Topological d plus s wave superconductors in a multiorbital quadratic band touching system

Abstract

Realization of topological superconductors is one of the most important goals in studies of topological phases in quantum materials. In this work we theoretically propose a way to attain topological superconductors with nontrivial Fermi surfaces of Bogoliubov quasiparticles. Considering the interacting Luttinger model with j = 3/2 electrons, we investigate the dominant superconducting channels for a multiorbital quadratic band touching system with finite chemical potential, which breaks the particle-hole symmetry in the normal state. Notably, while the system generally favors d-wave pairing, the absence of the particle-hole symmetry necessarily induces s-wave pairing and such emergence of s-wave pairing leads to new types of topological d s wave superconductors and selects particular d-wave pairing channels. Based on the Landau theory with SO(3) symmetry, we demonstrate that two kinds of topological superconductors are energetically favored; uniaxial nematic phase with secondary s-wave pairing (d(3z2-r2 )+ s) and time-reversal-symmetry broken phase with secondary s-wave pairing (d(3z2-r2) + d(xy) +id(x2-y2) + s). These superconductors contain either nodal lines or Fermi pockets of gapless Bogoliubov quasiparticles and moreover exhibit topological invariants, leading to nontrivial surface states such as drumhead like surface states or Fermi arcs. We discuss applications of our theory to relevant families of materials, especially half-Heusler compound YPtBi, and suggest possible future experiments.