Superconductivity in three-dimensional spin-orbit coupled semimetals

Abstract

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, projecting them to the Fermi surface and deriving the corresponding Eliashberg theory. Applying our method to a generic density-density interaction in YPtBi we establish the following results: (i) The pairing strength in each channel uniquely encodes the j=3/2 nature of the Fermi surface band structure--a manifestation of the fundamental difference with ordinary metals. In particular, this implies that Anderson's theorem, which addresses the effect of spin-orbit coupling and disorder on pairing states of spin-1/2 electrons, cannot be applied in this case. (ii) The leading pairing instabilities are different for electron and hole doping. This implies that superconductivity depends on carrier type. (iii) In the case of hole doping--relevant to YPtBi, we find two odd-parity channels in close competition with s-wave pairing. One of these two channels is a multicomponent pairing channel, allowing for the possibility of time-reversal symmetry breaking. (iv) In the case of Coulomb interactions mediated by the long-ranged electric polarization of optical phonon modes, a significant coupling strength is generated in spite of the extremely low density of carriers. Furthermore, non-linear response and Fermi liquid corrections can favor non-s-wave pairing and potentially account for the experimentally-observed Tc.Comment: 17 pages, 3 figures, 7 table

Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals

“…The Eliashberg equation [34] of the j = 3/2 electrons has recently been discussed in Refs. [13,16]. They describe the various pairing channels of Luttinger semimetals and the corresponding coupling strength due to polar optical phonons [13].…”

“…For most of these materials, such as diamond and silicon, experimental data and ab-initio calculations [2][3][4] point towards a conventional pairing mechanism mediated by phonons [5,6]. However, this picture does not seem to hold for some dilute semiconductors such as SrTiO 3 [7], PbTe [8] and bismuth-based half-Heusler materials like YPtBi [9] where other pairing mechanisms have been suggested [10][11][12][13]. In various works it is proposed that YPtBi is a three-dimensional (3D) quadratic bandtouching Luttinger semimetal [13][14][15], where the quasiparticles are characterized by a pseudospin j = 3/2 due to the strong spin-orbit coupling [13,[16][17][18].…”

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

“…The pairing functions J JM J ðkÞ corresponding to the latter pairing channels up to L ¼ 1 are tabulated in Ref. [31]. For well-screened short-ranged interactions, the s-wave (L ¼ 0) and p-wave (L ¼ 1) pairing channels are expected to have highest T c , with higher angular momentum L channels being suppressed.…”

“…As a first example, consider the (31). This is a time-reversal invariant pairing state with isotropy group fe iπ C 8z ; e iπ C 2x g. For odd-parity pairing states, this implies four symmetry-related mirror planes (e.g., the xz and yz planes are both mirror planes).…”

Anisotropic RKKY interactions mediated by j=32 quasiparticles in half-Heusler topological semimetals

“…Furthermore, most of the * agorbanz@iasbs.ac.ir half-Heusler systems show correlated symmetry-broken ground states including superconducting and antiferromagnetic phases [15,16]. Of particular interest, higher spin of low-energy quasiparticles lead to further Cooper pairing channels particularly the so-called j = 3 septet pairing [17][18][19][20][21][22][23].…”