Weak Coupling Renormalization Group Approach to Unconventional Superconductivity in 2D Lattice Systems
AffiliationSchool of Physics
Document TypePhD thesis
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© 2021 Sebastian Wolf
Unconventional superconductivity has experienced tremendous growth in research interest and activity ever since the discovery of high-Tc superconductors. The variety and rich phenomenology of superconducting phases are promising for future device applications and technological advancement. Topological superconductivity constitutes another class of unconventional superconductors which are sought after for their applications as a material platform for fault-tolerant quantum computing. Until now, however, only a handful of candidate materials are known, and the lack of understanding of what exactly drives those phases represents a major challenge. There is no "recipe" yet for how to systematically search for topological superconductors. Similarly, there is no widely accepted theory that explains the microscopic mechanisms behind unconventional superconductors in general. The presented work extends the weak coupling renormalization group method, which we employ to provide a systematic study of unconventional superconductivity in two dimensional lattice systems. One of the major goals is to find out which of the possible "ingredients" - lattice symmetries, longer-range effects, multi-orbital effects, topology of the non-interacting system, and spin-orbit interactions - can promote the formation of topological superconducting states. We apply our method to paradigmatic lattice models and use our results for benchmarking. We then study an application to real materials: a monolayer of tin adatoms on a silicon substrate and a comparison of the LNO/LAO heterostructure with a barium copper oxide superconductor. After that, we continue with an investigation of the effect of Rashba-spin orbit coupling, which breaks inversion symmetry and thus causes mixing of spin-singlet and spin-triplet states, and a study on the effect of different topologies of the non-interacting system on the superconducting state. One of the overarching conclusions is that strong longer-range effects, like longer-ranged hopping and nearest-neighbor interactions, tend to benefit topological superconductivity. Furthermore, lattices with hexagonal symmetry seem to be especially beneficial for topological superconducting states with (relatively) high critical temperature.
Keywordsunconventional superconductivity; renormalization group; Hubbard Model; strongly correlated electrons
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