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Register a new userTime-reversal symmetry-breaking charge order in a correlated kagome superconductor
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The kagome lattice, which is composed of a network of corner-sharing triangles, is a structural motif in quantum physics first recognized more than seventy years ago. It has been gradually realized that materials which host such special lattice structures can exhibit quantum diversity, ranging from spin-liquid phases, topological matter to intertwined orders. Recently, charge sensitive probes have suggested that the kagome superconductors AV_3Sb_5 (A = K, Rb, Cs) exhibit unconventional chiral charge order, which is analogous to the long-sought-after quantum order in the Haldane model or Varma model. However, direct evidence for the time-reversal symmetry-breaking of the charge order remains elusive. Here we utilize state-of-the-art muon spin relaxation to probe the kagome charge order and superconductivity in KV_3Sb_5. We observe a striking enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Remarkably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV_3Sb_5 and that the T_c/lambda_{ab}^{-2} ratio is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.
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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.
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 symmetry via chiral ordering of spins along a particular direction, but is spin-rotation symmetric. In this work, we prove the existence of this state via state-of-the-art density matrix renormalization group (DMRG) analysis on a spin-1 chain with nearest-neighbor bilinear-biquadratic interactions and additional third-neighbor ferromagnetic Heisenberg exchange. Despite the large entanglement introduced by the third-neighbor coupling, we are able to access system sizes up to $L=918$ sites. We find first order phase transitions from the DSSCO into the famous Haldane phase as well as a spin-quadrupolar phase where spin nematic correlations dominate. In the Haldane phase, we propose and demonstrate a method for detecting the topological edge states using DMRG that could be useful for other topological phases too.
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 observations 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.
The single helical Fermi surface on the surface state of three-dimensional topological insulator Bi2Se3 is constrained by the time-reversal invariant bulk topology to possess a spin-singlet superconducting pairing symmetry. In fact, the Cu-doped, and pressure-tuned superconducting Bi2Se3 show no evidence of the time reversal symmetry breaking. We report on the detection of the time reversal symmetry (TRS) breaking in the topological superconductor Sr0.1Bi2Se3 , probed by zero-field (ZF) {mu}SR measurements. The TRS breaking provides strong evidence for the existence of spin-triplet pairing state. The temperature dependent super-fluid density deduced from transverse-field (TF) {mu}SR measurement yields nodeless superconductivity with low superconducting carrier density and penetration depth {lambda} = 1622(134) nm. From the microscopic theory of unconventional pairing, we find that such a fully gapped spin triplet pairing channel is promoted by the complex interplay between the structural hexagonal warping and higher order Dresselhaus spin-orbit coupling terms. Based on Ginzburg-Landau analysis, we delineate the mixing of singlet to triplet pairing symmetry as the chemical potential is tuned far above from the Dirac cone. Our observation of such spontaneous TRS breaking chiral superconductivity on a helical surface state, protected by the TRS invariant bulk topology, can open new avenues for interesting research and applications.
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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