High Resolution Polar Kerr Effect Measurements ofSr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State

Abstract

Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3 He-A.PACS numbers: 74.25. Gz,74.70.Pq,74.25.Ha,78.20.Ls Soon after the discovery of the layered-perovskite superconductor Sr 2 RuO 4 [1], it was predicted to be an oddparity superconductor [2,3]. Subsequently, a large body of experimental results in support of odd-parity superconductivity has been obtained [4], with the most recent one being a phase-sensitive measurement [5]. The symmetry of the superconducting state is related simply to the relative orbital angular momentum of the electrons in each Cooper pair. Odd parity corresponds to odd orbital angular momentum and symmetric spin-triplet pairing. While a priori the angular momentum state can be p (i.e. L = 1), f ( i.e. L = 3), or even higher order [6,7], theoretical analyses of superconductivity in Sr 2 RuO 4 favor the p-wave order parameter symmetry [2,8]. There are many allowed p-wave states that satisfy the cylindrical Fermi surface for a tetragonal crystal which is the case of Sr 2 RuO 4 (see e.g. table IV in [4]). Some of these states break time-reversal symmetry (TRS), since the condensate has an overall magnetic moment because of either the spin or orbital (or both) parts of the pair wave function. While an ideal sample will not exhibit a net magnetic moment, surfaces and defects at which the Meissner screening of the TRS-breaking moment is not perfect can result in a small magnetic signal [7]. Indeed, muon spin relaxation (µSR) measurements on good quality single crystals of Sr 2 RuO 4 showed excess relaxation that spontaneously appear at the superconducting transition temperature. The exponential nature of the increased relaxation suggested that its source is a broad distribution of internal fields, of strength ∼ 0.5 Oe, from a dilute array of sources [9,10]. While TRS breaking is not the only explanation for the µSR observations, it was accepted as the most likely one [4]. However, since the existence of TRS breaking has considerable implications for understanding the superconductivity of Sr 2 RuO 4 , establishing the existence of this effect, and in particular in the bulk without relying on imperfections and defects is of utmost importance. The challenge is therefore to couple to the TRS-breaking part of the order parameter to demonstrate the effect unambiguously.In this paper we show results of polar Kerr effect (PKE) measurements on high quality single crystals of Sr 2 RuO 4 . In these measurements we are searching for an effect analogous to the magneto-optic Kerr effect (MOKE) which would cause a rotation of the direction of polarization of the reflected linearly polarized light normally incident to the superconducting planes. PKE is sensitive to TRS breaking since it measures the existenc...

Collective modes and electromagnetic response of a chiral superconductor

“…One experiment which directly probes the anomalous ac Hall conductivity considered here is the polar Kerr effect [1]. In this experiment, linearly polarized light beam which is normally incident on the superconducting planes is reflected back as elliptically polarized light.…”

“…We also uncover some unusual features of the collective modes of a chiral superconductor, namely, that they are not purely longitudinal and couple to external transverse fields. The experiment by Xia et al found a Kerr angle of approximately 60 nanoradians at a frequency, ω ≃ 0.8 eV, which is small compared to the Kerr angle observed in typical ferromagnets, but can be understood qualitatively if one notes that the superconducting gap (or order parameter) for Sr 2 RuO 4 is substantially reduced from that of a typical ferromagnet [1]. The Kerr angle at high frequencies is related to the ac Hall conductivity.…”

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Motivated by the recent controversy surrounding the Kerr effect measurements in strontium ruthenate [1], we examine the electromagnetic response of a clean chiral p-wave superconductor. When the contributions of the collective modes are accounted for, the Hall response in a clean chiral superconductor is smaller by several orders of magnitude than previous theoretical predictions and is too small to explain the experiment.

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Unconventional quantum oscillations in mesoscopic rings of spin-triplet superconductor Sr2RuO4

“…Sr 2 RuO 4 , the only superconducting layered perovskite without Cu, features an odd-parity, spin-triplet, likely chiral p-wave pairing state [1][2][3][4][5]. In addition to an exotic pairing symmetry, unconventional flux states have also been observed in this superconductor.…”

Enhanced spin-triplet superconductivity near dislocations in Sr2RuO4

“…Assuming that superconductivity in this material is two-dimensional in nature, the fourfold tetragonal crystalline symmetry dictates that the pairing symmetry must be one of the five representations 7 . Among those, only the two-component, p x ±ip y state is consistent with the muon spin rotation 8 and Kerr rotation 9 measurements that suggest the presence of a spontaneous magnetic field in the superconducting state of Sr 2 RuO 4 , making it an electronic analogue 7 of the superfluid 3 He A-phase, and a chiral p-wave superconductor for which a Majorana zero-energy mode bound to the normal core of a half-flux quantum vortex has been predicted 1,2 . An important question of interest is what is the microscopic mechanism responsible for such a highly exotic superconducting state.…”