Exotic superconductivity in quantum materials

Abstract

The theory of superconductivity developed by Bardeen, Cooper, and Schrieffer has proven to correctly describe a wide class of metals, where the effective attraction between electrons is mediated by phonons. Despite huge success, this theory fails to explain certain types of superconductivity, which includes but not limited to topological superconductivity and superconductivity in systems with low carrier density. We study new exciting properties of these materials and discuss possible microscopic mechanisms for exotic superconductivity. In Part I of this thesis, we explore the properties of two-component superconductors with strong spin-orbit coupling. Our study is motivated by the experiments on a topological superconductor candidate material, Bi2Se3 doped with Cu, Sn, or Nb atoms. Generally, superconductivity in such systems comes in two flavors: nematic, which breaks rotational symmetry of the crystal, and time-reversal breaking chiral.

We study the relative energetics and different features specific to each of these flavors. We find that, in three dimensions, the nematic superconductors generically possess full pairing gap on the Fermi surface, thus representing a solid-state realization of a time-reversal-invariant topological superconductor. On the contrary, chiral superconductors host non-degenerate point nodes on the Fermi surface and represent the superconducting analog of topological Weyl semimetals; the low-energy excitations in these materials are itinerant Majorana fermions. In Part II, we suggest possible microscopic mechanisms for unconventional superconductivity. We show that strong fluctuations of the inversion-breaking order parameter induce instability in an odd-parity superconducting channel, suggesting a route towards topological superconductivity. Using bosonization, we generalize this result to one-dimensional systems.

We apply our findings to study superconductivity in three-dimensional Dirac materials with extremely low density of carriers. Finally, we discuss the mechanism for nematic superconductivity from density wave fluctuations in two-dimensional systems, with possible application to twisted bilayer graphene. The results presented in this thesis are mainly based on Refs. [1, 2, 3, 4, 5, 6, 7].