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تسجيل مستخدم جديدSpontaneous breaking of time-reversal symmetry in topological superconductors
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Igor N. Karnaukhov
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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.
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States of matter that break time-reversal symmetry are invariably associated with magnetism or circulating currents. Recently, one of us proposed a phase, the directional scalar spin chiral order (DSSCO), as an exception: it breaks time-reversal symm
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to-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.
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 supe
rconductors 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 .
We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in the absence of external magnetic fields or Zeeman fields. Spin-singlet ($Delta_s$
) and spin-triplet ($Delta_t$) pairings can coexist in superconductors whose crystal structure lacks inversion symmetry. The TRS can be spontaneously broken once a relative phase of $pmpi/2$ is developed, forming a TRS-breaking unitary pairing state ($Delta_spm iDelta_t$). We demonstrate that such unitary pairing could give rise to spontaneous spin-polarization with the help of spin-orbit coupling. Our result provides an alternative explanation to the TRS breaking, beyond the current understanding of such phenomena in the noncentrosymmetric superconductors. The experimental results of Zr$_3$Ir and CaPtAs are also discussed in the view of our theory.
In a recent comment [1], Armitage and Hu have suggested that our experiment observing dichroism in angle resolved photoemission (ARPES) [2] could not be conclusively interpreted as arising from time reversal symmetry breaking, arguing that our observ
ations are likely due to structural effects. The concerns expressed by Armitage and Hu that our results could be due to a change in the mirror plane are as important as they are obvious. In fact the first part of their comment merely restates the results of Simon and Varma [3] about the relationship and contrast of effects due to time reversal symmetry breaking and those caused by crystallographic changes. In any test of time reversal symmetry one must ensure that parity alone is not inducing the observed changes. We have indeed considered this issue very carefully in the course of our study [2] and it is precisely the lack of temperature dependent structural changes significant enough to explain the magnitude of the observed dichroism that forced us to conclude that time reversal symmetry breaking is the only plausible explanation. Furthermore, recent experiments by Borisenko, et al. [4] confirm that changes in the mirror plane are unmeasurably small.
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