We investigate the influence of general forms of disorder on the robustness of superconductivity in multiband materials. Specifically, we consider a general two-band system where the bands arise from an orbital degree of freedom of the electrons. Within the Born approximation, we show that the interplay of the spin-orbital structure of the normal-state Hamiltonian, disorder scattering, and superconducting pairing potentials can lead to significant deviations from the expected robustness of the superconductivity. This can be conveniently formulated in terms of the so-called "superconducting fitness". In particular, we verify a key role for unconventional $s$-wave states, permitted by the spin-orbital structure and which may pair electrons that are not time-reversed partners. To exemplify the role of Fermi surface topology and spin-orbital texture, we apply our formalism to the candidate topological superconductor Cu$_x$Bi$_2$Se$_3$, for which only a single band crosses the Fermi energy, as well as models of the iron pnictides, which possess multiple Fermi pockets.
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.
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 robustness against local perturbations, as long as the symmetry of the system is preserved, is a distinctive feature of topological quantum states. Magnetic impurities and defects break time-reversal invariance and, consequently, time-reversal invariant (TRI) topological superconductors are fragile against this type of disorder. Non-magnetic impurities, however, preserve time-reversal symmetry and one naively expects a TRI topological superconductor to persist in the presence of non-magnetic impurities. In this work, we study the effect of non-magnetic disorder on a TRI topological superco…
We show, using a simple model, how ordinary disorder can gap an extended-$s$ ($A_{1g}$) symmetry superconducting state with nodes. The concommitant crossover of thermodynamic properties, particularly the $T$-dependence of the superfluid density, from pure power law behavior to an activated one is exhibited. We discuss applications of this scenario to experiments on the ferropnictide superconductors.
Effects of non-magnetic disorder on the critical temperature T_c and on diamagnetism of quasi-one-dimensional superconductors are reported. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between wires and that T_c vanishes discontinuously at a critical disorder-strength. The parallel and transverse components of the penetration-depth are evaluated. They diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-cohe…
The understanding of disorder has profoundly influenced the development of condensed matter physics, explaining such fundamental effects as, for example, the transition from ballistic to diffusive propagation, and the presence of quantized steps in the quantum Hall effect. For superconductors, the response to disorder reveals crucial information about the internal gap symmetries of the condensate, and thereby the pairing mechanism itself. The destruction of superconductivity by disorder is traditionally described by Abrikosov-Gor'kov (AG) theory, which however ignores spatial modulations and c…
We study the basic features of the local density of states (LDOS) observed in STM experiments on high-T$_c$ d-wave superconductors in the context of a minimal model of a d-wave superconductor which has {\it weakly} modulated off-diagonal disorder. We show that the low and high energy features of the LDOS are consistent with the observed experimental patterns and in particular, the anisotropic local domain features at high energies. At low energies, we obtain not only the scattering peaks predicted by the octet model, but also weak features that should be experimentally accessible. Finally, we …
The density of states of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, measured by scanning tunneling spectroscopy on \textit{in-situ} cleaved surfaces, reveals a logarithmic suppression near the Fermi edge persisting above the critical temperature $T_\mathrm{c}$. A soft Hubbard gap as predicted by the Anderson-Hubbard model for systems with disorder exactly describes the experimentally observed suppression. The electronic disorder also explains the diminished coherence peaks of the quasiparticle density of states below $T_\mathrm{c}$.
The effect of disorder on the superconducting transition temperature $T_{c}$ of cuprate superconductors is examined. Disorder is introduced into the cation sites in the plane adjacent to the CuO$_{2}$ planes of two single-layer systems, Bi$_{2.0}$Sr$_{1.6}$Ln$_{0.4}$CuO$_{6+δ}$ and La$_{1.85-y}$Nd$_{y}$Sr$_{0.15}$CuO$_{4}$. Disorder is controlled by changing rare earth (Ln) ions with different ionic radius in the former, and by varying the Nd content in the latter with the doped carrier density kept constant. We show that this type of disorder works as weak scatterers in contrast to the in-pla…
When periodicity of crystal is disturbed by atomic disorder, its electronic state becomes inhomogeneous and band dispersion is obscured. In case of Fe-based superconductors, disorder of chalcogen/pnictogen height causes disorder of Fe 3d level splitting. Here, we report an angle-resolved photoemission spectroscopy study on FeSe_1-xTe_x with the chalcogen height disorder, showing that the disorder affects the Fe 3d band dispersions in an orbital-selective way instead of simple obscuring effect. The reverse of the Fe 3d level splitting due to the chalcogen height difference causes the splitting …
Recent experimental and theoretical studies have highlighted the possible role of a electronic nematic liquid in underdoped cuprate superconductors. We calculate, within a model of d-wave superconductor with Hubbard correlations, the spin susceptibility in the case of a small explicitly broken rotational symmetry of the underlying lattice. We then exhibit how the induced spin response asymmetry is strongly enhanced by correlations as one approaches the instability to stripe order. In the disorder-induced stripe phase, impurities become spin nematogens with a C_2 symmetric impurity resonance st…
We propose a mechanism whereby disorder can enhance the transition temperature Tc of an unconventional superconductor with pairing driven by exchange of spin fluctuations. The theory is based on a self-consistent real space treatment of pairing in the disordered one-band Hubbard model. It has been demonstrated before that impurities can enhance pairing by softening the spin fluctuations locally; here, we consider the competing effect of pair-breaking by the screened Coulomb potential also present. We show that, depending on the impurity potential strength and proximity to magnetic order, this …
Non-magnetic impurities are known as strong pair breakers in superconductors with pure d-wave pairing symmetry. Here we discuss d-wave states under the combined influence of impurities and competing instabilities, such as pairing in a secondary channel as well as lattice symmetry breaking. Using the self-consistent T-matrix formalism, we show that disorder can strongly modify the competition between different pairing states. For a d-wave superconductor in the presence of a subdominant local attraction, Anderson's theorem implies that disorder always generates an s-wave component in the gap at …
Effects of non-magnetic randomness on the critical temperature T_c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T_c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking …
On the basis of the Hubbard model, we extend the fluctuation-exchange (FLEX) approach to investigating the properties of antiferromagnetic (AF) phase in electron-doped cuprate superconductors. Furthermore, by incorporating the effect of scatterings due to the disordered dopant-atoms into the FLEX formalism, our numerical results show that the antiferromagnetic transition temperature, the onset temperature of pseudogap due to spin fluctuations, the spectral density of the single particle near the Fermi surface, and the staggered magnetization in the AF phase as a function of electron doping can…
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…
We investigate the influence of disorders in terminal ethylene groups of BEDT-TTF molecules (ethylene-disorders) on the vortex pinning of the organic superconductor $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br. Magnetization measurements are performed under different cooling-processes. The second peak in the magnetization hysteresis curve is observed for all samples studied, and the hysteresis width of the magnetization becomes narrower by cooling faster. In contradiction to the simple pinning effect of disorder, this result shows the suppression of the vortex pinning force by introducing more ethylene-d…
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…
We calculate superfluid density for a dirty d-wave superconductor. The effects of impurity scattering are treated within the self-consistent t-matrix approximation, in weak-coupling BCS theory. Working from a realistic tight-binding parameterization of the Fermi surface, we find a superfluid density that is both correlated with T_c and linear in temperature, in good correspondence with recent experiments on overdoped La2-xSrxCuO4.
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 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…
Using model calculations of a disordered d-wave superconductor with on-site Hubbard repulsion, we show how dopant disorder can stabilize novel states with antiferromagnetic order. We find that the critical strength of correlations or impurity potential necessary to create an ordered magnetic state in the presence of finite disorder is reduced compared to that required to create a single isolated magnetic droplet. This may explain why in cuprates like LSCO low-energy probes have identified a static magnetic component which persists well into the superconducting state, whereas in cleaner systems…
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…
A model for high-temperature superconductors incorporating antiferromagnetism, d-wave superconductivity, and no double lattice-site occupancy can give energy surfaces exquisitely balanced between antiferromagnetic and superconducting order for specific ranges of doping and temperature. The resulting properties can reconcile a universal cuprate phase diagram with rich inhomogeneity, relate that inhomogeneity to pseudogaps, give a fundamental rationale for giant proximity effects and other emergent behavior, and provide an objective framework for separating essential from peripheral in the super…
We investigate the effect of site-disorder on the superconducting (SC) state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength ($U$), the SC order parameter (OP) decreases monotonically with increasing disorder ($x$), while the single-particle spectral gap (SG) decreases for small $x$, reaches a minimum and keeps increasing for larger $x$. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth…
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…
A powerful approach to analysing quantum systems with dimensionality $d>1$ involves adding a weak coupling to an array of one-dimensional (1D) chains. The resultant quasi-one-dimensional (q1D) systems can exhibit long-range order at low temperature, but are heavily influenced by interactions and disorder due to their large anisotropies. Real q1D materials are therefore ideal candidates not only to provoke, test and refine theories of strongly correlated matter, but also to search for unusual emergent electronic phases. Here we report the unprecedented enhancement of a superconducting instabili…
We apply the Coherent Potential Approximation (CPA) to an extended Hubbard model to describe disordered superconductors with d-wave pairing. We discuss the pair-breaking effect caused by non-magneticdisorder in presence of Van Hove Singularity.
We calculate the relaxation rate of a nuclear spin in s-wave superconductor with nonmagnetic impurities, including the strong-coupling effects. We show that in a weakly disordered three-dimensional system the corrections due to disorder are negligibly small.
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 the influence of weak disorder on the fluctuation driven first order transition found in a p-wave superconductor. The flow equations for the disorder averaged effective theory is derived in an $4-ε$ expansion. The fixed point structure of these flow equations and their stability is discussed.
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.
We implement the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We demonstrate explicitly that increasing disorder leads to the formation of islands where the superconducting order is enhanced and subsequently to the transition to a metal. We study the behavior of the superfluid density and of the conductivity as a function of the strength of disorder. We find explanations for various marked features in the conductivities in terms of hydrodynamic quasi-normal modes of the holographic superconductors. These identifications plus a …
While insensitive to weak non magnetic disorder, an s-wave superconductor can be driven insulating by strong disorder. Using a scheme that captures the correct ground state, and fully retains thermal amplitude and phase fluctuations, we describe the disorder driven superconductor-insulator transition at finite temperature. Our results on the resistivity suggest that beyond moderate disorder the low temperature superconducting state can arise out of an insulating normal state. We also find that the low frequency weight in the density of states and optical conductivity are non monotonic in disor…
We provide a self-contained account of the B vs. H constitutive relation near H_c1 in Type II superconductors with various types of quenched random disorder. The traditional Abrikosov result B ~ [ln (H - H_c1)]^{-2}, valid in the absence of disorder and thermal fluctuations, changes significantly in the presence of disorder. Moreover, the constitutive relations will depend strongly on the type of disorder. In the presence of point disorder, B ~ (H - H_c1)^{3/2} in three-dimensional (thick) superconductors, as shown by Nattermann and Lipowsky. In two-dimensional (thin film) superconductors with…
We study the effect of disorder symmetry in a disordered s-wave superconductor. We begin with an attractive Hubbard model on a two-dimensional square lattice in the presence of diagonal- and off-diagonal disorder. The model is studied numerically using Bogoliubov-deGennes mean-field approach. We find that the off-diagonal disorder is much more efficient in destroying superconducting order. A detailed analysis brings out very distinct qualitative pictures in the two cases: diagonal disorder leads to formation of small scale isolated superconducting islands separated by large region of normal me…
We study the effect of site diagonal disorder on the pairing amplitude by a perturbation method. Using an extended Hubbard model with the intersite attraction we analyze fluctuations of order parameter in presence of non-magnetic disorder and discuss the instability of various solutions with p-wave paring.
Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disorder on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting natu…
Isolated islands in two-dimensional strongly-disordered and strongly-coupled superconductors become optically active inducing sub-gap collective excitations in the ac conductivity. Here, we investigate the fate of these excitations as a function of the disorder strength in the experimentally relevant case of weak electron-phonon coupling. An explicit calculation of the ac conductivity, that includes vertex corrections to restore gauge symmetry, reveals the existence of collective sub-gap excitations, related to phase fluctuations and therefore identified as the Goldstone modes, for intermediat…
We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass and a Gaussian phase glass. The first two models, describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field while the last two describe the effects of random negative Josephson-junction couplings or $π$ junctions. Monte Carlo simulations in the path-integral representation of the models ar…
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…
We make the first testable predictions for the local two-particle spectral function of a disordered s-wave superconductor, probed by scanning Josephson spectroscopy (sjs), providing complementary information to scanning tunneling spectroscopy (sts). We show that sjs provides a direct map of the local superconducting order parameter that is found to be anticorrelated with the gap map obtained by sts. Furthermore, this anticorrelation increases with disorder. For the momentum resolved spectral function, we find the Higgs mode shows a non-dispersive subgap feature at low momenta, spectrally separ…
Motivated by the recent experimental observation of the topological Anderson insulator in disordered atomic wires based on the Su-Schrieffer-Heeger (SSH) model, we study disorder effects on a dimerized Kitaev superconductor chain which is regarded as the superconductor version of the SSH model. By computing the real-space winding number and the zero-bias differential conductance, we analyze the topological phase transitions occurring in a dimerized Kitaev superconductor chain with disorder. It is found that disorder can induce a topologically nontrivial superconductor phase hosting Majorana ze…
We study numerically the superconductor to insulator transition in two-dimensional phase-glass (or chiral-glass) models with varying degree of disorder. These models describe the effects of gauge disorder in superconductors due to random negative Josephson-junction couplings, or $π$ junctions. Two different models are considered, with binary and Gaussian distribution of quenched disorder, having nonzero mean. Monte Carlo simulations in the path-integral representation are used to determine the phase diagram and critical exponents. In addition to the usual superconducting and insulating phases,…
As a prototype of a disordered superconductor we consider the attractive Hubbard model with on-site disorder. We solve the Bogoljubov-de-Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the…
We isolated flux disorder effects on the transport at the critical point of the quantum magnetic field tuned Superconductor to Insulator transition (BSIT). The experiments employed films patterned into geometrically disordered hexagonal arrays. Spatial variations in the flux per unit cell, which grow in a perpendicular magnetic field, constitute flux disorder. The growth of flux disorder with magnetic field limited the number of BSITs exhibited by a single film due to flux matching effects. The critical metallic resistance at successive BSITs grew with flux disorder contrary to predictions of …
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…
Noncentrosymmetric superconductors with strong spin-orbit coupling and the B phase of ${}^3$He are possible realizations of topological superconductors with time-reversal symmetry. The nontrivial topology of these time- reversal invariant superconductors manifests itself at the material surface in the form of helical Majorana modes. In this paper, using extensive numerical simulations, we investigate the stability and properties of these Majorana states under strong surface disorder, which influences both bulk and surface states. To characterize the effects of strong disorder, we compute the l…
Measurements of transport properties of amorphous insulating indium oxide thin films have been interpreted as evidence of the presence of superconducting islands on the insulating side of a disorder-tuned superconductor-insulator transition. Although the films are not granular, the behavior is similar to that observed in granular films. The results support theoretical models in which the destruction of superconductivity by disorder produces spatially inhomogenous pairing with a spectral gap.
Weakly disordered two-dimensional (2D) superconductors can host richer quantum phase transitions than their highly-disordered counterparts. This is due to the insertion of a metallic state in the transition between a superconductor and an insulator. Disorders were predicted to show profound influences on the boundaries surrounding this intermediate metallic phase, affecting the existence of a metallic ground state called Bose metal and the dynamic processes in a quantum Griffiths state. Here we present a study on quantum phase transitions of a clean 2D superconductor, MoS2, under a perpendicul…
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.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a superconducting state stabilized by a large Zeeman splitting between up- and down-spin electrons in a singlet superconductor. In the absence of disorder, the superconducting order parameter has a periodic spatial structure, with periodicity determined by the Zeeman splitting. Using the Bogoliubov-de Gennes (BdG) approach, we investigate the spatial profiles of the order parameters of FFLO states in a two-dimensional s-wave superconductors with nonmagnetic impurities. The FFLO state is found to survive under moderate disorder strength, and …
The notion of spontaneous formation of an inhomogeneous superconducting state is at the heart of most theories attempting to understand the superconducting state in the presence of strong disorder. Using scanning tunneling spectroscopy and high resolution scanning transmission electron microscopy, we experimentally demonstrate that under the competing effects of strong homogeneous disorder and superconducting correlations, the superconducting state of a conventional superconductor, NbN, spontaneously segregates into domains. Tracking these domains as a function of temperature we observe that t…
More than fifty years old "Anderson's theorem" suggests disorder-independent pair-amplitude and critical temperature at low to moderate strength of disorders. In spite of the extension of this paradigm and several subsequent theoretical proposals, mechanism for the superconductor-insulator transition (SIT) at large disorder is still an open problem. The understanding of experimental data at intermediate disorder is also lacking. Here, we proceed beyond "Anderson's theorem" by calculating disorder-averaged two-point pair-amplitude fluctuations. We find this correlation to be finite and long-ran…
We study the effect of site diagonal, non-magnetic, disorder on the a pairing amplitude in an extended Hubbard model with the intersite attraction. Analyzing fluctuations of a pairing potential we discuss the instability of mixed solutions, 's+d' and 's+id', in presence of disorder. The influence of disorder on extended s- and d-wave superconductors appear to be comparable but in certain regions of the phase diagram, even weak disorder can change the symmetry of the order parameter.
