Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State

Abstract

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.

Pairing States of Spin- 32 Fermions: Symmetry-Enforced Topological Gap Functions

“…This was recognized in important papers focusing on a specific set of fully gapped pairing states [25,26] and on-site pairings [27]. Reference [27], in particular, has set the stage for studying superconductivity in the half-Heusler compounds [28][29][30][31][32][33][34]; the present authors have investigated the pairing instabilities in the p-wave pairing channels [31].…”

“…That such a degeneracy lifting should occur is expected from the gap structures of these states, as we demonstrate in the next section. Within weak-coupling BCS theory, it was found that the uniaxial nematic pairing is favored below T c [32].…”

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

“…In addition, Weyl SM (WSM), in which the low-energy fermionic excitations display linear dispersion around pairs of nodes with opposite chirality, was observed in TaAs, NbAs, TaP, and NbP by the angle-resolved photoemission spectroscopy (ARPES) [10][11][12][13][14]. There also exist other types of SMs, such as 3D nodal line SM (NLSM) [15][16][17][18], 2D semi-DSM , 3D double-WSM [47][48][49][50][51][52][53][54][55][56][57][58][59], 3D triple-WSM [49,53,[56][57][58][59][60][61][62], 3D anisotropic-WSM [49,[63][64][65], and 3D Luttinger SM [66][67][68][69][70].…”

“…The difference is owing to the fact that the fermion DOS vanishes at zero energy, namely ρ(0)=0. Cooper pairing instability may be achieved in other SMs, including 2D semi-DSM [43,44], 3D DSM [96], 3D WSM [97,98], 3D NLSM [17,18], and 3D Luttinger SM [67,69,70]. In these materials, there is also a threshold value for the strength of attraction.…”

Bogoliubov Fermi surfaces stabilized by spin-orbit coupling

“…Crucially for the appearance of BFSs, internally anisotropic pairing states are typically characterized by both intraband and interband pairing potentials [3]. Such pairing states have been proposed for a wide variety of multiband systems of current interest, such as iron-based superconductors [9][10][11][12][13][14], Cu x Bi 2 Se 3 [15], half-Heusler compounds [2,3,[16][17][18][19][20][21][22][23], the antiperovskite Sr 3−x SnO [24], Sr 2 RuO 4 [25], UPt 3 [26,27], * henri.menke@gmail.com † carsten.timm@tu-dresden.de ‡ philip.brydon@otago.ac.nz transition metal dichalcogenides [28,29], and twisted bilayer graphene [30][31][32]. This long list of materials-some of which are believed to support a time-reversal-symmetrybreaking (TRSB) state-is encouraging for the existence of BFSs.…”