Superconductivity in spin-$3/2$ systems: symmetry classification, odd-frequency pairs, and Bogoliubov Fermi surfaces

Abstract

The possible symmetries of the superconducting pair amplitude is a consequence of the fermionic nature of the Cooper pairs. For spin-$1/2$ systems this leads to the $\mathcal{S}\mathcal{P}\mathcal{O}\mathcal{T}=-1$ classification of superconductivity, where $\mathcal{S}$, $\mathcal{P}$, $\mathcal{O}$, and $\mathcal{T}$ refer to the exchange operators for spin, parity, orbital, and time between the paired electrons. However, this classification no longer holds for higher spin fermions, where each electron also possesses a finite orbital angular momentum strongly coupled with the spin degree of freedom, giving instead a conserved total angular moment. For such systems, we here instead introduce the $\mathcal{J}\mathcal{P}\mathcal{T}=-1$ classification, where $\mathcal{J}$ is the exchange operator for the $z$-component of the total angular momentum quantum numbers. We then specifically focus on spin-$3/2$ fermion systems and several superconducting cubic half-Heusler compounds that have recently been proposed to be spin-$3/2$ superconductors. By using a generic Hamiltonian suitable for these compounds we calculate the superconducting pair amplitudes and find finite pair amplitudes for all possible symmetries obeying the $\mathcal{J}\mathcal{P}\mathcal{T}=-1$ classification, including all possible odd-frequency (odd-$\omega$) combinations. Moreover, one of the very interesting properties of spin-$3/2$ superconductors is the possibility of them hosting a Bogoliubov Fermi surface (BFS), where the superconducting energy gap is closed across a finite area. We show that a spin-$3/2$ superconductor with a pair potential satisfying an odd-gap time-reversal product and being non-commuting with the normal-state Hamiltonian hosts both a BFS and has finite odd-$\omega$ pair amplitudes. We then reduce the full spin-$3/2$ Hamiltonian to an effective two-band model and show that odd-$\omega$ pairing is inevitably present in superconductors with a BFS and vice versa.

arXiv comment12 pages, 5 figures; published version

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• Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor
• Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate
• Symmetry, nodal structure, and Bogoliubov Fermi surfaces for nonlocal pairing
• Interplay of finite-energy and finite-momentum superconducting pairing
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Magnetically-textured superconductivity in elemental Rhenium
• Bogoliubov Fermi surfaces from pairing of emergent $j=3/2$ fermions on the pyrochlore lattice
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
• Identifying Bogoliubov Fermi surfaces via thermoelectric response in a $d$-wave superconductor heterostructure
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Quasiparticle interference as a direct experimental probe of bulk odd-frequency superconducting pairing
• Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field
• Nonlocal thermoelectricity in quantum wires as a signature of Bogoliubov-Fermi points
• Stability of Bogoliubov Fermi Surfaces within BCS Theory
• Strain-induced superconductivity in Sr2IrO4
• Impurity effect on Bogoliubov Fermi surfaces: Analysis based on iron-based superconductors
• Coexistence of Chiral Majorana Edge States and Bogoliubov Fermi Surfaces in Two-Dimensional Nonsymmorphic Dirac Semimetal/Superconductor Heterostructures
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems
• Antichiral edge states and Bogoliubov Fermi surfaces in a two-dimensional proximity-induced superconductor
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Eight-fold classification of superconducting orders
• Evolution and Instability of Bogoliubov Fermi Surfaces under Zeeman Field