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Recently, topologically protected ultranodal pairing states with so-called Bogoliubov Fermi surfaces have been predicted in time-reversal symmetry-breaking (TRSB) superconductors [1,2]. The iron-chalcogenide superconductors FeSe_1-xS_x are among the most promising candidates for such exotic superconducting states. In FeSe_1-xS_x, nematic order (tetragonal-to-orthogonal structural transition) can be completely suppressed at x = 0.17, above which the superconducting properties change drastically and the residual density of states in the superconducting state is significantly enhanced [3-5]. Our recent muon spin rotation (μSR) measurements reveal that TRSB occurs just below the superconducting transition temperature and a significant fraction of electrons remains unpaired in the superconducting state of the tetragonal phase [6]. These results are consistent with the ultranodal pairing state with BFSs. I will review recent studies of FeSe_1-xS_x superconductors, showing exotic superconducting states, including recent direct observations of BFSs in angle-resolved photoemission spectroscopy (ARPES) measurements [7] and a strong upturn of the nuclear magnetic relaxation (NMR) rate in the superconducting state associated with possible nesting properties between BFSs [8] as well as a possible impurity-induced disappearance of BFSs revealed by penetration depth measurements in the tetragonal FeSe_1-xS_x [9].

[1] D. F. Agterberg, P. M. R. Brydon, and C. Timm, Phys. Rev. Lett. 118, 127001 (2017).

[2] C. Setty et al, Nat. Commun. 11, 523 (2020).

[3] Y. Sato et al., Proc. Natl. Acad. Sci. USA 115, 1227 (2018).

[4] T. Hanaguri et al., Sci. Adv. 4, eaar6419 (2018).

[5] Y. Mizukami et al., Commun. Phys. 6, 183 (2023).

[6] K. Matsuura et al., Proc. Natl. Acad. Sci. USA 120, e2208276120 (2023).

[7] T. Nagashima, T. Hashimoto et al., preprint (2023).

[8] Z.-Y. Yu et al., Commun. Phys. 6, 175 (2023).

[9] T. Nagashima, K. Ishihara et al., preprint (2023).