The Aharonov-Casher effect is the analogue of the Aharonov-Bohm effect that applies to neutral particles carrying a magnetic moment.
This can be manifested by vortices or fluxons flowing in trajectories that encompass an electric charge. These have been predicted to result in a persistent voltage which fluctuates for different sample realizations. Here we show that disordered superconductors exhibit reproducible voltage fluctuation, antisymmetrical with respect to magnetic field, as a function of various parameters such as magnetic field amplitude, field orientations and gate voltage. These results are interpreted as the vortex equivalent of the universal conductance fluctuations typical of mesoscopic disordered metallic systems. We analyze the data in the framework of random matrix theory and show that the fluctuation correlation functions and curvature distributions exhibit behavior which is the fingerprint of Aronov-Casher physics. The results demonstrate the quantum nature of the vortices in highly disordered superconductors both above and below $T_c$.
We study the low-energy density of states of Dirac fermions in disordered d-wave superconductor. At zero energy, a finite density of states is obtained via the mechanism of dynamical mass generation in an effective (1+1)-dimensional relativistic field theory.
We show that strong correlations play a vital role in protecting low energy excitations in disordered high temperature superconductors. The impurity-induced low-energy density of states (DOS) is greatly reduced in the strongly correlated superconductor compared to d-wave Bogoliubov-deGennes theory. The gapless nodal quasiparticles, and the resulting `V' in the low-energy DOS, are much more robust against disorder compared to the large-gap antinodal excitations. We discuss the relevance of our results to angle-resolved photoemission and scanning tunneling spectroscopy experiments.
Through a detailed study of scaling near the magnetic field-tuned superconductor-to-insulator transition in strongly disordered films, we find that results for a variety of materials can be collapsed onto a single phase diagram. The data display two clear branches, one with weak disorder and an intervening metallic phase, the other with strong disorder. Along the strongly disordered branch, the resistance at the critical point approaches $R_Q = h/4e^2$ and the scaling of the resistance is consistent with quantum percolation, and therefore with the predictions of the dirty boson model.
The paramagnon contribution to the quasiparticle inelastic scattering rate in disordered superconductors is presented. Using Anderson's exact eigenstate formalism, it is shown that the scattering rate is Stoner enhanced and is further enhanced by the disorder relative to the clean case in a manner similar to the disorder enhancement of the long-range Coulomb contribution. The results are discussed in connection with the possibility of conventional or unconventional superconductivity in the borocarbides. The results are compared to recent tunneling experiments on LuNi$_{2}$B$_{2}$C.
The low-energy quasiparticle states of a disordered d-wave superconductor are investigated theoretically. A class of such states, formed via tunneling between the Andreev bound states that are localized around extended impurities (and result from scattering between pair-potential lobes that differ in sign) is identified. Its (divergent) contribution to the total density of states is determined by taking advantage of connections with certain one-dimensional random tight-binding models. The states under discussion should be distinguished from those associated with nodes in the pair potential.
The influence of static magnetic correlations on the temperature-dependent superfluid density ρ_s(T) is calculated for d-wave superconductors. In self-consistent calculations, itinerant holes form incommensurate spin density waves (SDW) which coexist with superconductivity. In the clean limit, the density of states is gapped, and ρ_s(T << T_c) is exponentially activated. In inhomogeneously-doped cases, the SDW are disordered and both the density of states and ρ_s(T) obtain forms indistinguishable from those in dirty but pure d-wave superconductors, in accordance with experiments. We conclude t…
We study the insulating phase of disordered indium oxide films that undergo a field-tuned superconductor-insulator transition. The transport measurements in a perpendicular magnetic field show distinct regimes of strongly fluctuating order-parameter amplitude and phase, and reveal a wide range of insulator strength in samples with differing disorder, despite the similarity in behavior near the SIT. We characterize the strength of the insulating phase and compare it to the superconducting strength. We find that the films do not return to the expected normal state even at high perpendicular magn…
Weakly disordered two-dimensional superconductors undergo a Kosterlitz-Thouless (KT) transition, where at a critical temperature vortices proliferate through the system and destroy the superconducting (SC) order. On the other hand, it was suggested that for large disorder the systems separates into regions of high SC order, and it is the percolation of coherence between these regions that is lost at the critical temperature. Here we demonstrate that these two descriptions are just the dual of each other. A vortex causes loss of local correlations, and thus the loss of percolation of correlatio…
We study analytically the effects of inhomogeneous pairing interactions in short coherence length superconductors, using a spatially varying Bogoliubov-deGennes model. Within the Born approximation, it reproduces all of the standard Abrikosov-Gor'kov pairbreaking and gaplessness effects, even in the absence of actual magnetic impurities. For pairing disorder on a single site, the T-matrix gives rise to bound states within the BCS gap. Our results are compared with recent scanning tunneling microscopy measurements on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ with Zn or Ni impurities.
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…
Strongly disordered superconductors in a magnetic field display many characteristic properties of type-II superconductivity--- except at low temperatures where an anomalous linear $T$-dependence of the resistive critical field $B_{c2}$ is routinely observed. This behavior violates the conventional theory of superconductivity, and its origin remains a long-standing puzzle. Here we report on systematic measurements of the critical magnetic field and current on amorphous indium oxide films of various levels of disorder. Surprisingly, our measurements show that the $B_{c2}$ anomaly near zero-tempe…
We study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in the disordered systems. We analyze the microscopic model, in which the d-wave superconductivity is stabilized near the antiferromagnetic quantum critical point, and investigate two kinds of disorder, namely, box disorder and point disorder, on the basis of the Bogoliubov-deGennes (BdG) equation. The spatial structure of modulated superconducting order parameter and the magnetic properties in the disordered FFLO state are investigated. We point out the possibility of "FFLO glass" state in the presence of strong point d…
The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a dramatic transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behavior proceeds via the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address thi…
The low-temperature thermal conductivity κ_0/T of d-wave superconductors is generally thought to attain a "universal" value independent of disorder at sufficiently low temperatures, providing an important measure of the magnitude of the gap slope near its nodes. We discuss situations in which this inference can break down because of competing order, and quasiparticle localization. Specifically, we study an inhomogeneous BCS mean field model with electronic correlations included via a Hartree approximation for the Hubbard interaction, and show that the suppression of κ_0/T by localization effec…
We calculate the density of states of a disordered inhomogeneous d-wave superconductor in a magnetic field. The field-induced vortices are assumed to be pinned at random positions and the effects of the scattering of the quasi-particles off the vortices are taken into account using the singular gauge transformation of Franz and Tesanovic. We find two regimes for the density of states: at very low energies the density of states follows a law ρ(ε) \sim ρ_0 + |ε|^α where the exponent is close to 1. A good fit of the density of states is obtained at higher energies, excluding a narrow region aroun…
The highly convergent form of superfluid density in disordered conventional superconductors available in the literature and independently obtained by us following the approach of an earlier paper [Phys. Rev. B $\bm{102}$, 024514 (2020)] has been reformulated to separate out the generally used so-called `dirty-limit' term and an additional term. We use this new expression for making an extensive comparison with previously published experimental data and show that the former, generally used, term is {\em not} sufficient for analyzing these results. We point out that consequently, there is a larg…
We calculate electronic single-particle properties of short-range ordered stripe states, using Monte-Carlo simulations of collective charge-density wave (CDW) order parameters coupled to fermions on a 2d square lattice. For superconducting bond-centered stripes with a d-wave form factor, we find a valence-bond "glass" which coexists with low-energy quasiparticles featuring interference phenomena, in agreement with recent scanning-tunneling-microscopy (STM) measurements on underdoped BSCCO and CaNaCuOCl. Together with earlier work, our calculations provide a link between CDW features seen in ST…
In this paper we present a method to compute the exact density of states induced by $N$ non magnetic impurities in a system of two dimensional Dirac fermions in the unitarity limit. We review the case of the $π$-flux phase of the Heisenberg model and also treat the disordered d-wave superconductor. In both case we find additional states in the gap with $δρ(ω) \simeq n_i/ |ω(\ln^2 |ω/Δ_0| + (π/2)^2)|$.
It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical potentials on N(w) and show that at weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a…
We investigate the role of disorder on the superconducting (SC) fluctuation in short coherence length d-wave superconductors. The particular intetest is focused on the disorder-induced microscopic inhomogeneity of SC fluctuation and its effect on the pseudogap phenomena. We formulate the self-consistent 1-loop order theory for the SC fluctuation in inhomogeneous systems and analyze the disordered $t$-$t'$-$V$ model. The SC correlation function, electronic DOS and the critical temperature are estimated. The SC fluctuation is localized like a nanoscale granular structure when the coherence lengt…
We develop an analytical theory for quantum phase transitions driven by disorder in magnets and superconductors. We study these transitions with a cavity approximation which becomes exact on a Bethe lattice with large branching number. We find two different disordered phases, characterized by very different relaxation rates, which both exhibit strong inhomogeneities typical of glassy physics.
It is analyzed what fundamental new information for the properties of the superconductors can be obtained by systematic investigation of the Bernoulli effect. It is shown that it is a tool to determine the effective mass of Cooper pairs, the volume density of charge carriers, the temperature dependence of the penetration depth and condensation energy. The theoretical results for disordered and anisotropic gap superconductors are systematized for this aim. For clean-anisotropic-gap superconductors is presented a simple derivation for the temperature dependence of the penetration depth
We explore the role of phase fluctuations in a 3-dimensional s-wave superconductor, NbN, as we approach the critical disorder for the destruction of the superconducting state. Scanning tunneling spectroscopy measurements reveal that in the presence of strong disorder, a finite gap in the electronic spectrum continues to persist at temperatures above Tc. With increase in disorder, the superfluid density is strongly suppressed at low temperatures and evolves towards a linear-T variation at higher temperatures. These observations provide strong evidence that phase fluctuation leads to the formati…
We investigate flux penetration in a disordered type II superconductor by molecular dynamics simulations of interacting vortices. We focus on the effect of different boundary conditions on the scaling laws for flux front propagation. The numerical results can be interpreted using a coarse grained description of the system in terms of a non-linear diffusion equation. We propose a phenomenological equation for the front position that captures the essential behavior of the system and recovers the scaling exponents.
We have fabricated quasi-two-dimensional arrays of nano-scale Pb grains coupled by an overlayer of Ag grains. Their temperature dependent resistive transitions follow predictions for an array of mesoscopic superconductor-normal-superconductor junctions. The decrease of their transition temperatures with Ag overlayer thickness systematically deviates from the Cooper limit theory of the proximity effect as the Pb grain size decreases. The deviations occur when the estimated number of Cooper pairs per grain is less than or equal to 1 and suggest the approach to a superconductor to metal transitio…
The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron cha…
Voltages parallel and transverse to electric current in slightly inhomogeneous superconductors can contain components proportional to the field and temperature derivatives of the longitudinal and Hall resistivities. We show that these anomalous contributions can be the origin of the zero field and even-in-field transverse voltage occasionally observed at the superconductor to normal state transition. The same mechanism can also cause an anomaly in the odd-in-field transverse voltage interfering the Hall effect signal.
Using a real-space renormalization group (RSRG) technique, we compute the microwave conductivity of a d-wave superconductor disordered by extended impurities. To do this, we invoke a semiclassical approximation which naturally accesses the Andreev bound states localized near each impurity. Tunneling corrections (which are captured using the RSRG) lead to a delocalization of these quasiparticles and an associated contribution to the microwave conductivity.
We investigate flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.
The electric conductivities in glass phases of three-dimensional (3D) granular superconductors in magnetic fields are examined based on a quantum disordered Josephson-junction array. A correct inclusion of the Ohmic dissipative dynamics leads to glass phases with divergent dc conductivity. In contrast, with no dissipative term, a metallic response in a glass phase is obtained irrespective of the range of correlation of quenched disorder, i.e., even in the so-called Bose-glass phase with experimentally vanishing resistivity.
We investigate the effect of thermal fluctuations on the two-particle spectral function for a disordered $s$-wave superconductor in two dimensions, focusing on the evolution of the collective amplitude and phase modes. We find three main effects of thermal fluctuations: (a) the phase mode is softened with increasing temperature reflecting the decrease of superfluid stiffness; (b) remarkably, the non-dispersive collective amplitude modes at finite energy near ${\bf q}=[0,0]$ and ${\bf q}=[π,π]$ survive even in presence of thermal fluctuations in the disordered superconductor; and (c) the scatte…
By performing experiments with thin-film resonators of NbSi, we elucidate a decoherence mechanism at work in disordered superconductors. This decoherence is caused by charged Two Level Systems (TLS) which couple to the conduction electrons in the BCS ground state; it does not involve any out-of-equilibrium quasiparticles, vortices, etc. Standard theories of mesoscopic disordered conductors enable making predictions regarding this mechanism, notably that decoherence should increase as the superconductor cross section decreases. Given the omnipresence of charged TLS in solid-state systems, this …
A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin density susceptibility and the electrical conductivity are used as examples. Results i…
We study the superconducting transition temperature, T_c, of an array of fluctuating, maximally gapped interacting ladders, embedded in a disordered plane. Renormalization group analysis indicates that geometrical fluctuations mitigate the suppression of the intra-ladder pairing correlations by the disorder. In addition, the fluctuations enhance the Josephson tunneling between the ladders. Both effects lead to an increase of T_c in the Josephson coupled array. These findings may be relevant to the understanding of the 1/8 anomaly in the lanthanum based high-temperature superconductors.
According to the Goldstone theorem the breaking of a continuous U(1) symmetry comes along with the existence of low-energy collective modes. In the context of superconductivity these excitations are related to the phase of the superconducting (SC) order parameter and for clean systems are optically inactive. Here we show that for strongly disordered superconductors phase modes acquire a dipole moment and appear as a subgap spectral feature in the optical conductivity. This finding is obtained with both a gauge-invariant random-phase approximation scheme based on a fermionic Bogoliubov-de Genne…
By solving the Bogoliubov-de Gennes equations for a $d$-wave superconductor, we explore how the interplay between disorder and the orbital depairing of an external magnetic field influences the superconductor-metal transition of the hole-overdoped cuprates. For highly disordered systems, we find granular Cooper paring to persist above the critical field where the superfluid stiffness goes to zero. We also show that because the vortices are attracted to regions where the superconducting pairing is already weak, the Caroli-de Gennes-Matricon zero-bias peak in the local density of states at the v…
Recent experiments on disordered superconductors find that the superfluid density $n_s(T)$ decreases dramatically and characteristically with disorder, differently from what is expected for a mean order parameter field or BCS, amplitude only, picture for the superconductor. We describe here a new microscopic free energy functional which explicitly describes its dependence on both the amplitude and phase of superconducting order, in a gauge invariant manner. We use this here in an approximation of noninteracting phase fluctuations (Gaussian or harmonic approximation) to obtain $n_s(T)$ in the p…
In this paper we introduce a novel method for fabricating MgB$_2$/MgO multilayers and demonstrate the potential for using them as a new model for disordered superconductors. In this approach we control the annealing of the MgB$_2$ to yield an interesting new class of disordered (amorphous) superconductors with relatively high transition temperatures. The multilayers appear to exhibit quasi-two-dimensional superconductivity with controlled anisotropy. We discuss the properties of the multilayers as the thickness of the components of the bilayers vary.
Tunneling density of states measurements of disordered superconducting (SC) Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov (dLO) phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The dLO superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states, which lea…
We apply the coherent potential approximation (CPA) to a simple model for disordered superconductors with d-wave pairing. We demonstrate that whilst the effectiveness of an electronic Van Hove singularity to enhance the transition temperature T$_c$ is reduced by disorder it is not eliminated. In fact we give a qualitative account of changes in the T$_c$ vs. doping curve with increasing disorder and compare our results with experiments on the Y_{0.8}Ca_{0.2}Ba_2(Cu_{1-c}Zn_c)_{3}O_{7-δ} alloys.
We investigate the quantum phase transitions of a disordered nanowire from superconducting to metallic behavior by employing extensive Monte Carlo simulations. To this end, we map the quantum action onto a (1+1)-dimensional classical XY model with long-range interactions in imaginary time. We then analyze the finite-size scaling behavior of the order parameter susceptibility, the correlation time, the superfluid density, and the compressibility. We find strong numerical evidence for the critical behavior to be of infinite-randomness type and to belong to the random transverse-field Ising unive…
Electronic heat capacity was calculated for a mesoscopically disordered s-wave superconductor treated as a spatial ensemble of domains with a continuously varying superconducting properties. The domains are assumed to have sizes larger than the coherence length. Each domain is characterized by a certain critical temperature. The averaging over the superconducting gap distribution leads to quadratic temperature dependence of the specific heat at low temperatures, whereas its anomaly at the critical temperature is substantially smeared. The results explain well the heat capacity data for MgB$_{2…
Superconductor-to-Insulator transition (SIT) is a phenomenon occurring for highly disordered superconductors and is suitable for a superconducting switch development. SIT has been demonstrated to be induced by different external parameters such as temperature, magnetic field, electric field, etc. However, electric field induced SIT (ESIT), which has been experimentally demonstrated for some specific materials, holds the promise of any practical device development. Here, we demonstrate, from theoretical considerations, the occurrence of ESIT. We also propose a general switching device architect…
We study, by means of three-dimensional Monte Carlo simulations, the current-voltage (IV) characteristics and the voltage noise spectrum at low temperatures of driven magnetic flux lines interacting with randomly placed point or columnar defects, as well as with periodically arranged linear pinning centers. Near the depinning current J_c, the voltage noise spectrum S(w) universally follows a 1/w^a power law. For currents J > J_c, distinct peaks appear in S(w) which are considerably more pronounced for extended as compared to point defects, and reflect the spatial distribution of the correlated…
Mechanical stress causes motion of defects in solids. We show that in a type-II superconductor a moving dislocation generates a pattern of current that exerts the depinning force on the surrounding vortex lattice. Concentration of dislocations and the mechanical stress needed to produce critical depinning currents are shown to be within practical range. When external magnetic field and transport current are present this effect generates voltage across the superconductor. Thus a superconductor can serve as an electrical sensor of the mechanical stress.
We study the non-equilibrium relaxation kinetics of interacting magnetic flux lines in disordered type-II superconductors at low temperatures by means of a three-dimensional elastic line model and Monte Carlo simulations. Investigating the vortex density and height autocorrelation functions as well as the flux line mean-square displacement, we observe the emergence of glassy dynamics, caused by the competing effects of vortex pinning due to point defects and long-range repulsive interactions between the flux lines. Our systematic numerical study allows us to carefully disentangle the associate…
Order-disorder transitions take place in many physical systems, but observing them in detail in real materials is difficult. In two- or quasi-two-dimensional systems, the transition has been studied by computer simulations and experimentally in electron sheets, dusty plasmas, colloidal and other systems. Here I show the different stages of defect formation in the vortex lattice of a superconductor while it undergoes an order-disorder transition by presenting real-space images of the lattice from scanning tunneling spectroscopy. When the system evolves from the ordered to the disordered state, …
We introduce a model describing vortices in strongly disordered three-dimensional superconductors. The model focuses on the topological defects, i.e., dislocation lines, in an elastic description of the vortex lattice. The model is studied using Monte Carlo simulations, revealing a glass phase at low temperatures, separated by a continuous phase transition to the high temperature resistive vortex liquid phase. The critical exponents nu ~ 1.3 and eta ~ -0.4 characterizing the transition are obtained from finite size scaling.
Applying a constant voltage to superconducting nanowires we find that its IV-characteristic exhibits an unusual S-behavior. This behavior is the direct consequence of the dynamics of the superconducting condensate and of the existence of two different critical currents: j_{c2} at which the pure superconducting state becomes unstable and j_{c1}<j_{c2} at which the phase slip state is realized in the system.
We examine the idea, postulated by Phillips et al., that a finite resistivity in $T \to 0$ limit in disordered granular superconducting (SC) films is explained as a consequence of the absence of phase stiffness in a phase glass (PG) peculiar to granular systems. It is found that a coupling between the nonzero PG order and the ordinary SC fluctuation makes the conductivity divergent. However, an actual drop of resistivity is argued to occur due to another SC glass ordering, induced by the precursory PG fluctuation, corresponding to the vortex-glass transition in a nonzero magnetic field.
We develop a theory of current-voltage (I-U) characteristics for superconductor-normal metal-superconductor (SNS) junctions. At small voltages and sufficiently low temperatures the I-U characteristics of the junction is controlled by the inelastic relaxation time, τ_{in}. In particular, the linear conductance is proportional to, τ_{in}. In this regime the I-U characteristics can be expressed solely in terms of dependence of the density of states in the normal region, ν(χ), on the phase difference of the order parameter across the the junction. In contrast, at large voltages the I-U characteris…
We study theoretically the ac Josephson effect in voltage biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current-voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resona…
We study suppression of superconductivity by disorder in d-wave superconductors, and predict the existence of (at least) two sequential low temperature transitions as a function of increasing disorder: a d -wave to -wave, and then an s-wave to metal transition. This is a universal property of the system which is independent of the sign of the interaction constant in the s-channel
We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological st…
