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Register a new userTime-reversal symmetry breaking by a $(d+id)$ density-wave state in underdoped cuprate superconductors
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It was proposed that the $id_{x^2-y^2}$ density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small $d_{xy}$ component to the DDW state breaks the symmetry between the counter-propagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a non-zero polar Kerr effect, which has recently been observed in the pseudogap phase.
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We show that the breakdown of time-reversal invariance, confirmed by the recent polar Kerr effect measurements in the cuprates, implies the existence of an anomalous Nernst effect in the pseudogap phase of underdoped cuprate superconductors. Modeling the time-reversal-breaking ordered state by the chiral d-density-wave state, we find that the magnitude of the Nernst effect can be sizable even at temperatures much higher than the superconducting transition temperature. These results imply that the experimentally found Nernst effect at the pseudogap temperatures may be due to the chiral d-density wave ordered state with broken time-reversal invariance.
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in the topological superconducting state is result of spontaneous breaking of time-reversal symmetry in the superconducting state. The peculiarities in the chiral gapless edge modes behavior are studied, the Chern numbers are calculated.
When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to understand if T* is just a crossover, controlled by fluctuations in order which will set in at the lower Tc (Refs. 3, 4), or whether some symmetry is spontaneously broken at T* (Refs. 5-10). Here, using angle-resolved photoemission with circularly polarized light, we find that, in the pseudogap state, left-circularly polarized photons give a different photocurrent than right-circularly polarized photons, and therefore the state below T* is rather unusual, in that it breaks time reversal symmetry11. This observation of a phase transition at T* provides the answer to a major mystery of the phase diagram of the cuprates. The appearance of the anomalies below T* must be related to the order parameter that sets in at this characteristic temperature .
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.
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 Sr$_2$RuO$_4$ 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.
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