开辟新的途径。

Widespread electronic technologies of the last few decades have been led by perfecting control over response of electrons in materials where interactions between them are essentially weak. This can now be reliably achieved, e.g., in simple metals and semiconductors, by tuning the Fermi surface and the effective electron mass. However, this technology has reached the limit of its potential due to the fundamentally limited range of electronic properties exhibited by such materials. A dramatic breakthrough can be achieved if one establishes reliable control over collective electronic behaviour in systems where strong interactions between electrons give rise to intriguing macroscopic quantum phenomena. Multiferroics, giant magnetoresistance in spintronic materials, electron correlations in polymeric systems, and high-temperature superconductivity are just are a few examples with vast potential for novel applications. A quantum computer, expected to revolutionise the modern world, and well-envisaged in principle, can still not be realised due to the lack of reliably controlled material base. The reason, largely, is that a priori accurate theoretical underpinning of electron correlation physics, which would allow to design desired electronic properties at will, has remained a challenge and is currently missing.In light of very recent developments of new accurate numerical tools for correlated systems, it is extremely timely to use the new methodology to address properties of certain correlated materials of great technological potential, which are currently in the focus of extensive experimental studies. In this project, cutting-edge numerics and advanced analytical techniques will allow us to develop a definitive and quantitative theoretical picture of key effects and mechanisms associated with quantum phase transitions in correlated electron systems, thereby enabling a priori control over the corresponding material properties. Specifically, we propose a comprehensive theoretical study of effects of deformations of the Fermi surface in the correlated regime by changing external parameters and the resulting emergence of new phases with unconventional physical behaviour. Our main goals are to: (i) gain quantitative understanding of the mechanisms and consequences of Fermi surface reconstruction and Lifshitz topological transitions in correlated-electron model systems, especially those with spin orbit coupling, and their relation to instabilities, under changes of chemical composition or magnetic field or application of pressure; (ii) accurately predict properties of specific benchmark materials of great technological importance, which exhibit intriguing behaviour associated with changes of the Fermi surface and are the focus of current experiments, such as strontium ruthenates, strontium iridates, and fermonic superconductors. (iii) make specific proposals for experiments on those materials to test new theories, (iv) ultimately, achieve reliable control over the properties of these classes of correlated materials.This is fundamental research with direct relevance to development of technology since our choice of the benchmark materials covers a wide range of potential applications. Superconducting SrRu2O4 is expected to harbour the Majorana bound states, making it a candidate for realising qubits of topological quantum computers. Strontium iridates feature a delicate interplay between spin-orbit coupling and Mott physics, which can lead to new-generation spintronic devices, while control over properties of superconductors under pressure, will open new avenues for the superconducting industry.