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

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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.