Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−

Abstract

We systematically generalize the exotic 3 He-B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically non-trivial, to arbitrary partial-wave channels with multi-component fermions. The concrete example with four-component fermions is illustrated including the isotropic f , p and d-wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically non-trivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N 2 in the p-wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multi-orbital condensed matter systems and multi-component ultra-cold large spin fermion systems are discussed. [5,6]. The p-wave superconductivity has also been extensively investigated in SrRu 2 O 4 [7-9], and heavy fermion systems including UGe 2 , URhGe, UCoGe [10]. The p-wave superfluid 3 He and superconductors exhibit rich topological structures of vortices and spin textures under rotations or in external magnetic fields, respectively [11,12]. In addition, experimental signatures of the possible nodal f -wave superconductivity have also been reported in UPt 3 [13,14].Among these unconventional pairing phases, the 3 He-B phase is distinct: in spite of its non-s-wave pairing symmetry and spin structure, the overall pairing structure remains isotropic and fully gapped. Its pairing exhibits the relative spin-orbit symmetry breaking fromwhere L, S, and J represent the orbital, spin, and total angular momentum, respectively. The relative spin-orbit symmetry-breaking has also been studied in the context of Pomeranchuk instability termed as unconventional magnetism leading to dynamic generation of spin-orbit coupling [15,16]. Furthermore, the 3 He-B phase possesses non-trivial topological properties [17][18][19]. Topological states of matter have become a major research focus since the discovery of the integer quantum Hall effect [20][21][22]. Recently, the study of topological band structures has extended from time-reversal (TR) breaking systems to TR invariant systems [23][24][25], from two to three dimensions [18,26,27], and from insulators to superconductors [17][18][19][28][29][30][31]. The 3 He-B phase is a 3D TR invariant topological Cooper pairing state. Its bulk Bogoliubov spectra are analogous to the 3D gapped Dirac fermions belonging to the DIII class characterized by an integer-valued index [18]. The non-trivial bulk topology gives rise to the gapless surface Dirac spectra of the mid-gap AndreevMajorana modes [32]. Evidence of these low energy states has been reported in recent experiments [33].Because the electron Cooper pair can only be either spin singlet or triplet, the p-wave 3 He-B phase looks the only choice of the unconventional 3D isotropic pairing state. In this article, we will show that actually there are much richer possibilities of this exotic c...

P23superfluids are topological

“…The formation of higher partial wave pairs, e.g., 3 P J , has also been discussed in cold atoms [53,54]. We here argue tangible systems to realize topological phenomena inherent to 3 P 2 phases.…”

Topological Crystalline Materials of J=3/2 Electrons: Antiperovskites, Dirac Points, and High Winding Topological Superconductivity

“…In crystals, the higher spin state can be identified as a J = 3/2 state, as discrete crystalline rotation allows at most fourfold degeneracy of the J = 3/2 spin. Superconductivity of J = 3/2 electrons has been discussed for Luttinger semimetals with a single J = 3/2 band such as half-Heusler systems [38][39][40][41][42][43][44][45][46][47][48][49]. While the half-Heuslers may host interesting higher-spin Cooper pairs, their actual realization is restricted because the systems support only a single J = 3/2 band.…”

Majorana Multipole Response of Topological Superconductors

“…Because inversion symmetry is absent, the Hamiltonian includes the antisymmetric SOI, which is proportional to δ and causes spin splitting at the Fermis surface [40]. In their superconducting states, Cooper pairs form between spin-3/2 electrons, which allows quintet and septet parings in addition to the conventional singlet and triplet pairings [42,59,60]. Furthermore, the antisymmetric SOI generally mixes the parity of the gap func-tion, so the even-and odd-parity components coexist in the gap function [61][62][63][64][65] and the odd-parity component is aligned with the antisymmetric SOI [62], providing the spin-septet pairing [40,42].…”