Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect.

Recent theoretical work predicted the emergence of a chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-T_{c} cuprate monolayers such as Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Here, we identify a large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the T-broken phase. Our modeling predicts the Kerr angle θ_{K} to be in the range of 10-100 µrad, which is a factor of 10^{3} to 10^{4} times larger than what is expected for the leading chiral superconductor candidate Sr_{2}RuO_{4}. In addition, we show that the optical Hall conductivity σ_{H}(ω) can be used to distinguish between the topological d_{x^{2}-y^{2}}±id_{xy} phase and the d_{x^{2}-y^{2}}±is phase, which is also expected to be present in the phase diagram but is topologically trivial.

Chiral superconductors.

Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from µSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.

Chiral p-wave order in Sr2RuO4.

Shortly after the discovery in 1994 of superconductivity in Sr(2)RuO(4), it was proposed on theoretical grounds that the superconducting state may have chiral p-wave symmetry analogous to the A phase of superfluid (3)He. Substantial experimental evidence has since accumulated in favor of this pairing symmetry, including several interesting recent results related to broken time-reversal symmetry (BTRS) and vortices with half of the usual superconducting flux quantum. Great interest surrounds the possibility of chiral p-wave order in Sr(2)RuO(4), since this state may exhibit topological order analogous to that of a quantum Hall state, and can support such exotic physics as Majorana fermions and non-Abelian winding statistics, which have been proposed as one route to a quantum computer. However, serious discrepancies remain in trying to connect the experimental results to theoretical predictions for chiral p-wave order. In this paper, I review a broad range of experiments on Sr(2)RuO(4) that are sensitive to p-wave pairing, triplet superconductivity and time-reversal symmetry breaking and compare these experiments to each other and to theoretical predictions. In this context, the evidence for triplet pairing is strong, although some puzzles remain. The 'smoking gun' experimental results for chiral p-wave order, those which directly look for evidence of BTRS in the superconducting state of Sr(2)RuO(4), are most perplexing when the results are compared with each other and to theoretical predictions. Consequently, the case for chiral p-wave superconductivity in Sr(2)RuO(4) remains unresolved, suggesting the need to consider either significant modifications to the standard chiral p-wave models or possible alternative pairing symmetries. Recent ideas along these lines are discussed.

Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field.

We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.

Imaginary-chemical-potential quantum Monte Carlo method for Hubbard molecules.

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method to the C60 Hubbard molecule are discussed.