Inhomogeneous Superconductors Research Articles

Probing inhomogeneous cuprate superconductivity by terahertz Josephson echo spectroscopy

AbstractInhomogeneities crucially influence the properties of quantum materials, yet methods that can measure them remain limited and can access only a fraction of relevant observables. For example, local probes such as scanning tunnelling microscopy have documented that the electronic properties of cuprate superconductors are inhomogeneous over nanometre length scales. However, complementary techniques that can resolve higher-order correlations are needed to elucidate the nature of these inhomogeneities. Furthermore, local tunnelling probes are often effective only far below the critical temperature. Here we develop a two-dimensional terahertz spectroscopy method to measure Josephson plasmon echoes from an interlayer superconducting tunnelling resonance in a near-optimally doped cuprate. The technique allows us to study the multidimensional optical response of the interlayer Josephson coupling in the material and disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening for interlayer superconducting tunnelling. We find that inhomogeneous broadening persists up to a substantial fraction of the critical temperature, above which this is overcome by the thermally increased lifetime broadening.

Majorana modes in striped two-dimensional inhomogeneous topological superconductors

Majorana zero modes have gained significant interest due to their potential applications in topological quantum computing and in the realization of exotic quantum phases. These zero-energy quasiparticle excitations localize at the vortex cores of two-dimensional topological superconductors or at the ends of one-dimensional topological superconductors. Here we describe an alternative platform: a two-dimensional topological superconductor with inhomogeneous superconductivity, where Majorana modes localize at the ends of topologically nontrivial one-dimensional stripes induced by the spatial variations of the order parameter phase. In certain regimes, these Majorana modes hybridize into a single highly nonlocal state delocalized over spatially separated points, with exactly zero energy at finite system sizes and with emergent quantum-mechanical supersymmetry. We then present detailed descriptions of braiding and fusion protocols and showcase the versatility of our proposal by suggesting possible setups that can potentially lead to the realization of Yang-Lee anyons and the Sachdev-Ye-Kitaev model.

Square-well Model for Superconducting Pair Potential

We study Andreev reflection in a one-dimensional square-well pair potential. We discuss the history of the model. The current-phase relation is presented as a sum over Matsubara frequencies. How the current arises from bound and continuum levels is found by analytic continuation. We discuss two limiting cases of the square-well potential, the zero-length well and the infinite well. The model is quantitatively valid in some cases but forms the basis for understanding a wide range of problems in inhomogeneous superconductivity and superfluidity.

Electric‐Field‐Induced in‐Plane Anisotropy of Superconducting Transition Temperature for FeSe0.5Te0.5 Thin Films

AbstractSuperconductor/ferroelectric heterostructures are very important for fundamental research and applications since superconductivity can be controlled by electric fields via ferroelectric polarization/piezostrain. Superconductivity is a macroscopic quantum phenomenon and it is commonly believed that the in‐plane superconducting transition temperature (Tc) should be isotropic for superconductors with crystal structures of stacking layers (quasi 2D). Here, the observation of piezostrain‐induced in‐plane anisotropy of Tc in FeSe0.5Te0.5 (FST) thin films grown on ferroelectric single crystals is reported. The as‐prepared FST shows a tetragonal phase with equal in‐plane lattice parameters and an absence of in‐plane anisotropy of Tc. Upon applying electric fields, piezostrain induces a difference in the in‐plane lattice parameters (a‐b) and in‐plane anisotropy of Tc. The in‐plane anisotropy of Tc correlates with a‐b and becomes more remarkable for larger values of a‐b. Some possible extrinsic effects are ruled out by experiments and analysis. A possible mechanism is proposed involving electronic nematicity and inhomogeneous superconductivity in FST to account for this unusual phenomenon. This work is significant for uncovering the exotic nature of unconventional superconductors, as well as applications.

Superfluid response of two-dimensional filamentary superconductors

Different classes of low-dimensional superconducting systems exhibit an inhomogeneous filamentary superconducting condensate whose macroscopic coherence still needs to be fully investigated and understood. Here, we present a thorough analysis of the superfluid response of a prototypical filamentary superconductor embedded in a two-dimensional metallic matrix. By mapping the system into an exactly solvable random impedance network, we show how the dissipative (reactive) response of the system non-trivially depends on both the macroscopic and microscopic characteristics of the metallic (superconducting) fraction. We compare our calculations with resonant microwave transport measurements performed on LaAlO_33/SrTiO_33 heterostructures over an extended range of temperatures and carrier densities finding that the filamentary character of superconductivity accounts for unusual peculiar features of the experimental data.

Flux jump and mechanical response in inhomogeneous high-temperature superconductor under the pulsed-field magnetization

The high-temperature bulk superconductors with high critical current density are brittle, and can be damaged by large Lorentz forces and thermal stress during magnetization. Several studies have reported the failure of bulk superconductors during flux jumps. In this study, we analyzed the magnetization characteristics and mechanical response of the HTS bulk with inhomogeneous current density along the c-axis. The numerical simulation was consistent with the experimental results presented in the reference. Moreover, a flux jump occurred near the area of the pre-arrangement flux during the second pulsed field magnetization. The maximum temperature is lower than the critical temperature during the flux jump. In the mechanical analysis, the flux jump led to an abrupt change in the maximum stress of the bulk, and the maximum radial stress was significantly higher than the maximum hoop stress during the flux jump. The maximum radial stress increased with decreasing ambient temperature during the flux jump, and the maximum stress area was always near the seeded plane. Subsequently, the magnetization characteristics and mechanical response were studied for different locations of the seeded surface, two concentric superconducting bulks, and non-uniform fields.

Edge effects on the electromagnetic response of inhomogeneous type-II superconductors

From a macroscopic point of view, the edges of a type II superconductor are degraded non-homogeneous regions compared with the bulk of the sample. This paper presents numerical simulations of a long superconducting bar with square cross section subjected to an axial external magnetic field, the edges effect on its electromagnetic properties is studied. The edges of the sample are modeled as finite width regions with lower critical current density than the rest of the material. The simulations are based on a continuum electrodynamics model which describes the magnetic induction dynamics of partially penetrated states. Unlike a simpler homogeneous superconductor, in an inhomogeneous material rough flux fronts are formed. It was established that the stochastic profile of the current density produces jets of magnetic flux near a macrodefect.

Type‐III Superconductivity

Superconductivity remains one of most fascinating quantum phenomena existing on a macroscopic scale. Its rich phenomenology is usually described by the Ginzburg-Landau (GL) theory in terms of the order parameter, representing the macroscopic wave function of the superconducting condensate. The GL theory addresses one of the prime superconducting properties, screening of the electromagnetic field because it becomes massive within a superconductor, the famous Anderson-Higgs mechanism. Here the authors describe another widely-spread type of superconductivity where the Anderson-Higgs mechanism does not work and must be replaced by the Deser-Jackiw-Templeton topological mass generation and, correspondingly, the GL effective field theory must be replaced by an effective topological gauge theory. These superconductors are inherently inhomogeneous granular superconductors, where electronic granularity is either fundamental or emerging. It is shown that the corresponding superconducting transition is a 3D generalization of the 2D Berezinskii-Kosterlitz-Thouless vortex binding-unbinding transition. The binding-unbinding of the line-like vortices in 3D results in the Vogel-Fulcher-Tamman scaling of the resistance near the superconducting transition. The authorsreport experimental data fully confirming the VFT behavior of the resistance.

Superconductivity and Fermi Surface Studies of β″-(BEDT-TTF)2[(H2O)(NH4)2Cr(C2O4)3]·18-Crown-6

We report rf-penetration depth measurements of the quasi-2D organic superconductor β″-(BEDT-TTF)2[(H2O)(NH4)2Cr(C2O4)3]·18-crown-6, which has the largest separation between consecutive conduction layers of any 2D organic metal with a single packing motif. Using a contactless tunnel diode oscillator measurement technique, we show the zero-field cooling dependence and field sweeps up to 28 T oriented at various angles with respect to the crystal conduction planes. When oriented parallel to the layers, the upper critical field, Hc2=7.6 T, which is the calculated paramagnetic limit for this material. No signs of inhomogeneous superconductivity are seen, despite previous predictions. When oriented perpendicular to the layers, Shubnikov–de Haas oscillations are seen as low as 6 T, and from these we calculate Fermi surface parameters such as the superconducting coherence length and Dingle temperature. One remarkable result from our data is the high anisotropy of Hc2 in the parallel and perpendicular directions, due to an abnormally low Hc2⊥=0.4 T. Such high anisotropy is rare in other organics and the origin of the smaller Hc2⊥ may be a consequence of a lower effective mass.

Inhomogeneous Superconductivity Onset in FeSe Studied by Transport Properties

Heterogeneous superconductivity onset is a common phenomenon in high-Tc superconductors of both the cuprate and iron-based families. It is manifested by a fairly wide transition from the metallic to zero-resistance states. Usually, in these strongly anisotropic materials, superconductivity (SC) first appears as isolated domains. This leads to anisotropic excess conductivity above Tc, and the transport measurements provide valuable information about the SC domain structure deep within the sample. In bulk samples, this anisotropic SC onset gives an approximate average shape of SC grains, while in thin samples, it also indicates the average size of SC grains. In this work, both interlayer and intralayer resistivity were measured as a function of temperature in FeSe samples of various thicknesses. To measure the interlayer resistivity, FeSe mesa structures oriented across the layers were fabricated using FIB. As the sample thickness decreases, a significant increase in superconducting transition temperature Tc is observed: Tc raises from 8 K in bulk material to 12 K in microbridges of thickness ∼40 nm. We applied analytical and numerical calculations to analyze these and earlier data and find the aspect ratio and size of the SC domains in FeSe consistent with our resistivity and diamagnetic response measurements. We propose a simple and fairly accurate method for estimating the aspect ratio of SC domains from Tc anisotropy in samples of various small thicknesses. The relationship between nematic and superconducting domains in FeSe is discussed. We also generalize the analytical formulas for conductivity in heterogeneous anisotropic superconductors to the case of elongated SC domains of two perpendicular orientations with equal volume fractions, corresponding to the nematic domain structure in various Fe-based superconductors.

The Dynamic Proximity Effect in Superconductor –Ferromagnetic Insulator Hybrid Structures

This paper presents a theoretical study of the dynamics of the induced magnetization and spin cur-rent arising in a layer of an impure superconductor due to the proximity to a ferromagnetic dielectric with a uniform periodically precessing magnetization. The dynamics of the observed physical quantities is described within the semi-classical Usadel–Floquet formalism, which makes it possible to study the effect of a periodic perturbation on an inhomogeneous superconducting system. The spatial distributions and temporal evolu-tion of the induced magnetization and the superconducting spin current inside the superconductor layer are found from the numerical solutions of the system of Usadel–Floquet equations.

Probing electron-hole weights of an Andreev bound state by transient currents

Andreev bound states (ABSs) are localized quantum states that contain both electron and hole components. They ubiquitously reside in inhomogeneous superconducting systems. Following theoretical analysis, we propose to probe the electron-hole weights of an ABS via a local tunneling measurement that detects the transient current under a steplike pulse bias. With our protocol, the ABS energy level can also be obtained from peaks of the Fourier spectrum of the transient current. Our protocol can be applied to detect robust zero-energy Majorana bound states (MBSs), which have equal electron-hole weights, in candidate platforms where local tunneling spectroscopy measurement is possible. In the one-dimensional Majorana nanowire model, we numerically calculate the electron-hole weights for different types of low-energy bound states, including ABSs, quasi-MBSs, and MBSs.

Intrinsic vortex pinning in superconducting quasicrystals

We numerically show that a vortex pinning occurs in superconducting quasicrystal without impurities and defects. This vortex pinning is intrinsic since the superconducting order parameter in quasicrystal is always inhomogeneous due to the lack of the translational symmetry. We propose that experiments influenced by vortex pinning effects can detect the atomic-scale inhomogeneous superconducting order parameter in quasicrystals. We develop a numerical method to solve the Bogoliubov-de Gennes equations and gap equations in large systems, which is based on the localized-Krylov subspace and a sparse modeling technique. Two two-dimensional quasicrystals, the Penrose and Amman-Beenker tiling, are considered.

Wohlleben Effect and Emergent π junctions in superconducting Boron doped Diamond thin films

Diamond is an excellent wide-bandgap electrical insulator. However, boron (B) doping is known to induce superconductivity in diamonds. We have performed electrical transport and magnetic measurements under pressure with doping concentrations of (1.4 and 2.6) × 1021 cm−3, in a temperature range 2 - 10 K and present two interesting effects in superconducting B doped diamond (BDD) thin films: (i) Wohlleben effect (paramagnetic Meissner effect, PME) and (ii) pressure-induced spin glass-like susceptibility anomaly. PME, a low field anomaly in inhomogeneous superconductors, could arise from flux trapping, flux compression, or for non-trivial reason such as emergent Josephson π junctions. The joint occurrence of PME and spin glass type anomalies points to the possible emergence of π junctions. BDD is a disordered s-wave superconductor; and π junctions could be produced by spin-flip scattering of spin ½ moments when present at weak superconducting regions. A frustrated network of 0 and π junctions will result in a distribution of spontaneous equilibrium supercurrents, a spin glass (phase glass) state. Anderson localized spin ½ spinons embedded in a metallic fluid (two-fluid model) could create π junction by spin-flip scattering. Our findings are consistent with the presence of π junctions, invoked to explain the observation of certain resistance anomaly in BDD.

Superconductors gain momentum.

Spin-density modulations point to inhomogeneous superconductivity in a perovskite.

Transverse Magnetoresistance Induced by the Nonuniformity of Superconductor.

The transverse magnetoresistance (Rxy) caused by inhomogeneous superconductivity is symmetric about the magnetic field around the critical magnetic field region. This has caused many disturbances during the study of vortex dynamics by Hall signals. Here, we found that the peak of Rxy measured in our samples was induced by the nonuniformity of the superconductors. The peak values of Rxy decrease with increasing applied current and temperature, which can be described by the theory of superconductivity inhomogeneity. Based on this, we have proposed and verified a method for separating the transverse voltage caused by the inhomogeneity of superconductivity. Additionally, quantity ΔB(0) can also be used to characterize the uniformity of superconductivity. This clears up the obstacles for studying vortex motion dynamics and reveals a way to study the influence of the domain wall on superconductivity.

Density functional Bogoliubov-de Gennes analysis of superconducting Nb and Nb(110) surfaces

We report on the implementation of the Bogoliubov-de Gennes method into the JuKKR code, an implementation of the relativistic all-electron, full-potential Korringa-Kohn-Rostoker Green function method, which allows a material-specific description of inhomogeneous superconductors and heterostructures on the basis of density functional theory. We describe the formalism and report on calculations for the $s$-wave superconductor Nb, a potential component of the materials platform enabling the realization of the Majorana zero modes in the field of topological quantum computing. We compare the properties of the superconducting state both in the bulk and for (110) surfaces. We compare slab calculations for different thicknesses, the effect of surface relaxations, and the influence of a softening of phonon modes on the surface for the resulting superconducting gap.

Checkerboard patterns of charge stripes in the two-gap superconductor ZrB12

Inhomogeneous superconductivity in the high quality single crystals of ZrB12 (Tc = 6 K) has been studied using the heat capacity and x-ray diffraction (XRD) data. Evidence of two-band superconductivity with two branches of upper critical field Hc2(Tc) is obtained in a magnetic field applied along the [110] axis of the crystal. On the contrary, at H //[100], the only dependence Hc2(Tc) is observed. This finding is supplemented with the checkerboard-type patterns of the charge stripes in ZrB12 deduced from the detailed analysis of XRD data. These patterns are compared to the structure of the charge stripes in the weakly bound superconductor LuB12, whose Tc is 15 times lower than that of ZrB12. Probable nature of the two-gap superconductivity in ZrB12 with strongly enhanced characteristics is discussed.

Current–voltage characteristics of strained, highly underdoped LaSr x CuO4 thin films

The temperature dependence of resistance and of current–voltage characteristics are studied for two underdoped La1.952Sr0.048CuO4 films with different thickness and different degrees of built-in compressive strain. Strain induces an inhomogeneous superconducting (SC) state in the films, with two-step SC transition, consistent with the presence of SC islands coupled by the proximity effect. On further cooling, superfluid density is suppressed and global phase coherence is never reached. Instead, a reentrant increase of resistance appears, reaching several orders of magnitude in the thinner, more strongly strained film, and saturating at lowest temperatures. The saturation is accompanied by Coulomb blockade, which resembles the blockade reported for Josephson junction (JJ) arrays. However, increasing magnetic field quickly diminishes the influence of Coulomb blockade on transport, which is distinct from the behavior observed for JJ arrays. The observation of Coulomb blockade indicates that Cooper pairs survive in the insulating state, suggesting the local character of pairing.

Disorder-robust high-field superconducting phase of FeSe single crystals

When exposed to high magnetic fields, certain materials manifest an exotic superconducting (SC) phase that has attracted considerable attention. A proposed explanation for the origin of the high-field SC phase is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. This state is characterized by inhomogeneous superconductivity, where the Cooper pairs have finite center-of-mass momenta. Recently, the high-field SC phase was observed in FeSe, and it was deemed to originate from the FFLO state. Here, we synthesize FeSe single crystals with different levels of disorder. The level of disorder is expressed by the ratio of the mean free path to the coherence length and ranges between 35 and 1.2. The upper critical field \textit{B}$_{\rm{c}2}$ was obtained by both resistivity and magnetic torque measurements over a wide range of temperatures, which went as low as $\sim$0.5 K, and magnetic fields, which went up to $\sim$38 T along the \textit{c} axis and in the \textit{ab} plane. In the high-field region parallel to the \textit{ab} plane, an unusual SC phase was confirmed in all the crystals, and the phase was found to be robust against disorder. This result suggests that the high-field SC phase in FeSe is not a conventional FFLO state.