Unconventional superconductivity in strongly spin-orbit coupled hexagonal lattice systems

Minerva Access (University of Melbourne)

Abstract

This thesis analyses the role of spin-orbit coupling on the unconventional superconducting phases in hexagonal lattice systems. Spin-orbit coupling locks an electron's momentum to its spin, causing a spin splitting of its energy bands, and induces topological features in electronic models of materials. As a relativistic correction to the Schrödinger equation, it breaks full SU(2) spin rotational freedom, so spin is no longer a good quantum number. We study spin-orbit coupled tight-binding models with a repulsive Hubbard interaction, a paradigmatic model of screened electronic interactions widely used in studies of unconventional superconducting phases. Low-temperature Fermi liquid instabilities are determined by many-body truncated unity functional renormalisation group (TUFRG) calculations, a quantum field theoretic technique unbiased toward any particular instability. As the instabilities drive spontaneous symmetry breaking phase transitions, we perform a symmetry-based analysis utilising a group-theoretic decomposition and Ginzburg-Landau theory to identify the ground state superconducting order parameter realised below the phase transition. We apply this methodology to a suite of models: a phenomenological triangular lattice model with nearest-neighbour hopping, Rashba spin-orbit coupling and on-site Hubbard interactions; an extended Hubbard model describing the material Sn/Si(111), experimentally proposed as a topological superconductor candidate, and three related materials Pb/Si(111), Sn/SiC(0001) and Pb/SiC(0001); and a toy model derived from the Kitaev-Kondo model, where electronic interactions are mediated by fractionalised magnetic fluctuations of the Kitaev quantum spin liquid via the Kondo coupling of electrons and lattice spins. By incorporating the TUFRG instabilities directly into mean-field Hamiltonians, we calculate the topological properties of the superconducting phases. In the triangular-lattice Rashba Hubbard model, we find a rich additional phase structure, using the TUFRG instability decomposition to analyse these topological phase transitions on a mean-field level. Finally, we study the role of material impurities on superconducting phases. We first analyse when a simple impurity can introduce a subgap state into a superconductor. While Anderson's theorem prevents subgap states for momentum-independent superconducting pairings, impurities are always present for higher-angular momentum pairings. We also find that impurity subgap states can be introduced with extended-s wave pairings and in spin-orbit coupled systems. We then extend this impurity modelling to simulating quasiparticle interference spectra for Sn/Si(111), where the TUFRG derived mean-field Hamiltonian allows us to directly compare to experimental data, which demonstrate a remarkable level of agreement.

Authors 1

1. Matthew Bunney corresponding Aachen

   RWTH Aachen University · The University of Melbourne

   Affiliation as printed

   RWTH Aachen

   University of Melbourne