A model was proposed to account for a new kind of history effect in the transport measurement of a sample with inhomogeneous flux pinning coupled with flux creep. The inhomogeneity of flux pinning was described in terms of alternating weak pinning (lower jc) and strong pinning region (higher jc). The flux creep was characterized by logarithmic barrier. Based on this model, we numerically observed the same clockwise V-I loops as reported in references. Moreover, we predicted behaviors of the V-I loop at different sweeping rates of applied current dI/dt or magnetic fields Ba, etc. Electric transport measurement was performed in Ag-sheathed Bi2-xPbxSr2Ca2Cu3Oy tapes immersed in liquid nitrogen with and without magnetic fields. V-I loop at certain dI/dt and Ba was observed. It is found that the area of the loop is more sensitive to dI/dt than to Ba, which is in agreement well with our numerical results.
We study subgap states induced by a single impurity in an s-wave superconductor with suppressed pairing. For concreteness, we consider a bulk superconductor containing a normal spherical region. We find that a point impurity in this system induces two Yu-Shiba-Rusinov states inside the minigap instead of one, which one would have in a homogeneous superconductor. Moreover, the subgap states appear even if the impurity is nonmagnetic. We prove that this result actually holds almost for any superconductor with a real and spatially inhomogeneous order parameter, if the quasiparticle spectrum is ga…
The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability.
The problem of the thermal and magnetic destruction of the critical state in composite superconductors is investigated. The initial distributions of temperature and electromagnetic field are assumed to be essentially inhomogeneous. The limit of the thermomagnetic instability in quasi-stationary approximation is determined. The obtained integral criterion, unlike the analogous criterion for a homogeneous temperature profile, is shown to take into account the influence of any part of the superconductor on the threshold for critical-state instability.
We consider a superconductor hosting mobile impurities, which locally change the superconducting transition temperature. The BCS interaction at the impurity is different both in magnitude and in sign from the BCS interaction in the bulk. It is shown that due to the attraction between impurities, they tend to form more condensed state. We also consider the distribution of mobile impurities with local BCS attraction or repulsion at the vicinity of the superconductor-normal metal interface.
A new method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit (or Andreev approximation) of the Bogoliubov-de Gennes (or wave function) formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of …
We propose a possible mechanism of topological Hall effect in inhomogeneous superconducting states. In our scenario, the Berry phase effect associated with spatially modulated superconducting order parameter gives rise to a fictitious Lorentz force acting on quasiparticles. In the case of the Fulde-Ferrell-Larkin-Ovchinnikov state, the topological Hall effect is detected by applying an electromagnetic wave with a tuned wave number on a surface of the system.
An inhomogeneous transport current, which is introduced through multiple electrodes in an open Nb microtube, is shown to lead to a controllable branching of the vortex nucleation period. The detailed mechanism of this branching is analyzed using the time-dependent Ginzburg-Landau equation. The relative change of the vortex nucleation period strongly depends on the geometry of multiple electrodes. The average number of vortices occurring in the tube in a nanosecond can be effectively reduced owing to the inhomogeneous transport current, what is important for noise and energy dissipation reducti…
We study various inhomogeneity effects on superconductivity as due to quantum confinement, surfaces and impurities, using the self-consistent Bogoliubov-de Gennes formalism on the attractive Hubbard model. The results are also compared with those obtained from the Anderson prescription, a BCS formalism for incorporating spatial inhomogeneity.
We study a magnetic proximity effect at superconductor (S) - ferromagnet (F) interface. It is shown that due to an exchange of electrons between the F and S metals ferromagnetic correlations extend into the superconductor, being dependent on interface parameters. We show that ferromagnetic exchange field pair breaking effect leads to a formation of subgap bands in the S layer local density of states, that accommodate only one spin-polarized quasiparticles. Equilibrium magnetization leakage into the S layer as function of SF interface quality and a value of ferromagnetic interaction have also b…
We propose a model and derive analytical expressions for conductivity in heterogeneous fully anisotropic conductors with ellipsoid superconducting inclusions. This model and calculations are useful to analyze the observed temperature dependence of conductivity anisotropy in various anisotropic superconductors, where superconductivity onset happens inhomogeneously in the form of isolated superconducting islands. The results are applied to explain the experimental data on resistivity above the transition temperature $T_c$ in the high-temperature superconductor $\mathrm{YBa_2Cu_4O_8}$ and in the …
Nonequilibrium properties of short-coherence-length s-wave superconductors are analyzed in the presence of extrinsic and intrinsic inhomogeneities. In general, the lowest-energy configurations of quasiparticle excitations are topological textures where quasiparticles segregate into antiphase domain walls between superconducting regions whose order-parameter phases differ by $π$. Antiphase domain walls can be probed by various experimental techniques, for example, by optical absorption and NMR. At zero temperature, quasiparticles seldom appear as self-trapped bag states. However, for low concen…
The critical temperature (TC) of MgB2, one of the key factors limiting its application, is highly desired to be improved. On the basis of the meta-material structure, we prepared a smart meta-superconductor structure consisting of MgB2 micro-particles and inhomogeneous phases by an ex situ process. The effect of inhomogeneous phase on the TC of smart meta-superconductor MgB2 was investigated. Results showed that the onset temperature (Ton C) of doping samples was lower than those of pure MgB2. However, the offset temperature (Toff C) of the sample doped with Y2O3:Eu3+ nanosheets with a thickne…
Motivated by the recent optical conductivity experiments on Bi_2Sr_2CaCu_2O_{8+delta} films, we examine the possible origin of low-frequency dissipation in the superconducting state. In the presence of spatial inhomogeneity of the local phase stiffness rho_s, it is shown that some spectral weight is removed from omega=0 to finite frequencies and contribute to dissipation. A case where both rho_s and the local normal fluid density are inhomogeneous is also considered. We find an enhanced dissipation at low frequency if the two variations are anti-correlated.
The application of inhomogeneous niobium point-contacts in the superconducting stata for reconstructing the electron-phonon interaction function is considered. The method is based on the use of the nonlinearity of current-voltage curve, which is due to the inelastic processes of suppressing excess point contact current when nonequilibrium phonons are scattered from the electrons undergoing Andreev reflection. A new model of background occurrence in point-contact Yanson spectra and some ways to correct this background are proposed.
Scanning tunneling spectroscopy studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ suggest the presence of electronic inhomogeneity with a large spatial variation in gap size. Andersen {\it et al} have modelled this variation by assuming a spatially-varying pairing interaction. We show that their calculated specific heat is incompatible with the experimental data which exhibit narrow transitions. This calls into question the now-common assumption of gap and pairing inhomogeneity.
The vortex hopping motion in a type-II superconductor determines the current-carrying ability and consequently the application fields of the superconductor. However, it is not clear how the vortices hop between the different pinning regions in the superconductor. Here we proposed that there should be magnetic \textit{flux exchange} between two contacting pinning regions. A system of differential equations was constructed to describe the flux exchange phenomenon. The qualitative analysis methods were used. The approximate numerical solutions and approximate analytical solutions of the system we…
We study the holographically dual description of superconductor in (2+1)-dimensions in the presence of inhomogeneous magnetic field and observe that there exists type I and type II superconductor. A new feature of type changing is observed for type I superconductor near critical temperature.
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…
The microscopic approach was developed for obtaining of the free energy of a superconductor with help direct calculation of the vacuum amplitude. The functional of free energy of the spatially inhomogeneous superconductor in a magnetic field was obtained with help the developed approach. The obtained functional is generalization of Ginzburg-Landau functionals for any temperature, for arbitrary spatial variations of the order parameter and for the nonlocality of the order parameter and the magnetic response. Moreover the nonlocality of the magnetic response is the consequence of the order param…
On the basis of the idea that the injecting energy will improve the conditions for the formation of Cooper pairs, a smart meta-superconductor (SMSC) was prepared by doping inhomogeneous phase of luminescent nanocomposite Y2O3:Eu3+/Ag, which has the strong luminescence characteristic, in MgB2 to improve the superconducting transition temperature (TC) of the MgB2-based superconductor. Two types of Y2O3:Eu3+/Ag with different sizes were prepared and marked as m-Y2O3:Eu3+/Ag and nY2O3:Eu3+/Ag. MgB2 SMSC was prepared through an ex situ process. Results show that when the inhomogeneous phase content…
Incorporating with inhomogeneous phases with high electroluminescence (EL) intensity to prepare smart meta-superconductors (SMSCs) is an effective method of increasing the superconducting transition temperature (Tc) and has been confirmed in both MgB2 and Bi(Pb)SrCaCuO systems. However, the increase of ΔTc has been quite small because of the low optimal concentrations of inhomogeneous phases. In this work, three kinds of MgB2 raw materials, namely, aMgB2, bMgB2, and cMgB2, were prepared with particle sizes decreasing in order. Inhomogeneous phases, Y2O3:Eu3+ and Y2O3:Eu3+/Ag, were also prepare…
The high-T_c cuprate superconductors are now believed to be intrinsically inhomogeneous. We develop a theory to describe how this inhomogeneity affects the intermodulation coefficient of such a material. We show that the continuum equations describing intermodulation in a superconducting layer with spatially varying properties are formally equivalent to those describing an inhomogeneous dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we calculate the effect of inhomogeneity on the intermodulation coefficient in a high-T_c material, using several assumptions about the t…
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting (SC) state, first- and second-order phase transitions, and quantum criticality induced by spin accumulation in a ferromagnet-$d_{x^{2}-y^{2}}$-wave superconductor-ferromagnet tunnel junction are theoretically predicted. A complex phase diagram in the temperature-bias voltage plane is determined. It is found that the phase transitions from the homogeneous BCS state to the inhomogeneous FFLO state, and from the FFLO state with the momentum $\mathbf{% q}$'s azimuthal angle $θ_{\mathbf{q}}=0$ to that with $θ_{% \mathbf{q}}=π/4$, …
Thin film heterostructures provide a powerful means to study the antagonism between superconductivity (SC) and ferromagnetism (FM). One interesting issue in FM-SC hybrids which defies the notion of antagonistic orders is the observation of magnetic field induced superconductivity (FIS). Here we show that in systems where the FM domains/islands produce spatial inhomogeneities of the SC order parameter, the FIS can derive significant contribution from different mobilities of the magnetic flux identified by two distinct critical states in the inhomogeneous superconductor. Our experiments on nanoe…
We show that the conclusion reported in Ref. 1, that there are no spontaneous magnetic fields in multiband superconductors that break time reversal symmetry, is incorrect. We demonstrate that the state proposed in Ref. 1 is not a solution of the Ginzburg-Landau equations for the considered model. The reason is that in Ref. 1 one of the Ginzburg-Landau equations is neglected and substituted by the spurious zero current restriction. This restriction together with all of the Ginzburg-Landau equations leads to an overdetermined system which does not have a solution. This inconsistency invalidates …
We argue that the superconducting state found in high-$T_c$ cuprates is inhomogeneous with a corresponding inhomogeneous superfluid density. We introduce two classes of microscopic models which capture the magnetic and superconducting properties of these strongly correlated materials. We start from a generalized t-J model, in which appropriate inhomogeneous terms mimic stripes. We find that inhomogeneous interactions that break magnetic symmetries are essential to induce substantial pair binding of holes in the thermodynamic limit. We argue that this type of model reproduces the ARPES and neut…
The in-plane optical properties of the inhomogeneous iron-chalcogenide superconductor K_{0.8}Fe_{2-y}Se_2 with a critical temperature Tc = 31 K have been modeled in the normal state using the Bruggeman effective medium approximation for metallic inclusions in an insulating matrix. The volume fraction for the inclusions is estimated to be ~ 10%; however, they appear to be highly distorted, suggesting a filamentary network of conducting regions joined through weak links. The value for the Drude plasma frequency in the inclusions is much larger than the volume average, which when considered with …
We discuss the low-frequency absorption arising from quenched inhomogeneity in the superfluid density rho_s of a model superconductor. Such inhomogeneities may arise in a high-T_c superconductor from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. Using standard classical methods for treating randomly inhomogeneous media, we show that both mechanisms produce additional absorption at finite frequencies. For a two-fluid model with weak mean-square fluctuations <(d rho_s)^2 > in rho_s and a frequency-independent quasiparticle conducti…
Vortex matter in mesoscopic superconductors is known to be strongly affected by the geometry of the sample. Here we show that in nanoscale superconductors with coherence length comparable to the Fermi wavelength the shape resonances of the order parameter results in an additional contribution to the quantum topological confinement - leading to unconventional vortex configurations. Our Bogoliubov-de Gennes calculations in a square geometry reveal a plethora of asymmetric, giant multi-vortex, and vortex-antivortex structures, stable over a wide range of parameters and which are very different fr…
Nanoscale inhomogeneity seems to be a central feature of the d-wave superconductivity in the cuprates. Such a feature can strongly affect the local density of states (LDOS) and the spectral weight functions. Within the Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations of the superconducting order parameter to see which ones better agree with the experimental data. Nanoscale large amplitude oscillations in the order parameter seem to fit the LDOS data for the underdoped cuprates. The one-particle spectral function for a general inhomogeneous configuration exhibits a…
The force exerted by a semi-infinite inhomogeneous superconductor with a planar interface to vacuum on a magnetic tip is studied theoretically in the absence of external magnetic fields. It is shown that the force has a contribution from inhomogeneities due to material defects with unique characteristics. Defects are taken into account in the London limit by allowing the mass parameter to vary spatially. The contribution from defects to the force is calculated analytically to first order in the deviation of the mass parameter from its constant value for the homogeneous superconductor, assuming…
Using high speed scanning tunneling spectroscopy, we perform a full mapping of the quasiparticle density of states (DOS) in single crystals of BiPbSrCaCuO(2212). The measurements carried out at 5 K showed a complex spatial pattern of important variations of the local DOS on the nanometer scale. Superconducting areas are co-existing with regions of a smooth and larger gap-like DOS structure. The superconducting regions are found to have a minimum size of about 3 nm. The role of Pb-introduced substitutional disorder in the observed spatial variations of the local DOS is discussed.
We investigate the effect of an inhomogeneous exchange field on the proximity effect in superconductor-ferromagnet hybrid structures within the quasi-classical theory of superconductivity. As an example we study the proximity effect in a superconductor-ferromagnet bilayer with an in-plane spiral magnetic order in the ferromagnet. This model simulates a multiple magnetic domain structure where the domain walls of the Néel type are of equal size as the domains. Triplet correlations are induced in the bilayer by the superconducting proximity effect, which are sensitive to the local quantization a…
We report the results of a muon spin rotation (muSR) study of the bulk of Bi{2+x}Sr{2-x}CaCu2O{8+δ}, as well as pure and Ca-doped YBa2Cu3Oy, which together with prior measurements reveal a universal inhomogeneous magnetic-field response of hole-doped cuprates extending to temperatures far above the critical temperature (Tc). The primary features of our data are incompatible with the spatially inhomogeneous response being dominated by known charge density wave (CDW) and spin density wave (SDW) orders. Instead the normal-state inhomogeneous line broadening is found to scale with the maximum valu…
A smart meta-superconductor Bi(Pb)SrCaCuO (B(P)SCCO) may increase the critical transition temperature (TC) of B(P)SCCO by electroluminescence (EL) energy injection of inhomogeneous phases. However, the increase amplitude ΔTC (ΔTC=TC-T(C,pure)) of TC is relatively small. In this study, a smart meta-superconductor B(P)SCCO with different matrix sizes was designed. Three kinds of raw materials with different particle sizes were used, and different series of Y2O3:Sm3+, Y2O3, Y2O3:Eu3+, and Y2O3:Eu3++Ag doped samples and pure B(P)SCCO were prepared. Results indicated that the TC of the Y2O3 or Y2O3…
We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from non-trivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.
Increasing and improving the critical transition temperature (Tc), current density (Jc) and Meissner effect (Hc) of conventional superconductors are the most important problems in superconductivity research, but progress has been slow for many years. In this study, by introducing the p-n junction electroluminescent inhomogeneous phase with red wavelength to realize energy injection, we found the improved property of smart meta-superconductors MgB2, the critical transition temperature Tc increases by 0.8K, the current density Jc increases by 37%, and the diamagnetism of Meissner effect Hc also …
We study a model describing a four-dimensional holographic superconductor whose properties depend non-trivially on a particular spatial direction, namely a Josephson junction. We analyze the parameter dependence of the condensate and compare it to the condensed matter expectations.
We review the recent progress in the theory of inhomogeneous superconductors. It was shown that Gor'kov's self-consistency equation needs a pairing constraint derived from the Anomalous Green's function. The Bogoliubov-de Gennes equations also need a pairing constraint in order to obtain a correct vacuum state by the corresponding unitary transformation. This new study opens up a reinvestigation of inhomogeneous superconductors. We discuss (i) problems of the conventional Green's function theory, (ii) reinvestigation of impure superconductors, and (iii) impurity doping effect in high $T_{c}$ s…
We propose the ultra-fast numerical approach to large-scale inhomogeneous superconductors, which we call the Localized Krylov Bogoliubov-de Gennes method (LK-BdG). In the LK-BdG method, the computational complexity of the local Green's function, which is used to calculate the local density of states and the mean-fields, does not depend on the system size $N$. The calculation cost of self-consistent calculations is ${\cal O}(N)$, which enables us to open a new avenue for treating extremely large systems with millions of lattice sites. To show the power of the LK-BdG method, we demonstrate a sel…
For an inhomogeneous high-Tc superconductor, band-filling dependence of Josephson I_cR_n product is deduced at T=0 K by means of measurement; this is an extension of the Ambegaokar - Baratoff (AB) theory based on the s-wave theory. The product is given by J_{obs}R_n ={1.57}{rho}{Gap_i}={rho}J_iR_n, where 0<{rho}<=1 is band filling (or local density), and {Gap_i} is the intrinsic superconducting true gap and small. When {rho}=1, J_{obs}R_n=J_iR_n is the intrinsic Josephson true product (or the AB product), where J_i is the intrinsic Josephson true current occurring by Cooper pair. When 0<{rho}<…
We study numerically the time evolution of the transport properties of layered superconductors after different preparations. We show that, in accordance with recent experiments in BSCCO performed in the second peak region of the phase diagram (Portier et al, 2001), the relaxation strongly depends on the initial conditions and is extremely slow. We investigate the dependence on the pinning center density and the perturbation applied. We compare the measurements to recent findings in tapped granular matter and we interpret our results with a rather simple picture.
By combining very low temperature scanning tunneling microscopy and spectroscopy on a TiN film we have observed a non uniform state comprising of superconducting (S) and normal (N) areas. The local density of states displays a spatial dependence between S and N different from the usual proximity effect. We conclude that mesoscopic fluctuations might play a major role in accordance with recent theories on superconductor-normal metal quantum transition.
We study the spectral and thermodynamic properties of inhomogeneous d-wave superconductors within a model where the inhomogeneity originates from atomic scale pair disorder. This assumption has been shown to be consistent with the small charge and large gap modulations observed by scanning tunnelling spectroscopy (STS) on BSCCO. Here we calculate the specific heat within the same model, and show that it gives a semi-quantitative description of the transition width in this material. This model therefore provides a consistent picture of both surface sensitive spectroscopy and bulk thermodynamic …
The current-voltage characteristics (IVC) of $S-c-N$ point contacts of superconductors with a small coherence length ${ξ_{0}}$ reveal steps with discrete values of the differential resistance. This peculiarity is associated with a transition of the contact region of the superconductor to a spatially inhomogeneous state under the influence of the current injection of nonequilibrium quasiparticles penetrating the superconductor to a depth ${{l}_{E}}$ . The role of the relaxation of the disbalance between the occupancies of electron- and hole-like branches of the quasiparticle spectrum is manifes…
We calculate transport properties of disordered 2D d-wave superconductors from solutions of the Bogoliubov-de Gennes equations, and show that weak localization effects give rise to a finite frequency peak in the optical conductivity similar to that observed in experiments on disordered cuprates. At low energies, order parameter inhomogeneities induce linear and quadratic temperature dependencies in microwave and thermal conductivities respectively, and appear to drive the system towards a quasiparticle insulating phase.
Among the mysteries surrounding unconventional, strongly correlated superconductors is the possibility of spatial variations in their superfluid density. We use atomic-resolution Josephson scanning tunneling microscopy to reveal a strongly inhomogeneous superfluid in the iron-based superconductor FeTe0.55Se0.45. By simultaneously measuring the topographic and electronic properties, we find that this inhomogeneity in the superfluid density is not caused by structural disorder or strong inter-pocket scattering, and does not correlate with variations in Cooper pair-breaking gap. Instead, we see a…
We study the effect of morphology on the low temperature behavior of superconducting nanowires of length $\approx$100 nm. A well-defined superconductor-insulator transition (SIT) is observed only in homogenous wires, in which case the transition occurs when the normal resistance is close to $h/4e^2$. Inhomogeneous wires, on the other hand, exhibit a mixed behavior, such that signatures of the superconducting and insulating regimes can be observed in the same sample. The resistance versus temperature curves of inhomogeneous wires show multiple steps, each corresponding to a weak link constricti…
The nature of five-quadrant magnetic isotherms for is different from that for in a single crystal of YNi2B2C, pointing towards an anisotropic behaviour of the flux line lattice (FLL). For, a well defined peak effect (PE) and second magnetization peak (SMP) can be observed and the loop is open prior to the PE. However, for, the loop is closed and one can observe only the PE. We have investigated the history dependence of magnetization hysteresis data for by recording minor hysteresis loops. The observed history dependence in across different anomalous regions are rationalized on the basis of su…
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…
For an inhomogeneous high-T_c superconductor, band-filling dependence of Josephson current and Josephson product is deduced at T=0 K by means of measurement; this is an extension of Ambegaokar-Baratoff Josephson current and product. The observed Josephson current, J_{obs}, is given by J_{obs}=ρJ_i, where 0<ρ<=1 is band filling (or local density). When ρ=1, J_{obs} = J_i is the intrinsic supercurrent occurring by Cooper pair. When 0<ρ<1, J_{obs} is an average of J_i over the measurement region and is the effect of measurement. The observed Ambegaokar-Baratoff Josephson product, based on the s-w…
Impurity resonances observed by scanning tunneling spectroscopy in the superconducting state have been used to deduce properties of the underlying pure state. Here we study a longstanding puzzle associated with these measurements, the apparent extinction of these resonances for Ni and Zn impurities in large-gap regions of the inhomogeneous BSCCO superconductor. We calculate the effect of order parameter and hopping suppression near the impurity site, and find that these two effects are sufficient to explain the missing resonances in the case of Ni. There are several possible scenarios for the …
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 …
We analyze non-equilibrium states in a tunnel superconductor-normal metal (NSN) structure in the presence of a tunnel current $I$. We use an approximation of an effective temperature $T$ and calculate the current-voltage I-V characteristics. It is shown that the I-V dependence may have an S-shaped form. We determine nonuniform current $I(x)$ and temperature $T(x)$ distributions that arise as a result of instability of the uniform state with negative differential conductance ($dI/dV<0$). We discuss an analogy with equilibrium superconductors with an exchange field in which nonuniform states pre…
Spatial fluctuations of the effective pairing interaction between electrons in a superconductor induce variations of the order parameter which in turn lead to significant changes in the density of states. In addition to an overall reduction of the quasi-particle energy gap, theory suggests that mesoscopic fluctuations of the impurity potential induce localised tail states below the mean-field gap edge. Using a field theoretic approach, we elucidate the nature of the states in the `sub-gap' region. Specifically, we show that these states are associated with replica symmetry broken instanton sol…
First- and second-order phase transitions, Fulde-Ferrel (FF) inhomogeneous superconducting (SC) state and quantum criticality in ferromagnet/superconductor/ferromagnet double tunnel junctions are investigated. For the antiparallel alignment of magnetizations, it is shown that a first-order phase transition from the homogeneous BCS state to the inhomogeneous FF state occurs at a certain bias voltage $V^{\ast}$; while the transitions from the BCS state and the FF state to the normal state at $% V_{c}$ are of the second-order. A phase diagram for the central superconductor is presented. In additi…
Particle-wave duality suggests we think of electrons as waves stretched across a sample, with wavevector k proportional to their momentum. Their arrangement in "k-space," and in particular the shape of the Fermi surface, where the highest energy electrons of the system reside, determine many material properties. Here we use a novel extension of Fourier transform scanning tunneling microscopy to probe the Fermi surface of the strongly inhomogeneous Bi-based cuprate superconductors. Surprisingly, we find that rather than being globally defined, the Fermi surface changes on nanometer length scale…
