In cubic crystals, such as the cubic semimetal YPtBi, the presence of j = 3/2 fermions gives rise to the intriguing possibility of exotic quintet (J = 2) and septet (J=3) superconducting states [1,2]. Investigating the characteristics of these quintet and septet states, and discerning them from the more conventional singlet and triplet pairing states, has become an area of active research. In our study, we employ an analytical field-theoretical approach to analyse the collective modes associated with quintet superconducting states in the paradigmatic Luttinger-Kohn model. We focus on the evolution of the collective mode spectrum as a function of the spin-orbit coupling strength, which for the quintet states tunes the system between fully-gapped single-band and nodal multi-band behaviour. Notably, in the singlet state we observe softening of the quintet Bardasis-Schrieffer modes at finite wavevector, while in the quintet state we find collective modes corresponding to both imaginary fluctuations into the singlet state and real fluctuations into other quintet states appear at subgap energies.
[1] P. M. R. Brydon, Limin Wang, M. Weinert, and D. F. Agterberg, Phys. Rev. Lett. 116, 177001 (2016).
[2] Igor Boettcher and Igor F. Herbut, Phys. Rev. Lett. 120, 057002 (2018).
We express our gratitude for the generous support provided by the Marsden Fund in New Zealand.