Effect of the type-I to type-II Weyl semimetal topological transition on superconductivity

Abstract

The influence of recently discovered topological transition between type-I and type-II Weyl semimetals on superconductivity is considered. A set of Gorkov equations for weak superconductivity inWeyl semimetal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spikes in the transition point as functions of the tilt parameter of the Dirac cone determined, in turn, by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: The sharp cone pinnacle is characteristic for type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition to demonstrate the different weights of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.