Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking

Abstract

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 Sr2RuO4. 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.

Muon spin rotation and relaxation study on topological noncentrosymmetric superconductor PbTaSe$_2$

“…Therefore, there is no TRS breaking, excluding the existence of triplet pairing [23]. Recently, it is reported that muon could modify its local environment in ZF µSR, making µSR results on TRS differ from other techniques [36]. This is not in our case since our result is consistent with previous µSR work, and there is no results using other techniques to study TRS so far.…”

Unconventional superconductivity in topological Kramers nodal-line semimetals

“…Both free-and fixed- ZF analyses show a robust increase in  ZF (T) below T c , further confirming that the signal of spontaneous magnetic fields is an intrinsic effect. Very recently, theoretical works have confirmed the intrinsic nature of spontaneous magnetic fields in superconductors with TRS breaking (52). The ground-state spontaneous fields can be estimated by using B spont.…”

Muon spin rotation and relaxation study on topological noncentrosymmetric superconductor PbTaSe2

“…Therefore, there is no TRS breaking, excluding the existence of triplet pairing [23]. Recently, it is reported that although the positive charge of muon could modify the local environment in ZF-μSR experiments, TRS property shown by μSR is intrinsic since the effect induced by muon's charge is several eV below Fermi energy, which is much larger than the magnitude of superconducting gap (at the decade of meV) [36].…”