超導體的電聲交互作用及拓樸性質之研究

Abstract

First-principles calculations are performed to investigate the superconductivity and topological properties of materials. For superconductors of BCS-type, the electron-phonon (e-ph) interactions play the essential role. The studies of superconductors of this kind rely on the appropriate description of the e-ph interactions. In this thesis, the e-ph interactions are calculated using the density functional perturbation theory that treats the interaction in a subtle way without the need of using the supercells. The correctness and the reliability of this method provides a powerful means to study and predict superconductors of BCS-type. With this method, we successfully reproduce the superconducting phase diagram of a semimetallic superconductor SnO. And then we also predict a new superconductor, C2SiB, that shows a high Tc ~ 60 K. The origin of the strong e-ph coupling is also discussed. In addition to the superconductivity, the topological property of a material is also investigated owing to its growing importance in the field of condensed matter physics. Here we adopt a method based on Wannier functions to calculate the Z2 invariant, a quantity that defines the topological state of a material. Unlike the parity analysis that works only for systems with inversion symmetry, this method can be applied be all kinds of system as long as the Z2 invariant is defined. We apply this method to some superconductors and reveal the nontrivial topology of some superconductors. This work paves the way to further investigate the interplay between superconductivity and the nontrivial topology.