Designing and exploring new quantum materials based on Fermi surface topological transitions

在过去的几十年里，电子技术的进步是通过完善对材料中非相互作用电子的控制而实现的。这种控制现在可以可靠地获得，例如，在简单的金属和半导体中，通过调整费米能量和有效电子质量。然而，这种技术已经达到了其潜力的极限，因为这种材料所表现出的电子特性基本上是有限的。如果在电子之间的强相互作用产生有趣的宏观量子现象的系统中建立对集体电子行为的可靠控制，就可以实现一个戏剧性的突破。多铁性、自旋电子材料中的巨磁电阻、聚合物系统中的电子相关性和高温超导性只是具有巨大新应用潜力的几个例子。量子计算机有望彻底改变现代世界，并且在原则上得到了很好的设想，但由于缺乏可靠控制的物质基础，它仍然无法实现。究其原因，在很大程度上，是先验的准确的电子相关物理学的理论基础，这将允许设计所需的电子性质的意志，仍然是一个挑战，目前是缺失的。为了描述固体中相互作用电子的效应，费米液体理论已经成为一个强有力的起点。其应用的显著成就包括常规超导的微观理论和液氦-3的物理学。即使在某些情况下，FL理论被证明是不充分的，它的失败也为新的发现铺平了道路，在许多情况下，结果决定了新的方向。费米曲面（FS）和其不同部分的态密度（DOS）的概念是费米曲面（FS）的核心概念，它自然地出现在FL的背景下，但与基本FL理论所描述的情况远远相关。在DOS高的地方，交互效应可能变得更加明显，系统的特性可以通过它们来控制。DOS的高值甚至奇异值都伴随着不同类型fs的拓扑变化。在这个项目中，我们将以种子工作为基础，继续使用先进的数学工具对DOS中的奇点进行分类，并对交互的影响建立全面的理解。这项理论工作将伴随着广泛的搜索，通过第一性原理计算，新的量子材料可以作为不同种类的奇点的例子。我们的实验伙伴热衷于制造和表征即将确定的新材料。与此同时，现有的材料，如钌酸锶和二维金属硫族化合物，具有无法解释和未探索的性质，具有巨大的科学兴趣和潜在的技术应用，将为测试我们理论的力量提供直接的游乐场。虽然这些想法非常集中，但所提出的工作的范围和影响非常广泛，因此需要几个世界领导人在凝聚态理论和实验方面的共同努力才能实现所有目标。因此，这个合作项目涉及来自三个不同国家的八个机构的研究人员、学术访问人员和项目合作伙伴。

The advances in electronic technology that have been achieved over the last few decades have been enabled by perfecting control over non-interacting electrons in materials. This control can now be reliably obtained, e.g., in simple metals and semiconductors, by tuning the Fermi energy 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.To describe effects of interacting electrons in solids, Fermi liquid (FL) theory has been a powerful starting point. Notable successes of its application include the microscopic theory of conventional superconductivity and the physics of liquid Helium-3. Even in cases where FL theory has proven inadequate, its failure paved the way for new discoveries, and in many cases the results dictated the new directions. A central concept, naturally emerging in the FL context but relevant far beyond the cases described by the basic FL theory, is the notion of the Fermi Surface (FS) and the density of states (DOS) at different parts of the FS. In places with high DOS the interaction effects may become more pronounced and the properties of the system can be governed through them.High, or even singular values of DOS are accompanied by topological changes of the FSs of different types. In this project, we will build on seed work and we will continue the classification, using advanced mathematical tools, of the singularities in DOS and to build a comprehensive understanding of the effects of interactions. This theoretical work will be accompanied by a wide search, through first principles calculations, of new quantum materials that can serve as examples of the different classes of singularities. Our experimental partners are keen to fabricate and characterise the new materials that will be identified. In parallel, existing materials, such as strontium ruthenates and the two-dimensional metallic chalcogenides with unexplained and unexplored properties which are of enormous scientific interest with potential technological applications, will provide the immediate playground to test the power of our theories. Although the ideas are very focused, the scope and the impact of the proposed work is very wide, therefore a concerted effort of several world leaders in condensed matter theory and experiments is necessary to achieve all the objectives. As a result, this collaborative project involves researchers, academic visitors and project partners from eight institutions in three different countries.