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

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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.