Tensorial (d-wave) superconductivity in three-dimensional Luttinger semimetals

Synopsis

I will discuss unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to the quadratic band touching point in the band dispersion. The latter arises when the bands are inverted due to strong spin-orbit coupling, in materials such as mercury telluride or half-Heuslers, for example. Featureless contact interaction can then lead to either the familiar s-wave, or to some of unconventional d-wave states, with five complex components that transform as an irreducible, symmetric, second-rank tensor under rotations. The general structure of the Ginzburg-Landau free energy for such a three-dimensional d-wave state with an emphasis on its unusual features that stem from the tensorial nature of the superconducting order parameter will be elucidated. The one-loop computation of the coefficients in the Ginzburg-Landau free energy implies that in the isotropic limit there remains a large residual symmetry-unrelated accidental degeneracy at the quartic level between different d-wave configurations, as noted by Mermin already in 1974.  For a vanishing chemical potential the ground state is the superconducting analogue of the uniaxial nematic, which preserves time-reversal, and features two parallel circular line nodes in the quasiparticle spectrum (ref. 1).  At a finite chemical potential and at weak coupling, however, a large number of time-reversal-symmetry-broken superconducting states becomes energetically preferred.  The unexpected recent solution of the classic BCS d-wave pairing problem that results from their fierce competition will be presented and discussed (ref. 2). 
 
  REFERENCES
  1. I. Boettcher and I. F. Herbut, Physical Review Letters 20, 057002 (2018).
  2. I. F. Herbut, I. Boettcher, and S. Mandal, Physical Review B 100, 104503 (2019).