Superconductivity: theory, models, experiment. Cross-linked with physics.supr-con.
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Hybrid superconductor/semiconductor devices play a crucial role in advancing quantum science and technology by merging the properties of superconductors and semiconductors. To operate these devices at high temperature, Niobium could substitute the widespread aluminum as superconducting element. Niobium devices show the best superconducting properties when shaped by etching, but this technique is often incompatible with semiconductors and two-dimensional materials. Our work investigates the influence of oxygen diffusion on the superconducting transition of Nb nanowires fabricated by lift-off technique. To this scope, we fabricate and measure Nb devices of different width (W) and thickness (t). By using the Berezinskii-Kosterlitz-Thouless (BKT) model for charge transport, we demonstrate that our nanowires behave as two-dimensional superconductors regardless of W and t. While the normal-state transition temperature (TN) remains constant with decreasing W, the temperature of the fully superconducting state (TS) decreases. Thus, the superconducting transition width (δTC) increases as W shrinks, due to oxygen diffusion from the lithography resist occurring during deposition. These insights provide essential knowledge for optimizing Nb-based hybrid quantum devices, paving the way for operating temperatures above 2 K and contributing to the development of next-generation quantum technologies.
Niobium is a practical material platform for superconducting microwave circuits; however, device-level performance can vary significantly depending on film growth and processing conditions. We compare three epitaxial Nb films grown on $c-$plane sapphire substrates under nominally identical conditions, except for the deposition temperature. To correlate internal quality factors, $Q_{\mathrm {i}}$, with material properties, we combine magneto-optical imaging of magnetic flux distribution with quasiparticle spectroscopy via measurements of the London penetration depth, $λ(T)$. In the low-$Q_{\mathrm i}$ film, there is a lesser ability to screen the magnetic field and an irregular temperature variation of $λ(T)$, implying the existence of localized in-gap states. High $Q_{\mathrm i}$ films show the opposite trend. We conclude that our measurements provide an efficient method for characterizing and optimizing superconducting films for quantum informatics applications.
We introduce a zero-bias superconducting voltage amplifier that harvests energy from a thermal gradient by exploiting negative differential resistance (NDR) in an asymmetric tunnel junction. The device is based on an asymmetric superconductor-insulator-superconductor (SIS) junction with an energy-gap ratio of $Δ_1/Δ_2 = 0.5$, connected in series with a load resistor. Owing to the superconducting bipolar thermoelectric effect, the current-voltage characteristic of the junction exhibits a region of NDR, in which the net current flows opposite to the applied voltage. This mechanism enables voltage amplification in the absence of any external electrical bias, relying solely on the temperature difference between the electrodes ($T_H \simeq 1$ K, $T_B \simeq 20$ mK). Numerical simulations predict a voltage gain of 20 dB, a 1 dB compression point at an input amplitude of 2 $μ$V, and a total harmonic distortion below $-50$ dB. The input-referred noise is approximately 1 nV/$\sqrt{Hz}$, with an associated thermal load on the order of nanowatts. The frequency response is broadband from near DC, with a $-3$ dB cutoff around 180 MHz, set by the RC time constant of the junction. Using Al-, Al-Cu-, and AlO$_x$-based technologies, the amplifier is compatible with conventional superconducting circuit fabrication processes. These findings demonstrate that thermoelectric superconducting junctions can deliver bias-free voltage amplification from near DC up to about 200 MHz, making them promising candidates for transition-edge sensor readout, quantum circuit instrumentation, and low-frequency cryogenic signal processing.
We report reproducible magnetization anomalies appearing below room temperature in copper-doped apatite materials belonging to the LK-99 family synthesized via hydrothermal methods. These anomalies are observed consistently across samples prepared under comparable conditions. Although the extracted Mydosh parameter lies within the range often associated with vortex-glass behavior in superconductors, a detailed analysis of DC magnetization, AC susceptibility, field dependence, and magnetic memory effects demonstrates that the observed phenomena are not related to superconductivity. Instead, the data are consistent with glassy magnetic freezing of interacting clusters. Compositional and structural analysis identifies covellite (CuS), an ubiquitous secondary phase in these intrinsically multiphase materials, as the primary origin of the observed behavior. Our results clarify the magnetic origin of LK-99-related anomalies and highlight the importance of phase complexity in interpreting apparent superconducting signatures in this materials family.
Superconductivity and nematicity coexist in the phase diagram of many correlated systems, including iron-based superconductors. We investigate how Hund-driven correlations reshape boson-mediated superconductivity in a multiorbital nematic metal. We find that dynamical correlation effects beyond a quasiparticle-only description are essential to capture the robustness of superconductivity in the Hund regime. In the nematic phase, Hund correlations simultaneously enhance the orbital differentiation of the superconducting gaps and inhibit the most extreme nematic-driven orbital polarization and coherence collapse that would otherwise suppress pairing at strong coupling. A controlled cutoff analysis reveals a nontrivial, orbital-dependent buildup of the gaps, indicating that different frequency windows of the correlated spectrum contribute unevenly to pairing in the nematic Hund regime. This implies that pairing mechanisms with different characteristic boson energies can lead to distinct gap structures and trends.
We propose an explanation of the observed dependence of the maximal critical temperature $T_{c,max}$ on the number of conducting layers $n$ in layered copper-oxide superconductors within the preformed pair mechanism. Copper-oxygen planes fine-tune the lattice anisotropy and regulate the balance between the attractive and kinetic energies of carrier holes. To maximize the Bose-Einstein condensation temperature, real-space pairs must be compact and light at the same time. Generally, $T_{c,max}$ increases between $n = 1$ and $n = 3$ because pairs become lighter. For $n > 3$, the rising kinetic energy weakens the pairs, leading to inflated pair volumes and reduced $T_{c,max}$. By varying model parameters, the peak of $T_{c,max}(n)$ can be tuned to $n = 2$, $n = 3$, or $n > 3$. We also discuss strategies for using this knowledge to boost $T_{c,max}$ beyond the current record of 138 K.
We study a four-fold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of X$_9$ type at the Fermi energy. First, we analyze in detail its form, type and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature T$_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate Sr$_3$Ru$_2$O$_7$ which has been shown to exhibit this type of singularity.
Control of oxygen vacancies by electrical currents in complex oxides such as YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) has attracted considerable interest due to the relative simplicity of its implementation and its potential for both fundamental studies and the tuning of superconducting device properties. However, the structural evolution and depth-dependent effects associated with current-based techniques remain largely unexplored, particularly with respect to the connection between optical signatures and the spatial distribution of oxygen vacancies. Here, we combine nanoprobe X-ray Diffraction (NanoXRD), Cu K-edge X-ray Absorption Near-Edge Structure (XANES), X-ray Photoelectron Spectroscopy (XPS), electrical transport, and optical measurements to reveal modifications induced in YBCO microbridges by pulsed electromigration. We observe a c-axis expansion correlated with spectroscopic features of oxygen depletion in the Cu-O chains, and we confirm that oxygen redistribution, crystallographic changes, and copper coordination evolve consistently across techniques. Notably, the spatial profile of unit-cell expansion closely follows the optical contrast observed after electromigration, demonstrating that the different signatures capture the same underlying oxygen reordering. We further show that optical microscopy cannot reliably capture bipolar electromigration involving strong resistance modifications, as surface deoxygenation appears largely irreversible. Taken together, our findings provide a significant step toward a microscopic understanding of current-assisted oxygen migration in YBCO and establish a framework for effectively exploiting vacancy control in high-temperature superconducting devices.
The thermodynamic critical field $B_{\rm c}$ provides direct access to the superconducting condensation energy, yet its pressure dependence has been studied much less extensively than that of the transition temperature. Here, muon-spin-rotation/relaxation measurements of the thermodynamic critical field $B_{\rm c}$ of elemental Pb under hydrostatic pressure up to $\simeq2.3$ GPa are reported. From the magnetic-field distribution in the intermediate state, $B_{\rm c}(T)$ is determined and $B_{\rm c}(0)$ is extracted at different pressures. In combination with previously reported high-pressure data for $B_{\rm c}$ and $T_{\rm c}$, it is shown that the pressure dependence of $B_{\rm c}(0)$ follows that of the superconducting gap $Δ(0)$ more closely than that of the transition temperature $T_{\rm c}$. At higher pressures, the logarithmic pressure derivatives of $B_{\rm c}(0)$ and $T_{\rm c}$ are found to converge, indicating that the coupling strengths ratio $α=Δ(0)/k_{\rm B}T_{\rm c}$ becomes nearly pressure independent. This behavior is interpreted as thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb.
We report muon-spin rotation measurements of the pressure dependence of the oxygen-isotope ($^{16}$O/$^{18}$O) effect on the spin-density wave (SDW) transition in the trilayer Ruddlesden-Popper nickelate Pr$_4$Ni$_3$O$_{10}$. At ambient pressure, the SDW transition shows a finite isotope shift, with $^{16}T_{\rm SDW}=158.04(5)$ K and $^{18}T_{\rm SDW}=159.81(6)$ K. Under hydrostatic pressure, $T_{\rm SDW}$ decreases linearly at nearly identical rates for the two isotope compositions, ${\rm d}\,^{16}T_{\rm SDW}/{\rm d}p=-4.93(5)$ K/GPa and ${\rm d}\,^{18}T_{\rm SDW}/{\rm d}p=-4.90(7)$ K/GPa, such that the isotope shift remains essentially unchanged under compression. The absence of pressure enhancement of the isotope effect points to a predominantly electronic origin of the SDW transition and is consistent with recent inelastic x-ray scattering results, suggesting a new regime of intertwined order in trilayer RP nickelates, which is stabilized by strong spin interactions.
We report the realization of multilayer three-dimensional nanobridge Josephson junctions based on Nb/NbN and Nb/TiN superconducting stacks fabricated using electron-beam lithography and chlorine-based dry etching. In this architecture, a high-resistivity nitride layer defines the geometrical weak link, while the top Nb layer sets the overall critical temperature and film quality of the stack. This multilayer design enables engineering of the superconducting gap and proximity effects without relying on focused ion beam milling or oxide tunnel barriers. The devices are successfully integrated into dc SQUIDs, demonstrating reliable circuit-level operation. By combining material selectivity with three-dimensional geometry, this platform provides a scalable route toward oxide-free Josephson junctions suitable for superconducting electronics.
Quantum noise has long served as a powerful probe of quantum transport in mesoscopic junctions. Recently, temperature-driven noise, or $Δ_T$ noise, has attracted growing interest due to its presence even in the absence of average charge current. In this work, we investigate a normal metal-insulator-iron-pnictide junction and demonstrate how thermovoltage, Seebeck coefficient, zero temperature quantum shot noise, finite temperature quantum noise, and $Δ_T$ noise can discriminate between $S_{++}$ and $S_{+-}$ pairing symmetries, which are relevant to iron-based superconductors. We introduce $Δ_T$ noise as a novel probe for distinguishing between the two pairing symmetries. In contrast to conductance, which exhibits a single peak for both $S_{++}$ and $S_{+-}$ states with only a difference in magnitude, the $Δ_T$ noise reveals qualitatively distinct features: a twin-peak structure for the $S_{++}$ pairing symmetry and a single-peak profile for the $S_{+-}$ state. A similar symmetry-dependent contrast is observed in both zero temperature quantum shot noise and finite temperature quantum noise, where the $S_{++}$ state consistently exhibits a twin-peak structure, while the $S_{+-}$ state shows a single-peak response. Furthermore, both the thermovoltage and the Seebeck coefficient display sign reversals for the two pairing symmetries, with opposite trends in the $S_{++}$ and $S_{+-}$ cases. Our results demonstrate that noise-based measurements, together with Seebeck coefficient and thermovoltage, form a mutually reinforcing set of probes that enables reliable identification of superconducting gap symmetry in Iron Pnictide superconductors.
Motivated by the interplay between 2D and 3D scaling signatures observed in unconventional layered superconductors, we present a systematic Monte Carlo study of the three-dimensional classical XY model with anisotropic in-plane $J_\parallel$ and inter-plane $J_\perp$ couplings. Our study includes very small values of the system anisotropy $Δ=J_\perp /J_\parallel$ not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with $Δ$, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length $\ell_J$, which diverges at small $Δ$ with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.
In this work, microwave measurements carried out in dielectric-loaded resonators exposed to high magnetic fields are exploited to yield the surface impedance of Nb$_3$Sn superconducting coatings deposited via two different techniques: vapor tin diffusion, and DC magnetron sputtering. The obtained data lead to qualitative interpretations on both the Nb$_3$Sn superconducting properties, and vortex-dynamics and pinning, of each coating separately, as well as simple distinctive features when comparing those. When examining the respective surface impedances at varying field, it is expected that the studied films perform at substantially diverse magnitudes of flux-flow resistivity, but also in well-differentiated pinning regimes, yet the obtained surface resistances of both samples are comparable, thus demonstrating that there is room for film optimization at the expense of certain compromise between the parameters involved.
Experimentally relevant signatures of superconductivity require access to real-frequency quantities, such as the spectral functions, optical response, and transport properties, yet Migdal-Eliashberg calculations are commonly performed on the imaginary axis and then analytically continued, a step that is numerically delicate and can obscure physically relevant spectral features. Here we present a practical route to solving the finite-temperature Migdal-Eliashberg equations directly on the real-frequency axis, while retaining the effects from the full-bandwidth electronic structure. Our formulation accounts for particle-hole asymmetry through an energy-dependent electronic density of states, avoiding the constant density of states approximation often used in real-axis calculations, and includes a static screened Coulomb contribution. We introduce an efficient numerical technique to solve the Migdal-Eliashberg integrals whose computational cost scales linearly with the real-frequency grid, making high-resolution, full-bandwidth real-axis calculations feasible and providing direct access to the interacting Green's function and derived observables without analytic continuation. As an illustration, we apply the method to H$_{3}$S, where a van-Hove singularity near the Fermi level produces strong particle-hole asymmetry. The full-bandwidth solution yields noticeably different spectra than the constant density of states approximation and brings the superconducting gap and lineshapes into closer agreement with experiment, highlighting when band-structure details are essential. Furthermore, the methods presented here open the door to time-dependent, nonequilibrium simulations within Eliashberg theory.
We develop a microscopic theory of the inverse Faraday effect in d-wave superconductors. An extended version of the Keldysh-Nambu quasiclassical formalism is used to compute the dc-component of the current density induced by an external monochromatic radiation. Our work explicitly demonstrates how branch population imbalance produces nonvanishing nonlinear and nonlocal dc-response. We evaluate the magnitude of the induced current and obtain estimates for the induced static magnetization. Experimental implications of our theory and future extensions of our work are briefly discussed.
The candidate topological superconductor UTe$_2$ exhibits a complex phase diagram with multiple superconducting states, yet the nature of their coexistence has remained a central mystery. In particular, the apparent intersection of two second-order phase boundaries at a ``triple point'' in the pressure-temperature phase diagram is thermodynamically forbidden, suggesting hidden phase transitions or a fundamental misunderstanding of the superconductivity in UTe$_2$. Here, we use pulse-echo ultrasound to resolve this puzzle by discovering a new phase boundary that is characterized by a unique ``upward jump" in the sound velocity -- direct thermodynamic evidence for a re-entrant phase transition. Our results establish $\left(P^{\star},T^{\star}\right)$ as a tetracrtical point, beyond which the ambient and pressure-induced superconducting order parameters form a multi-component state. We use the measured phase diagram to construct a Ginzburg-Landau theory that shows that strong competition between the two superconducting order parameters drives the re-entrance and leads to phase locking that suppress superconducting fluctuations. These findings provide the definitive magnetic field-temperature-pressure phase diagram and establish a thermodynamic foundation for multi-component -- and potentially topological -- superconductivity in UTe$_2$.
The Remeika series superconductor, $(\text{Ca}_x\text{Sr}_{1-x})_3\text{Rh}_4\text{Sn}_{13}$, shows a rare nonmagnetic quantum critical point (QCP) associated with the continuous charge-density wave (CDW) and structural transition under the ``dome'' of superconductivity achieved by tuning composition and applying pressure. Here we use a nonmagnetic point-like disorder induced by 2.5 MeV electron irradiation to suppress the CDW and drive the system to and even beyond the QCP. This conclusion is based on a clear evolution of temperature-dependent resistivity, $ρ\left(T\right)$, from the Fermi liquid to the non-Fermi liquid regime with increasing amount of disorder. Starting on the CDW side, below the suggested QCP concentration of $x_c=0.9$, added disorder resulted in a progressively larger linear term and a reduced quadratic term in $ρ\left(T\right)$. Nearly perfect $T-$linear dependence is observed at the dose at which long-range CDW order is suppressed to $T=$0, consistent with the expectations. We refine the QCP location in this system and place it in the interval between $x=$0.75 and 0.85. Our results strongly support the concept that the disorder can tune the system to the quantum critical regime and even beyond. It follows from the argument by Imry and Ma that any ordered phase is unstable toward quenched disorder. Introduced in a controlled way, this disorder becomes a novel non-thermal tuning parameter likely applicable to a variety of different systems.
In 2023, superconductivity in La$_3$Ni$_2$O$_7$ was discovered under high pressures above approximately 14 GPa. In addition to its high transition temperature ($T_{\mathrm{c}} \simeq 80$ K), the structural resemblance to high-$T_{\mathrm{c}}$ cuprates has strongly stimulated research, soon followed by the discovery of superconductivity in La$_4$Ni$_3$O$_{10}$. These compounds belong to the Ruddlesden--Popper phases, comprising double- and triple-layered NiO$_2$ square lattices separated by LaO rock-salt slabs. Research on these systems has rapidly developed along three major directions, as in other prominent families of superconductors such as the cuprates and iron arsenides: expanding the chemical variety of compounds, enhancing $T_{\mathrm{c}}$ through elemental substitution, and elucidating the superconducting mechanism. These challenges, being closely interconnected, continue to drive the field. The clarification of the pairing mechanism encounters a particular difficulty, since the key experiments must be performed under high pressures. This situation highlights the significance of developing nickel oxides that exhibit superconductivity at much lower pressures, ideally at ambient pressure, which would in turn broaden the scope of chemical tuning and detailed physical characterization. In this context, it is timely and meaningful to summarize the present state of knowledge. Here, we emphasize sample synthesis and characterization, which are already well established and often decisive for progress in unconventional superconductors, while providing a brief overview of the currently available electronic properties.
We report a systematic magnetotransport study on high-crystallinity La$_{1-x}$Sr$_{x}$NiO$_2$ (LSNO) thin films with $x=0.20-0.24$. By conducting pulsed-field transport experiment up to 62 T, we reveal two salient features of the normal-state transport in overdoped LSNO thin films: (1) the magnetoresistance does not follow the Kohler's rule but exhibits a $H$-linear behavior in the high $H/T$ limit and (2) the normal-state $ρ(T)$ below 30 K consistently follows a $T^2$ behavior across the overdoped regime. Our results demonstrate a coexistence of $H$-linear magnetoresistance and $T^2$ resistivity in a model unconventional superconductor and provide new information on the transport characteristics of the normal ground state that host superconductivity in infinite-layer nickelates.