Superconductivity and Topological Properties in a Topological Semimetal

Topological superconductors (TSCs) in which superconductivity and topological properties are combined are characterized by topologically protected gapless states in the superconducting gaps. Realized in the gapless states of TSCs, Majorana fermions, which are particles and their own antiparticles, have crucial importance in quantum computation and spintronic device applications because of the exotic nature. Despite extensive study for the confirmation of TSCs, the observation of Majorana fermions in bulk superconductors has not been settled yet. Recently, the binary stannide semimetal CaSn3 with a cubic structure has been proposed to be a promising candidate for realizing topological superconductivity. In this dissertation, to clarify whether CaSn3 is a TSC or not, we investigated the superconducting and normal states of CaSn3, based on two criteria proposed by Fu and Berg. In a detailed study of the superconducting state of CaSn3, we find that the anisotropy of the upper critical field shows two-fold symmetry about a C4 axis which can be ascribed to an unconventional pairing state associated with nematic superconductivity. Besides the anisotropy, the temperature dependence of upper critical fields strongly deviates from that of the conventional depairing field described by Werthamer-Helfand-Hohenberg theory, consistent with odd-parity pairing. The possible odd-parity nematic superconducting state in CaSn3, together with a fully-gapped state suggested by Muon spin rotation measurements, meets one of the proposed prerequisites for topological superconductivity. We also present a detailed study of de Haas van Alphen quantum oscillations in a single crystal of CaSn3 with torque magnetometry. In conjunction with density functional theory-based calculations, the observed quantum oscillation frequencies indicate that the Fermi surfaces of CaSn3 enclose an odd number of time-reversal-invariant momenta, satisfying one of the other proposed criteria to realize topological superconductivity. Our findings will provide a new insight to identify topological superconductivity in quantum materials