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To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation/relaxation ($mu$SR) studies of superconducting noncentrosymmetric Re$_{0.82}$Nb$_{0.18}$ ($T_c = 8.8$ K) and centrosymmetric Re ($T_c = 2.7$ K). In Re$_{0.82}$Nb$_{0.18}$, the low temperature superfluid density and the electronic specific heat evidence a fully-gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re$_{0.82}$Nb$_{0.18}$ and pure Re, the spontaneous magnetic fields revealed by zero-field $mu$SR below $T_c$ indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric Re$T$ ($T$ = transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg$_{10}$Ir$_{19}$B$_{16}$ and Nb$_{0.5}$Os$_{0.5}$, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and Re$T$. We discuss the superconducting order parameter symmetries that are compatible with the observations.
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In the recent search for unconventional- and topological superconductivity, noncentrosymmetric superconductors (NCSCs) rank among the most promising candidate materials. Surprisingly, some of them -- especially those containing rhenium -- seem to exhibit also time-reversal symmetry (TRS) breaking in their superconducting state, while TRS is preserved in many other isostructural NCSCs. To date, a satisfactory explanation for such discrepant behavior, albeit crucial for understanding the unconventional superconductivity of these materials, is still missing. Here we review the most recent developments regarding the Re-based class, where the muon-spin relaxation ($mu$SR) technique plays a key role due to its high sensitivity to the weak internal fields associated with the TRS breaking phenomenon. We discuss different cases of Re-containing superconductors, comprising both centrosymmetric- and noncentrosymmetric crystal structures and ranging from pure rhenium, to Re$T$ ($T$ = 3$d$-5$d$ early transition metals), to the dilute-Re case of ReBe$_{22}$. $mu$SR results suggest that the rhenium presence and its amount are two key factors for the appearance and the extent of TRS breaking in Re-based superconductors. Besides summarizing the existing findings, we also put forward future research ideas regarding the exciting field of materials showing TRS breaking.
Topological superconductivity has been sought for in a variety of heterostructure systems, the interest being that a material displaying such a phenomenon could prove to be the ideal platform to support Majorana fermions, which in turn could be the basis for advanced qubit technologies. Recently the high Tc family of superconductors, $FeSe_{x}Te_{1-x}$, have been shown to exhibit the property of topological superconductivity and further, evidence has been found for the presence of Majorana fermions. We have studied the interplay of topology, magnetism and superconductivity in the $FeSe_{x}Te_{1-x}$ family using high-resolution laser-based photoemission. At the bulk superconducting transition, a gap opens at the chemical potential as expected. However, a second gap is observed to open at the Dirac point in the topological surface state. The associated mass acquisition in the topological state points to time-reversal symmetry breaking, probably associated with the formation of ferromagnetism in the surface layer. The presence of intrinsic ferromagnetism combined with strong spin-orbit coupling provides an ideal platform for a range of exotic topological phenomena.
We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in the absence of external magnetic fields or Zeeman fields. Spin-singlet ($Delta_s$) and spin-triplet ($Delta_t$) pairings can coexist in superconductors whose crystal structure lacks inversion symmetry. The TRS can be spontaneously broken once a relative phase of $pmpi/2$ is developed, forming a TRS-breaking unitary pairing state ($Delta_spm iDelta_t$). We demonstrate that such unitary pairing could give rise to spontaneous spin-polarization with the help of spin-orbit coupling. Our result provides an alternative explanation to the TRS breaking, beyond the current understanding of such phenomena in the noncentrosymmetric superconductors. The experimental results of Zr$_3$Ir and CaPtAs are also discussed in the view of our theory.
We report muon spin relaxation measurements on the superconductor Sr2RuO4 that reveal the spontaneous appearance of an internal magnetic field below the transition temperature: the appearance of such a field indicates that the superconducting state in this material is characterized by the breaking of time-reversal symmetry. These results, combined with other symmetry considerations, suggest that superconductivity in Sr2RuO4 is of p-wave (odd-parity) type, analogous to superfluid 3He.
We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems and Sr$_2$RuO$_4$. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry broken superconducting state.
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