Singlet-Quintet Mixing in Spin-Orbit Coupled Superconductors with j=3/2 Fermions

Abstract

In non-centrosymmetric superconductors, spin-orbit coupling can induce an unconventional superconducting state with a mixture of s-wave spin-singlet and p-wave spin-triplet channels, which leads to a variety of exotic phenomena, including anisotropic upper critical field, magnetoelectric effect, topological superconductivity, et al. It is commonly thought that inversion symmetry breaking is substantial for pairing-mixed superconducting states. In this work, we theoretically propose that a new type of pairing-mixed state, namely the mixture of s-wave spin-singlet and d-wave spin-quintet channels, can be induced by spin-orbit coupling even in the presence of inversion symmetry when electrons effectively carry "spin-3/2" in superconductors. As a physical consequence of the singlet-quintet pairing mixing, topological nodal-line superconductivity is found in such system and gives rise to flat surface Majorana bands. Our work provides a possible explanation of unconventional superconducting behaviors observed in superconducting half-Heusler compounds.

28 pages, 8 figures. Updated version: cited more references and added Sec.C8 to the appendix

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• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
• Experimental consequences of Bogoliubov Fermi surfaces
• Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals
• Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces
• Majorana multipole response of topological superconductors
• Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor
• Topological d+s wave superconductors in a multi-orbital quadratic band touching system
• A Spin Quintet in a Silicon Double Quantum Dot: Spin Blockade and Relaxation
• Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
• Ground state of the three-dimensional BCS d-wave superconductor
• Optical response of Luttinger semimetals in the normal and superconducting states
• Antiferromagnetic spin fluctuations and unconventional superconductivity in topological superconductor candidate YPtBi revealed by ${}^{195}$Pt-NMR
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• High orbital-moment Cooper pairs by crystalline symmetry breaking
• Identifying Bogoliubov Fermi surfaces via thermoelectric response in a $d$-wave superconductor heterostructure
• Time reversal symmetry breaking and $d$-wave superconductivity of triple-point fermions
• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
• p-wave superconductivity in Luttinger semimetals
• Josephson effect of superconductors with $J=3/2$ electrons
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• Helical Topological Superconducting Pairing at Finite Excitation Energies
• Infrared fixed points of higher-spin fermions in topological semimetals
• Phases of three-dimensional $d$-wave superconductors with two attractive interactions