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Several recent experiments have challenged the premise that cuprate high-temperature superconductors approach conventional Landau-BCS behavior in the high-doping limit. We argue, based on an analysis of their superconducting spectra, that anomalous properties seen in the most-studied overdoped cuprates require a pairing interaction that is strongly inhomogeneous on nm length scales. This is consistent with recent proposals that the “strange-metal” phase above $T_c$in the same doping range arises from a spatially random interaction. We show, via mean-field Bogoliubov-de Gennes (BdG) calculations and time-dependent Ginzburg-Landau (TDGL) simulations, that key features of the observed tunneling spectra are reproduced when both inhomogeneity and thermal phase fluctuations are accounted for. In accord with experiments, BdG calculations find that low- $T$spectra are highly inhomogeneous and exhibit a low-energy spectral shoulder and broad coherence peaks. However, the spectral gap in this approach becomes homogeneous at high $T$, in contrast to experiments. This is resolved when thermal fluctuations are included within TDGL; in this case, global phase coherence is lost at the superconducting $T_c$via a broadened BKT transition, while robust phase-coherent superconducting islands persist well above $T_c$. The local spectrum remains inhomogeneous at $T_c$, and the gap is found to fill instead of close with increasing temperature. 

Abstract Scanning tunneling spectroscopy (STS) and scanning tunneling microscopy (STM) are perhaps the most promising ways to detect the superconducting gap size and structure in the canonical unconventional superconductor Sr₂RuO₄directly. However, in many cases, researchers have reported being unable to detect the gap at all in STM conductance measurements. Recently, an investigation of this issue on various local topographic structures on a Sr-terminated surface found that superconducting spectra appeared only in the region of small nanoscale canyons, corresponding to the removal of one RuO surface layer. Here, we analyze the electronic structure of various possible surface structures using first principles methods, and argue that bulk conditions favorable for superconductivity can be achieved when removal of the RuO layer suppresses the RuO₄octahedral rotation locally. We further propose alternative terminations to the most frequently reported Sr termination where superconductivity surfaces should be observed. 

A growing number of superconducting materials display evidence for spontaneous time-reversal symmetry breaking (TRSB) below their critical transition temperatures. Precisely what this implies for the nature of the superconducting ground state of such materials, however, is often not straightforward to infer. We review the experimental status and survey different theoretical mechanisms for the generation of TRSB in superconductors. In cases where a TRSB complex combination of two superconducting order parameter components is realized, defects, dislocations and sample edges may generate superflow patterns that can be picked up by magnetic probes. However, even single-component condensates that do not break time-reversal symmetry in their pure bulk phases can also support signatures of magnetism inside the superconducting state. This includes, for example, the generation of localized orbital current patterns or spin-polarization near atomic-scale impurities, twin boundaries and other defects. Signals of TRSB may also arise from a superconductivity-enhanced Ruderman-Kittel-Kasuya-Yosida exchange coupling between magnetic impurity moments present in the normal state. We discuss the relevance of these different mechanisms for TRSB in light of recent experiments on superconducting materials of current interest. 

Abstract Visualizing atomic-orbital degrees of freedom is a frontier challenge in scanned microscopy. Some types of orbital order are virtually imperceptible to normal scattering techniques because they do not reduce the overall crystal lattice symmetry. A good example is d xz / d yz (π,π) orbital order in tetragonal lattices. For enhanced detectability, here we consider the quasiparticle scattering interference (QPI) signature of such (π,π) orbital order in both normal and superconducting phases. The theory reveals that sublattice-specific QPI signatures generated by the orbital order should emerge strongly in the superconducting phase. Sublattice-resolved QPI visualization in superconducting CeCoIn 5 then reveals two orthogonal QPI patterns at lattice-substitutional impurity atoms. We analyze the energy dependence of these two orthogonal QPI patterns and find the intensity peaked near E  = 0, as predicted when such (π,π) orbital order is intertwined with d -wave superconductivity. Sublattice-resolved superconductive QPI techniques thus represent a new approach for study of hidden orbital order.