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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. 

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. 

Beginning with high- $T_c$cuprate materials, it has been observed that many superconductors exhibit so-called “Homes scaling,” in which the zero-temperature superfluid density ${\rho }_{s0}$is proportional to the product of the normal-state dc conductivity and the superconducting transition temperature ${\sigma }_{\mathrm{dc}}{T}_c$. For conventional, $s$-wave superconductors, such scaling has been shown to be a natural consequence of elastic-scattering disorder, not only in the extreme dirty limit, but across a broad range of scattering parameters. Here we show that when an analogous calculation is carried out for elastic scattering in $d$-wave superconductors, a stark contrast emerges, with ${\rho }_{s0}\propto {\left({\sigma }_{\mathrm{dc}}{T}_c\right)}^2$in the dirty limit, in apparent violation of Homes scaling. Within a simple approximate Migdal-Eliashberg treatment of inelastic scattering, we show how the observed Homes scaling is recovered. The normal-state behavior of near-optimally-doped cuprates is dominated by inelastic scattering, but significant deviations from Homes scaling occur for disorder-dominated cuprate systems, such as underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.333}$and overdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, and in very clean materials with little inelastic scattering, such as ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. We present a revised analysis where both axes of the original Homes scaling plot are normalized by the Drude plasma weight ${\omega }_{p,D}^2$and show that a new universal scaling emerges, in which the superfluid fractions of dirty $s$-wave and dirty $d$-wave superconductors coalesce to a single point at which normal-state scattering is occurring at the Planckian bound. The combined result is a new tool for classifying superconductors in terms of order parameter symmetry, as well as scattering strength and character. Although our model starts from a Fermi-liquid assumption, it describes underdoped cuprates surprisingly well. 

The superconducting state of the heavy-fermion metal ${\mathrm{UTe}}_2$has attracted considerable interest because of evidence of spin-triplet Cooper pairing and nontrivial topology. Progress on these questions requires identifying the presence or absence of nodes in the superconducting gap function and their dimension. In this article, we report a comprehensive study of the influence of disorder on the thermal transport in the superconducting state of ${\mathrm{UTe}}_2$. Through detailed measurements of the magnetic-field dependence of the thermal conductivity in the zero-temperature limit, we obtain clear evidence of the presence of point nodes in the superconducting gap for all samples with transition temperatures ranging from 1.6 to 2.1 K obtained by different synthesis methods, including a refined self-flux method. This robustness implies the presence of symmetry-imposed nodes throughout the range studied, further confirmed via disorder-dependent calculations of the thermal transport in a model with a single pair of nodes. In addition to capturing the temperature dependence of the thermal conductivity up to $T_c$, this model provides some information about the locations of the nodes, suggesting a $B_{1u}$or $B_{2u}$symmetry for the superconducting order parameter. Additionally, comparing the new, ultrahigh conductivity samples to older samples reveals a crossover between a low-field and a high-field regime at a single value of the magnetic field in all samples. In the high-field regime, the thermal conductivity at different disorder levels differs from each other by a simple offset, suggesting that some simple principle determines the physics of the mixed state, a fact which may illuminate trends observed in other clean nodal superconductors. Published by the American Physical Society2025 

Josephson scanning tunneling microscopy (JSTM) is a powerful probe of the local superconducting order parameter, but studies have been largely limited to cases where the superconducting sample and superconducting tip both have the same gap symmetry—either s-wave or d-wave. It has been generally assumed that, in an ideal s-to-d JSTM experiment, the critical current would vanish everywhere, as expected for ideal c-axis planar junctions. We show here that this is not the case. Employing first-principlesWannier functions for Bi2Sr2CaCu2O8+δ , we develop a scheme to compute the Josephson critical current (Ic) and quasiparticle tunneling current measured by JSTM with subangstrom resolution. We demonstrate that the critical current for tunneling between an s-wave tip and a superconducting cuprate sample has the largest magnitude above O sites and it vanishes above Cu sites. Ic changes sign under π/2 rotation and its average over a unit cell vanishes, as a direct consequence of the d-wave gap symmetry in cuprates. Further, we show that Ic is strongly suppressed in the close vicinity of a Zn-like impurity owing to suppression of the superconducting order parameter. More interestingly, Ic acquires nonvanishing values above the Cu sites near the impurity. The critical current modulations produced by the impurity occur at characteristic wave vectors distinct from the quasiparticle interference (QPI) analog. Furthermore, the quasiparticle tunneling spectra in the JSTM setup shows coherence peaks and impurity-induced resonances shifted by the s-wave tip gap. We discuss the similarities and differences in JSTM observables and conventional STM observables, making specific predictions that can be tested in future JSTM experiments. 

Considerable evidence shows that the heavy fermion material UTe₂is a spin-triplet superconductor, possibly manifesting time-reversal symmetry breaking, as measured by Kerr effect below the critical temperature, in some samples. Such signals can arise due to a chiral orbital state or possible nonunitary pairing. Although experiments at low temperatures appear to be consistent with point nodes in the spectral gap, the detailed form of the order parameter and even the nodal positions are not yet determined. Thermal conductivity measurements can extend to quite low temperatures, and varying the heat current direction should be able to provide information on the order parameter structure. Here, we derive a general expression for the thermal conductivity of a spin-triplet superconductor and use it to compare the low-temperature behavior of various states proposed for UTe₂. 

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.