The polar Kerr effect in the high-T c superconductor YBa 2 Cu 3 O 6x was measured at zero magnetic field with high precision using a cyogenic Sagnac fiber interferometer. We observed nonzero Kerr rotations of order 1 rad appearing near the pseudogap temperature T and marking what appears to be a true phase transition. Anomalous magnetic behavior in magnetic-field training of the effect suggests that time reversal symmetry is already broken above room temperature. , large compared to the superconducting (SC) transition temperature, T c . Two major classes of theories have been introduced in an attempt to describe the pseudogap state: One in which the pseudogap temperature T represents a crossover into a state with preformed pairs with a d wave gap symmetry [6,7], and another in which T marks a true transition into a phase with broken symmetry that ends at a quantum critical point, typically inside the superconducting dome. While at low doping this phase may compete with superconductvity, it might provide fluctuations that are responsible for the enhanced transition temperature near its quantum critical point (e.g., as in Ref. [8] In this Letter, we report high resolution optical Kerreffect measurements on YBa 2 Cu 3 O 6x crystals with various hole concentrations p. (p is, in turn, a monotonic function of the oxygen concentration x, and it also depends on oxygen ordering in the chains [12].) We identify a sharp phase transition at a temperature T s p, below which there is a nonzero Kerr angle, indicating the existence of a phase with broken time reversal symmetry (TRS). Both the magnitude and hole concentration dependence of T s are in close correspondence with those of the pseudogap crossover temperature, T , which has been identified in other physical quantities. In particular, as shown in Fig. 1, T s is substantially larger than the superconducting T c in underdoped materials, but drops rapidly with increasing hole concentration, so that it is smaller than T c in a near optimally doped crystal and extrapolates to zero at a putative quantum critical point under the superconducting dome. The magnitude of the Kerr rotation in YBa 2 Cu 3 O 6x (YBCO) is smaller by 4 orders of magnitude than that observed in other itinerant ferromagnetic oxides [13,14], and the temperature dependence is ''superlinear'' near T c , FIG. 1 (color online). The onset of the Kerr-effect signal, T s (circles), and T c (red squares) for the YBa 2 Cu 3 O 6x samples reported in this Letter. Also shown are T c p (from [12]) and T N p (from [22]).

Models of superconductivity in unconventional materials can be experimentally differentiated by the predictions they make for the symmetries of the superconducting order parameter. In the case of the heavy-fermion superconductor UPt3, a key question is whether its multiple superconducting phases preserve or break time-reversal symmetry (TRS). We tested for asymmetry in the phase shift between left and right circularly polarized light reflected from a single crystal of UPt3 at normal incidence and found that this so-called polar Kerr effect appears only below the lower of the two zero-field superconducting transition temperatures. Our results provide evidence for broken TRS in the low-temperature superconducting phase of UPt3, implying a complex two-component order parameter for superconductivity in this system.

The search for broken time reversal symmetry (TRSB) in unconventional superconductors intensified in the past year as more systems have been predicted to possess such a state. Following our pioneering study of TRSB states in Sr2RuO4 using magneto-optic probes, we embarked on a systematic study of several other of these candidate systems. The primary instrument for our studies is the Sagnac magneto-optic interferometer, which we recently developed. This instrument can measure magneto-optic Faraday or Kerr effects with an unprecedented sensitivity of 10 nanoradians at temperatures as low as 100 mK. In this paper we review our recent studies of TRSB in several systems, emphasizing the study of the pseudogap state of high temperature superconductors and the inverse proximity effect in superconductor/ferromagnet proximity structures.

Recent experimental and theoretical interest in the superconducting phase of the heavy fermion material URu2Si2 has led to a number of proposals in which the superconducting order parameter breaks time-reversal symmetry (TRS). In this study we measured polar Kerr effect (PKE) as a function of temperature for several high-quality single crystals of URu2Si2. We find an onset of PKE below the superconducting transition that is consistent with a TRS-breaking order parameter. This effect appears to be independent of an additional, possibly extrinsic, PKE generated above the hidden order transition at THO = 17.5 K, and contains structure below Tc suggestive of additional physics within the superconducting state.