Abstract
The possible symmetries of the superconducting pair amplitude is a consequence of the fermionic nature of the Cooper pairs. For spin- systems this leads to the classification of superconductivity, where , and 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 classification, where is the exchange operator for the component of the total angular momentum quantum numbers. We then specifically focus on spin- fermion systems and several superconducting cubic half-Heusler compounds that have recently been proposed to be spin- 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 classification, including all possible odd-frequency (odd-) combinations. Moreover, one of the very interesting properties of spin- 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- superconductor with a pair potential satisfying an odd-gap time-reversal product and being noncommuting with the normal-state Hamiltonian hosts both a BFS and has finite odd- pair amplitudes. We then reduce the full spin- Hamiltonian to an effective two-band model and show that odd- pairing is inevitably present in superconductors with a BFS and vice versa.
- Received 28 June 2021
- Revised 26 August 2021
- Accepted 31 August 2021
DOI:https://doi.org/10.1103/PhysRevResearch.3.033255
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society