Ironchalcogenide superconductors FeSe_{1−x}S_{x}possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the socalled Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken timereversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (
This is an expanded written version of a plenary talk delivered at ICMP 2021. We describe some rigorous results in quantum field theory that have been obtained in recent years, with particular emphasis on those results on relative entropies in the setting of conformal field theory. These results are motivated in part by recent work of physicists which, however, depends on heuristic arguments—such as introducing cutoff and using path integrals and replica trick—which are hard to justify mathematically. Our main technical tools are from the theory of operator algebras, such as modular theory and the theory of subfactors. A discussion about open problems is presented at the end the paper.
more » « less NSFPAR ID:
 10378138
 Publisher / Repository:
 American Institute of Physics
 Date Published:
 Journal Name:
 Journal of Mathematical Physics
 Volume:
 63
 Issue:
 10
 ISSN:
 00222488
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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μ SR) measurements in FeSe_{1−x}S_{x}superconductors for0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zerofield muon relaxation rate is enhanced below the superconducting transition temperatureT _{c}for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transversefieldμ SR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17 ). This implies that a significant fraction of electrons remain unpaired in the zerotemperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zeroenergy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe_{1−x}S_{x}, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity. 
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