Triplet-Superconductivity in Triple-Band Crossings

In this talk, we will introduce the triplet superconductivity in the newly discovered form of the topological semimetal, where the electrons with pseudospin J=1 form triple-band crossings. The peculiar property of J=1 electrons is that Fermi statistics rules out on-site spin singlet pairing. Performing the exact decoupling of on-site electron interactions into pairing channels, we adopt the Landau theory of spin-triplet pairings and study the Landau free energy functional to plot out the global phase diagram. We find two distinct phases; (i) time-reversal symmetric (Sz) state, (ii) time-reversal broken (Sx + i Sy) state. Remarkably, both of these states have gapless Bogoliubov quasiparticles and furthermore have topological invariants for each nodal line or Bogoliubov Fermi surface.