The two-component model of high temperature superconductors in its real space version has been solved using Bogoliubov-de Gennes equations. The disorder in the electron and boson subsystem has been taken into account. It strongly modifies the superconducting properties and leads to local variations of the gap parameter and density of states. The assumption that the impurities mainly modify boson energies offers natural explanation of the puzzling positive correlation between the positions of impurities and the values of the order parameter found in the scanning tunnelling microscopy experiments.
The inhomogeneities inherent to the random distribution of Sr dopants in La_{2-x}Sr_xCuO_4 superconductors are probed by measuring the x-ray diffraction linewidths and the Meissner transition widths, and then consistently explained on the grounds of a simple model in which the local Sr content is calculated by averaging over distances close to the in-plane electronic mean free path. By taking into account these intrinsic bulk inhomogeneities with long characteristic lengths (much larger than the superconducting coherence length amplitudes), the precursor diamagnetism measured above Tc, a finge…
We present a novel technique for the investigation of local variations of the critical current density in large bulk superconductors. In contrast to the usual Hall probe scanning technique, the sample is not magnetized as a whole before the scan, but locally by a small permanent magnet, which is fixed near the Hall probe, during the scanning process. The resulting signal can be interpreted as a qualitative measure of the local shielding currents flowing at the surface.
The measurements of temperature dependence of AC magnetic susceptibility were used to study the influence of inhomogeneities on intragranular superconducting properties of YBa2Cu3-xMxOy (M=Fe,x=0.005; Al,x=0.01; Cr,x=0.01), Bi1.7Pb0.2Sb0.1Sr2Ca2Cu3Oy and Bi1.5Pb0.3Sb0.2Sr2Ca2Cu3Oy ceramics. It is found that step-like regions are revealed on AC magnetic field dependence curves Tmg(ho) of hysteresis losses peak temperature for superconducting granuls. The steps at temperature scale depend on sample's composition as well as on the type of atoms sabstituted for the copper. They range from 1 to 2 K…
We perform calculations to obtain the $H_{c2}$ curve of high temperature superconductors (HTSC). We consider explicitly the fact that the HTSC possess intrinsic inhomogeneities by taking into account a non uniform charge density $ρ(r)$. The transition to a coherent superconducting phase at a critical temperature $T_c$ corresponds to a percolation threshold among different superconducting regions, each one characterized by a given $T_c(ρ(r))$. Within this model we calculate the upper critical field $H_{c2}$ by means of an average linearized Ginzburg-Landau (GL) equation to take into account the…
The magnetic field dependence of the magnetization was measured above the superconducting transition in a high-Tc underdoped cuprate La1.9Sr0.1CuO4 and in a low-Tc alloy (Pb55In45). Near the superconducting transition [typically for (T-Tc)/Tc<0.05] and under low applied magnetic field amplitudes [typically for H/Hc2(0)<0.01, where Hc2(0) is the corresponding upper critical field extrapolated to T=0 K] the magnetization of both samples presents a diamagnetic contribution much larger than the one predicted by the Gaussian Ginzburg-Landau (GGL) approach for superconducting fluctuations. These ano…
We discuss the Meissner response to a known field source of superconductors having inhomogeneities in their penetration depth. We simplify the general problem by assuming that the perturbations of the fields by the penetration depth inhomogeneities are small. We present expressions for inhomogeneities in several geometries, but concentrate for comparison with experiment on planar defects, perpendicular to the sample surfaces, with superfluid densities different from the rest of the samples. These calculations are relevant for magnetic microscopies, such as Scanning Superconducting Quantum Inte…
We analyze numerically how the voltage-current (V-I) characteristics near the so-called Berezinskii-Kosterlitz-Thouless (BKT) transition of 2D superconductors are affected by a random spatial Gaussian distribution of critical temperature inhomogeneities with long characteristic lengths (much larger than the in-plane superconducting coherence length amplitude). Our simulations allow to quantify the broadening around the average BKT transition temperature of both the exponent alpha in V I^alpha and of the resistance V/I. These calculations reveal that strong spatial redistributions of the local …
Scanning tunneling spectroscopy at very low temperature on homogeneously disordered superconducting Titanium Nitride thin films reveals strong spatial inhomogeneities of the superconducting gap $Δ$ in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature $T_c$ towards zero, enhancement of spatial fluctuations in $Δ$, and growth of the $Δ/T_c$ ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.
Nanoscale electronic inhomogeneity in optimally doped single-layer Bi_2Sr_{1.6}L_{0.4}CuO_{6+delta}, (L-Bi2201, L=La and Gd) as well as bilayer Bi_2Sr_2CaCu_2O_{8+delta} (Bi2212), superconductors has been investigated by the low-temperature scanning-tunneling-microscopy and spectroscopy. The inhomogeneous gap structures are observed above and below Tc on Gd-Bi2201. Increasing the out-of-plane disorder which is controlled by mismatch of the ionic radius between Sr and Ln results in the enhancement of pseudogap region with suppressed coherence peaks in the conductance spectrum, making the gap av…
We show that inhomogeneities in the spatial distribution of Cooper pairs and in the phase of the local superconducting order parameter in the vicinity of a superconductor-normal state transition (SNT) in two dimensions can be highly sensitive to a perpendicular magnetic field. We focus on the role of orbital effects in the field-dependence of local superfluid stiffness and superconducting phase disorder in homogeneously-disordered two-dimensional superconductor thin films. The relative importance of these orbital effects is analyzed in different physical regimes dominated by Coulomb blockade, …
We study a short coherence length d-wave superconductor with finite density of unitary scatterers using the Bogoliubov-deGennes technique. We find that the low-energy density of states is reduced, the superfluid stiffness is significantly larger and off-diagonal long range order is more robust than the self-consistent T-matrix prediction. These results are a consequence of the inhomogeneous pairing amplitude in the ground state and of the low-lying excitations formed by hybridized impurity resonances. These features, with their nontrivial spatial structure, cannot be adequately described withi…
Type II superconductors, consisting of superconducting domains embedded in a normal or insulating matrix, undergo a rounded phase transition. Indeed, the correlation length cannot grow beyond the spatial extent of the domains. Accordingly, the thermodynamic properties will exhibit a finite size effect. It is shown that the specific heat and penetration depth data of a variety of type II superconductors, including cuprates, exhibit the characteristic properties of a finite size effect, arising from domains with nanoscale extent. The finite size scaling analysis reveals essential features of the…
A superconductor is influenced by an applied magnetic field. Close to the transition temperature $T_{c}$ fluctuations dominate and the correlation length $ξ$ increases strongly when $T_{c}$ is approached. However, for nonzero magnetic field $H$ there is another length scale $L_{H}=\sqrt{Φ_{0}/aH}$ where $a$ is a universal amplitude. It is comparable to the average distance between vortex lines. We show that the correlation length is bounded by this length scale, so that $ξ$ cannot grow beyond $L_{H}$. This implies that type II superconductors in a magnetic field do not undergo a phase transiti…
Holographic duality is a powerful tool to investigate the far-from equilibrium dynamics of superfluids and other phases of quantum matter. For technical reasons it is usually assumed that, after a quench, the far-from equilibrium fields are still spatially uniform. Here we relax this assumption and study the time evolution of a holographic superconductor after a temperature quench but allowing spatial variations of the order parameter. Even though the initial state and the quench are spatially uniform we show the order parameter develops spatial oscillations with an amplitude that increases wi…
Proper characterisation of investigated samples is vital when studying superconductivity as impurities and doping inhomogeneities can affect the physical properties of the measured system. We present a method where a polarised neutron imaging setup utilises the precession of spin-polarised neutrons in the presence of a trapped field in the superconducting sample to spatially map out the critical temperature for the phase transition between superconducting and non-superconducting states. We demonstrate this method on a superconducting crystal of the prototypical high-temperature superconductor …
We review briefly several approaches used to investigate the stability of stripe phases in high temperature superconductors, where charge inhomogeneities arise from competing kinetic and magnetic energies. The mechanism of stripe formation, their consequences for the normal state and enhancement of pairing interaction triggered by charge inhomogeneities are briefly summarized. Finally, we demonstrate that orbital degeneracy ($i$) leads to a more subtle mechanism of stripe formation, and ($ii$) plays an important role and determines the symmetry of the superconducting state in pnictides.
The observation of the characteristic Kosterlitz-Thouless behavior requires the attaintment of the two dimensional limit where the correlation-length anisotropy, gamma=gsiab/gsic, diverges. Our findings strongly suggest that the failure of several experiments on films and single crystals to observe any trace of KT-behavior is attributable either to inhomogeneities or doping by means of chemical substitution.
We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local order parameters change drastically from what are obtained in a simple Hartree-Fock-Bogoliubov theory. While both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find them to compete with each other leading to a relatively smooth variation of the local density. Our self-consistent calculations modify the spat…
We compute the spectral function $A({\bf k}, ω)$ of a model two-dimensional high-temperature superconductor, at both zero and finite temperatures $T$. We assume that an areal fraction $c_β$ of the superconductor has a large gap $Δ$ ($β$ regions), while the rest has a smaller $Δ$ ($α$ regions), both of which are randomly distributed in space. We find that $A({\bf k}, ω)$ is most strongly affected by inhomogeneity near the point $\mathbf k = (π, 0)$ (and the symmetry-related points). For $c_β\simeq 0.5$, $A({\bf k}, ω)$ exhibits two double peaks (at positive and negative energy) near this k-poin…
The effect of smooth inhomogeneities near a superconductor boundary on the magnetic penetration depth $λ$ is studied with emphasis on the proximity-induced spatial dependence of the Cooper pair amplitude. The influence of surface pair breaking or pair formation on $λ$ is described within the Ginzburg-Landau theory, with no model assumptions, for both strongly type-II and strongly type-I homogeneous superconductors. Generic values of $λ$, which can differ greatly from the London penetration depth, are identified and demonstrated to be induced by large-scale inhomogeneities, when superconductivi…
We present a magnetic-penetration-depth study on polycrystalline and granular samples of SrPtAs, a pnictide superconductor with a hexagonal structure containing PtAs layers that individually break inversion symmetry (local noncentrosymmetry). Compact samples show a clear-cut s-wave-type BCS behavior, which we consider to be the intrinsic penetration depth of SrPtAs. Granular samples display a sample-dependent second diamagnetic drop, attributed to the intergrain coupling. Our experimental results point to a nodeless isotropic superconducting energy gap in SrPtAs, which puts strong constraints …
Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20%$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared op…
The number of bound states due to inhomogeneities in a BCS superconductor is usually established either by variational means or via exact solutions of particularly simple, symmetric perturbations. Here we propose estimating the number of sub-gap states using the Birman-Schwinger principle. We show how to obtain upper bounds on the number of sub-gap states for small normal regions and derive a suitable Cwikel-Lieb-Rozenblum inequality. We also estimate the number of such states for large normal regions using high dimensional generalizations of the Szego theorem. The method works equally well fo…
In this study we perform numerical calculations of the spatial and time variation of the magnetic induction, current density and temperature in an infinite superconducting slab with macroscopic inhomogeneities. We also modeled an homogeneuos superconductor as a referential material, considering characteristic magnetothermal properties of a high-T$_c$ single crystal. The theoretical formalism is enclosed in the dynamical regime and a continuum electrodynamic approach. In particular, we studied the correlation between the magnetic jumps and temperature rise occurrence with the presence of macros…
Purely local experimental probes of many copper oxide superconductors show that their electronic states are inhomogeneous in real space. For example, scanning tunneling spectroscopic (STS) imaging shows strong variations in real space, and according to nuclear quadrupole resonance (NQR) studies the charge distribution in the bulk varies on the nanoscale. However, the analysis of the experimental results utilizing spatially-averaged probes often ignores this fact. We have performed a detailed investigation of the doping-dependence of the energy and line width and position of the zone-boundary C…
In this communication we consider the doping dependence of the strong antiferromagnetic spin fluctuations in the cuprate superconductors. We investigate the effect of an incommensurate magnetic response, as recently observed in inelastic neutron scattering (INS) experiments on several YBa_2Cu_3O_{6+x} compounds, on the spin-lattice and spin-echo relaxation rates measured in nuclear magnetic resonance (NMR) experiments. We conclude that a consistent theoretical description of INS and NMR can be reached if one assumes spatially inhomogeneous but locally commensurate spin correlations and that NM…
In the last few years the gap symmetries of many new superconductors,including Sr$_2$RuO$_4$, CeCoIn$_5$, $κ$-(ET)$_{2}$Cu(NCS)$_{2}$, YNi$_{2}$B$_{2}$C and PrOs$_{4}$Sb$_{12}$, have been identified via angle-dependent magnetothermal conductivity measurements. However, a controversy still persists as to the nature of the superconductivity in Sr$_2$RuO$_4$. For PrOs$_{4}$Sb$_{12}$, spin-triplet superconductivity has recently been proposed. Here, we also propose g-wave superconductivity for UPd$_2$Al$_3$ (i.e., $Δ({\bf k})=Δ\cos(2χ), χ= ck_{z}$) based on recent thermal conductivity data.
We investigate the effects of mesoscopic inhomogeneities on the metal-superconductor transition occurring in several two-dimensional electron systems. Specifically, as a model of systems with mesoscopic inhomogeneities, we consider a random-resistor network, which we solve both with an exact numerical approach and by the effective medium theory. We find that the width of the transition in these two-dimensional superconductors is mainly ruled by disorder rather than by fluctuations. We also find that "tail" features in resistivity curves of interfaces between LaAlO3 or LaTiO3 and SrTiO3 can ari…
We discuss the temperature, frequency, and power-dependent surface resistance of the boride superconductor MgB2 in relation to possible applications for passive microwave devices. The data available in the literature are compared with results for polycrystalline Nb3Sn and epitaxial YBa2Cu3O7-x, which are representative of the classical and cuprate superconductors. MgB2 displays all specific features that make superconductors attractive for high-performance devices, even though the fabrication technology is not yet mature. We attempt to identify promising areas of applications, as well as mater…
The influence of the atomic-scale inhomogeneities of the pairing interaction on the superconducting order parameter distribution and the LDOS is studied in the framework of mean-field BCS theory for two-dimensional lattice model. It is found that the ratio of the local low-temperature gap in differential conductance to the local temperature of vanishing the gap $2Δ_g/T_p$ can take large enough values compared to the homogeneous case. This ratio practically does not depend on the location in the sample and is independent on the concentration of local pair interaction perturbations in wide range…
Combined scanning tunneling microscopy, spectroscopy and local barrier height (LBH) studies show that low-temperature-cleaved optimally-doped Ba(Fe1-xCox)2As2 crystals with x=0.06, with Tc = 22 K, have complicated morphologies. Although the cleavage surface and hence the morphologies are variable, the superconducting gap maps show the same gap widths and nanometer size inhomogeneities irrelevant to the morphology. Based on the spectroscopy and LBH maps, the bright patches and dark stripes in the morphologies are identified as Ba and As dominated surface terminations, respectively. Magnetic imp…
We investigate the microwave absorption arising from inhomogeneity in the superfluid density of a model high-T_c superconductor. Such inhomogeneities may arise from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. We show that both mechanisms will inevitably produce additional absorption at finite frequencies. We present simple model calculations for this extra absorption, and discuss applications to other transport properties in high-T_c materials. Finally, we discuss the connection of these predictions to recent measurements by Co…
Stripe phases are observed experimentally in several copper-based high-Tc superconductors near 1/8 hole doping. However, the specific characteristics may vary depending on the degree of dopant disorder and the presence or absence of a low- temperature tetragonal phase. On the basis of a Hartree-Fock decoupling scheme for the t-J model we discuss the diverse behavior of stripe phases. In particular the effect of inhomogeneities is investigated in two distinctly different parameter regimes which are characterized by the strength of the interaction. We observe that small concen- trations of impur…
We analyze the superconductors TiNCl and ZrNCl from a local bonding perspective. Although TiNCl crystallizes in an orthorhombic structure and ZrNCl crystallizes in a hexagonal structure, both compounds show significant structural similarities, for example that both consist of layered metal-Nitrogen networks. The local bonding in those two structures is very similar, giving rise to a dispersive conduction band mostly consisting of metal-d -states. Upon doping both compounds show structural changes, which lead to short metal-metal distances, indicating a bonding interaction that might be importa…
We present a self-consistent real space formulation of spin-fluctuation mediated d-wave pairing. By calculating all relevant inhomogeneous spin and charge susceptibilities in real space within the random phase approximation (RPA), we obtain the effective pairing interaction and study its spatial dependence near both local potential and hopping impurities. A remarkably large enhancement of the pairing interaction may be obtained near the impurity site. We discuss the relevance of our result to inhomogeneities observed by scanning tunneling spectroscopy on the surface of cuprate superconductors.
A theoretical overview of the classes of superconductors encompassing (a) high-Tc cuprate, (b) iron-based and (c) aromatic superconductors is given. Emphasis is put on the multiband natures of all the three classes, where the differences in the multiorbits and their manifestations in the electronic structures and pairing are clarified. From these, future directions and prospects are discussed.
The interface properties of high-temperature cuprate superconductors have been of interest for many years, and play an essential role in Josephson junctions, superconducting cables, and microwave electronics. In particular, the maximum critical current achievable in high-Tc wires and tapes is well known to be limited by the presence of grain boundaries, regions of mismatch between crystallites with misoriented crystalline axes. In studies of single, artificially fabricated grain boundaries the striking observation has been made that the critical current Jc of a grain boundary junction depends …
Through variational Monte Carlo calculation on Gutzwiller projected wave functions, we study the quasiparticle(qp) weight for adding and removing an electron from a high temperature superconductor. We find the qp weight is particle-hole symmetric at sufficiently low energy. We propose to use the tunneling asymmetry as a tool to study the mechanism of electron incoherence in high temperature superconductors.
Perspectives on Magnetic/Superconductor Hybrid Systems: Long-range Electromagnetic Phenomena Induced by Proximity Effect and Interfacial Spin-orbit Coupling
Institute for Physics of Microstructures, Russian Academy of Sciences（俄罗斯科学院微观物理研究所）；Moscow Institute of Physics and Technology (National Research University)（莫斯科物理技术学院（国立研究型大学））；Institute for Computer Science and Mathematical Modeling, Sechenov First Moscow State Medical University（谢切诺夫第一莫斯科国立医科大学计算机科学与数学建模研究所）；University Bordeaux, LOMA UMR-CNRS 5798（波尔多大学，LOMA CNRS联合研究实验室）
Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity such an early influential relation showed that the critical temperature of superconductivity ($T_c$) correlates with the density of the superfluid measured at low temperatures. This famous Uemura relation has been inspiring the community ever since. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO$_2$ plane, accessible with nuclear magnetic resonance (NMR), is tied to the Uemura scaling. This charge distribution between c…
Iron-based superconductors (FeSC) present an unprecedented variety of features both in the superconducting and in the normal state. Different families differ in the value of the critical temperature, in the shape of the Fermi surface, in the existence or absence of quasi-nesting conditions, in the range of doping in which the antiferromagnetic (AFM) and the superconducting phase coexist and in the structure of the order parameter in the reciprocal space, and so on. In this paper the most important results of point-contact spectroscopy (PCS) in Fe-based superconductors are reviewed, and the mos…
We report the first observation of superconductivity in heterostructure consisting of an insulating ferroelectric film (Ba$_{0.8}$Sr$_{0.2}$TiO$_3$) grown on an insulating parent compound of La$_2$CuO$_4$ with [001] orientation. The heterostructure was prepared by magnetron sputtering on a non-atomically-flat surface with inhomogeneities of the order of 1-2 nm. The measured superconducting transition temperature T$_c$ is about 30K. We have shown that superconductivity is confined near the interface region. Application of a weak magnetic field perpendicular to the interface leads to the appeara…
We study the modulations of the superconducting order parameter in the vicinity of edges, magnetic and non-magnetic impurities by self-consistently solving the gap equations of a system with competing interactions in the Cooper channel. It is shown that the presence or absence of Friedel-like oscillations of the superconducting order parameter crucially depends on its symmetry and can, hence, be used to obtain information about the symmetry properties of the condensate. Furthermore, the appearance of competing order parameters at inhomogeneities is discussed. We show that this can lead to the …
In many cases inhomogeneities are known to exist near the metal (or superconductor)-insulator transition, as follows from well-known domain-wall arguments. If the conducting regions are large enough (i.e. when the T=0 superconducting gap is much larger than the single-electron level spacing), and if they have superconducting correlations, it becomes energetically favorable for the system to go into a Josephson-coupled zero-resistance state before (i.e. at higher resistance than) becoming a "real" metal. We show that this is plausible by a simple comparison of the relevant coupling constants. F…
We study mesoscopic disorder fluctuations in an anisotropic gap superconductor, which lead to the spatial variations of the local pairing temperature and formation of superconducting islands above the mean-field transition. We derive the probability distribution function of the pairing temperatures and superconducting gaps. It is shown that above the mean-field transition, a disordered BCS superconductor with an unusual pairing symmetry is described by a network of superconducting islands and metallic regions with a strongly suppressed density of states due to superconducting fluctuations. We …
High-entropy alloys (HEAs) are a new class of materials which are being energetically studied around the world. HEAs are characterized by a multi-component alloy in which five or more elements randomly occupy a crystallographic site. The conventional HEA concept has developed into simple crystal structures such as face-centered-cubic (fcc), body-centered-cubic (bcc) and hexagonal-closed packing (hcp) structures. The highly atomic-disordered state produces many superior mechanical or thermal properties. Superconductivity has been one of the topics of focus in the field of HEAs since the discove…
The boson-fermion (BF) model has been proposed to describe superconductivity in short coherence length superconductors. In this work we use it to study impurity induced inhomogeneities in high temperature superconductors (HTS) as found in numerous scanning tunnelling measurements. The model has been formulated in real space and solved with help of Bogolubov-de Gennes approach. Disorder in the boson or fermion subsystem is directly coupled to the superconducting order parameter and leads to severe changes of superconducting properties like local order parameter and density of states. We present…
The geometric structure of an intermediate state in the high pure Gallium single crys-tal at the external magnetic field Hext at the temperature T=0.4 K is researched, using the longi-tudinal ultrasonic signal attenuation method at the ultrasonic signal frequency of 30 MHz. It is experimentally shown that the edge inhomogeneities of the magnetic field distribution have an influence on the structure of an intermediate state in the cylindrical superconductor samples at the transverse orientation of external magnetic field Hext. It is shown that the use of the super-conducting plane screens of Nb…
Using magnetic force microscopy operating at sub-Kelvin temperatures we characterize the heavy-fermion superconductor CeCoIn$_5$. We pinpoint the absolute London penetration depth $λ(0) = 435 \pm 20$ nm and report its temperature dependence, which is closely linked to the symmetry of the superconducting gap. In addition, we directly measure the pinning force of individual Abrikosov vortices and estimate the critical current density $j_c = 9 \times 10^4$ A/cm$^2$. In contrast to the related, well-established tunnel diode oscillator technique, our method is capable of resolving inhomogeneities $…
