Split superconducting and time-reversal symmetry-breaking transitions, and magnetic order in Sr$_2$RuO$_4$ under uniaxial stress

Abstract

Among unconventional superconductors, Sr 2 RuO 4 has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-µSR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset tempera-

Theory of Strain-Induced Magnetic Order and Splitting of $T_c$ and $T_{\rm TRSB}$ in Sr$_2$RuO$_4$

“…Until recently, the material was a prime suspect in the search for topological chiral triplet superconductivity. However, several new experimental results have challenged this picture [6][7][8][9], and the hunt is on to find a new consistent explanation for the panoply of observations on this fascinating material. These developments have not consigned Sr 2 RuO 4 to the junk heap of "ordinary" unconventional superconductors, but led to a discussion of new ways that the system may be extraordinary, if not odd.…”

Possibility of mixed helical p-wave pairings in Sr$_2$RuO$_4$

“…Arguably, one principal property of the superconductivity in Sr 2 RuO 4 is the condensation of at least two superconducting order parameters. This has been inferred from a variety of experiments, including µSR [11,12], optical polar Kerr effect [13], Josephson interferometry [14], and ultrasound [15,16], etc. A multi-component pairing is realized if the Cooper pairing is developed in a multi-dimensional irreducible representation (irrep) of the crystal point symmetry group.…”

“…In light of the evidence of time-reversal symmetry breaking from the µSR and the polar Kerr effect measurements [11][12][13], the multiple components presumably form a complex pairing, such that the state does not return to itself after a time-reversal operation. The Kerr effect, and the closely re- lated anomalous Hall effect, intuitively imply an underlying chiral pairing with nonzero orbital angular momentum, such as p + ip and d + id, as is substantiated by a recent study [17].…”

Superconducting state of Sr$_2$RuO$_4$ in the presence of longer-range Coulomb interactions

“…The difficulty with such a suggestion, however, is that the available pairing channels in tetragonal crystal symmetry of even parity are one-component representations with the exception of the d xz /d yz (E g ) gap, which requires a pronounced three-dimensionality of the electronic structure [9], unlikely in the case of Sr 2 RuO 4 . Nevertheless, a two-component solution is required to explain recent resonant ultrasound spectroscopy [10] and ultrasound velocity measurements [11] as well as measurements supporting time-reversal symmetry breaking (TRSB) in the ground state [12][13][14]. One way to obtain a two-component solution of dominant spin-singlet character is to combine two even-parity representations in a complex admixture, requiring an accidental degeneracy.…”

“…One way to obtain a two-component solution of dominant spin-singlet character is to combine two even-parity representations in a complex admixture, requiring an accidental degeneracy. While this possibility was initially considered inelegant compared to scenarios with 2D representations, evidence in favor has been provided recently by µSR experiments, which found that applied strain splits T c and the temperature at which TRSB occurs [14].…”