Josephson-coupled Layered Superconductors Research Articles

Intrinsic pinning of vortices as a direct probe of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell state in layered superconductors.

Previously the search for the modulated superconducting Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state was performed by means of measurements which do not give direct information on spatial modulation of the superconducting state. We propose to measure interlayer conductivity in Josephson-coupled layered superconductors as a function of the strength and the orientation of the parallel magnetic field. We show that interlayer critical current and the conductivity have peaks when the magnetic field is perpendicular to the in-plane wave vector of the LOFF state and when the period of the Josephson vortex lattice induced by the magnetic field is commensurate with the LOFF period.

Charging effects on the critical temperature of the Josephson-coupled layered superconductors

Effects of quantum phase fluctuations on the critical temperature T c of Josephson-coupled layered superconductors are considered. T c is shown to decrease nonlinearly with increasing charge fluctuations. The results obtained for the critical temperature by applying the self-consistent mean field method reveal no phase transition from superconducting state to normal metal for a finite value of charging energy. The destruction of the long range phase coherence appeared to occur at asymptotically large values of self-capacitance charging. For the weak quantum phase fluctuations limit, T c is obtained to be vary in the interval of T c *< T c< T c (2), where T c (2) is the critical temperature for a single superconducting layer evaluated by the mean field theory, and T c * is the temperature when the phase coherence between the nearest neighboring layers is lost. Since T c approaches T c * with vanishing interlayer tunneling integral J ⊥. Calculation of the dependence of the transverse stiffness on the charging energy is carried out at T=0. The reentrance found can in principle occur at a sufficiently large value of the interlayer tunneling integral J ⊥> J ⊥ cr= k T c (2), where J ⊥ cr≈ k T c (2) is the value of J ⊥ when the superconductor normal metal phase transition takes place. However, the condition J ⊥≥ k T c (2) contradicts to the existence of the Josephson coupling between superconducting layers.

Quantum theory for the longitudinal Josephson plasma in Josephson-coupled layered superconductors

A theory for the longitudinal Josephson plasma in 1D series of Josephson junctions is formulated in the presence of a bias current. The plasma level lowers as the bias current increases. The critical current shows significant deviation from the Ambegaokar-Baratoff result when the plasma-plasma scattering is strong.

Interlayer electrical transport in Bi-2212 intrinsic Josephson junctions

The field and temperature dependence of the critical current I c has been investigated on the intrinsic Josephson junctions of Bi 2Sr 2CaCu 2O 8+δ single crystals. Under the magnetic fields at a few kG along the c-axis, I c shows a distinct maximum at ≈ 20 K, which possibly corresponds to an anomaly observed in the recent plasma-resonance measurements. The field dependence of I c exhibits power-law behavior, as predicted theoretically for the Josephson-coupled layered superconductors in a strong pinning regime.

I-V characteristics of Josephson-coupled layered superconductors with longitudinal plasma excitations.

Coupled equations for the interlayer phase differences in Josephson-coupled layered superconductors are derived in both current-biased and voltage-biased cases. These equations have a solution corresponding to the longitudinal Josephson plasma propagating along the {ital c} axis. Using the numerical solutions for the systems composed of 100 junctions, we calculate the {ital I}-{ital V} characteristics of the Josephson-coupled layered superconductors in the absence of an external magnetic field. Various types of {ital I}-{ital V} characteristics reflecting the dynamics of the phase differences are obtained. {copyright} {ital 1996 The American Physical Society.}

Interaction of Pancake Vortices with c-Axis Plasmon in Josephson-Coupled Layered Superconductors

The power-law dependence of plasma resonance frequency on magnetic field applied along the c-axis is explained in the model of strong disorder in pancake positions along the c-axis. The line width of plasma resonance is explained by inhomogeneous broadening caused by random positions of pancake vortices in the vortex glass phase. This leads to a nearly temperature independent line width which is inversely proportional to magnetic field. The dynamic interaction of vortices with plasmon is calculated. It is ineffective in fields studied but may become stronger in crystals with weaker pinning or in higher magnetic fields.

Inertial Mass and Viscosity of Tilted Vortex Lines in Layered Superconductors.

The dynamics of tilted vortex lines in Josephson-coupled layered superconductors is considered within the time-dependent Ginzburg-Landau theory. The frequency and angular dependences of the complex-valued vortex mobility $\mu$ are studied. The components of the viscosity and inertial mass tensors are found to increase essentially for magnetic field orientations close to the layers. For superconducting/normal metal multilayers the frequency ($\omega$) range is shown to exist where the $\mu^{-1}$ value depends logarithmically on $\omega$.

Collective mode and the c-axis critical current of a Josephson-coupled superconductor at high parallel magnetic fields.

Using Maxwell and time-dependent Ginzburg-Landau equations in the framework of a Lawrence-Doniach model we derive dynamical equations for the order parameter phase difference in Josephson-coupled layered superconductors. These equations allow the description of nonstationary Josephson effects in magnetic fields parallel to the layers. We obtain the dispersion relation and relaxation rate of collective modes in the absence of a magnetic field and in a strong parallel magnetic field. The dispersion with respect to the momentum in the $\mathrm{ab}$ plane in high fields is much stronger that in a single Josephson junction due to the multilayer structure. This leads to a very weak $c$-axis critical current in high magnetic fields. The relaxation rate of collective modes is found to be weak in comparison with its frequency. We discuss experimental data for the $c$-axis plasma resonance and critical current in parallel magnetic fields.

Field Dependence ofc-Axis Plasma Resonance in Josephson-Coupled Superconductors

The field and temperature dependence of the $c$-axis plasma frequency in Josephson-coupled layered superconductors is considered. In the zero-temperature limit the field dependence is expressed via the correlator of pancake density between adjacent layers. In the case of strong pinning, when ordering of pancakes along the $c$ axis is destroyed, the predicted power-law field dependence is found to be in agreement with the experimental data for ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$. For weaker pinning, the field dependence is different. Thus information on the pancake arrangement in the vortex glass phase can be obtained from plasma frequency measurements.

Dynamics of tilted vortex lines in Josephson-coupled layered superconductors

Specific features of the vortex dynanmics in Josephson-coupled layered superconductors are considered within the time-dependent Ginzburg-Landau theory. For a tilted vortex line consisting of 2D pancake vortices connected by the Josephson ones the equation of motion in the presence of a transport current parallel to the layers is obtained. Frequency dependece of the dynamic response of tilted vortices and nonlinear effects in their motion are studied.

I–V characteristics of Josephson-coupled layered superconductors

The equation for the gauge-invariant phase difference in Josephson-coupled layered superconductors is derived in the presence of a bias current along thec-axis. Numerical results for the I–V charactersistics in the systems composed of N=100 junctions are presented.

Low Frequency Magneto-optical Properties of Josephson-Coupled Superconductors.

The low temperature transverse dielectric function is found for Josephson-coupled layered superconductors for polarization of an electric field perpendicular to the layers in the presence of a dc magnetic field oriented parallel and perpendicular to the layers. The plasma edge lays well below the superconducting gap in highly anisotropic systems and it is reduced to zero in strong parallel fields due to the overlap of nonlinear regions of Josephson vortices. In strong perpendicular fields the plasma edge is also reduced due to displacements of pancake vortices from straight lines caused by pinning centers. Corresponding characteristic fields for plasma edge reduction are found.

Upper critical field, penetration depth, and GL parameter of Tl-2223 single crystals

A Tl 2Ca 2Ba 2Cu 3O 10 single crystal of platelet shape with T c=121.5 K was investigated by SQUID magnetometry. Zero field cooled (=ZFC) and field cooled (=FC) measurements were carried out in different fields with the applied field parallel to the crystallographic c-axis. Taking the fluctuations of the vortices in Josephson-coupled layered superconductors into account, the temperature dependent penetration depth λ ab, the Ginzburg Landau parameter κ, and the upper critical field H c2 are calculated from the reversible ZFC/FC magnetization data. The H c2-data (Hc) can be fitted linearly at higher temperatures. The temperature dependent penetration depth does not follow the empirical law λ( T)=λ(0)/(1−( T/T c ) 4) 1 2 .

Time-dependent equations for phase differences and a collective mode in Josephson-coupled layered superconductors.

A time-dependent equation for the interlayer phase differences is derived for Josephson-coupled layered superconductors. It generalizes the sine-Gordon equation for the phase in a standard Josephson junction to the case of multilayer systems. With the help of this equation, the dispersion of a collective mode is found at low temperatures. In highly anisotropic systems the gap in the spectrum of this mode lies below the superconducting gap and is suppressed strongly by a magnetic field parallel to the layers. The effect of this mode on the dielectric function and specific heat is calculated.

Josephson-coupled layered superconductors with two order parameters. I. Upper critical magnetic field

By using the Gor'kov-Nambu microscopic theory, an expression for the free-energy functional is obtained for Josephson-coupled layered superconductors with two order parameters corresponding to intra- and interlayer Cooper pairs. The existence of two order parameters in a system leads to the appearance of new terms in the free-energy functional known as the 'Josephson' terms and the Lifshitz invariant. Of these, the Josephson terms characterize the tunnelling of both intra- and interlayer Cooper pairs between neighbouring superconducting sheets. The upper critical field, Hc2, is studied for the superconductors under investigation. It is found that a magnetic field parallel to the superconducting layers does not destroy the superconductivity for temperatures T<T*, where T* depends on the resonance integral between two neighbouring superconducting layers. This effect gives rise to a positive curvature in the temperature dependence of Hc2/sup ///.

Josephson-coupled layered superconductors with two order parameters. II. Lower critical magnetic field

For pt.I. see ibid, vol.6, p. 2245-58, (1994). A model for high-Tc oxides, consisting of Josephson-coupled superconducting layers with both intra- and interlayer pairings, is used to study the anomalous positive curvature in the temperature dependence of the lower critical magnetic field, Hc1(T). An equilibrium distribution of magnetic fields in a single vortex is calculated for magnetic field parallel and perpendicular to the superconducting layers. By using this distribution the lower critical field Hc1 is obtained. For Josephson-coupled layered superconductors with only intralayer pairing, the cross section of the single vortex parallel to the layers is known to have an elliptic form. The existence of two order parameters in our model gives rise to an additional anisotropy in the distribution of the magnetic field in a single vortex. The results obtained for Hc1 make it possible to understand the experimentally observed anomalous enhancement of Hc1 at low temperatures in YBa2Cu3O7, as well as in Tl- and Bi-based superconductors.

Role of vortex fluctuations in determining superconducting parameters from magnetization data for layered superconductors.

The fluctuations of vortices in Josephson-coupled layered superconductors are shown to have a profound effect on values of the temperature-dependent penetration depth, Ginzburg-Landau parameter, and upper critical field extracted from reversible magnetization data below the critical temperature.

Distorted vortex in Josephson-coupled layered superconductors.

The free energy functional for a single vortex in a system of Josephson-coupled superconducting layers is derived in terms of coordinates of two-dimensional vortices, ``pancakes,'' which make the vortex ``line.'' The energy consists of equally important two-, three-, and four-pancake interactions.

Theory of the tilted vortex lattice in Josephson-coupled layered superconductors

Field penetration is studied for arbitrary directions in Josephson-coupled layered superconductors, in the quasi-2D regime described by the Lawrence-Doniach model with transverse coherence length ξ ⊥ = ξ‖/ Γ ⪡ d , the interlayer distance. Flux lines appear as oblique lines of 2D vortices piercing the layers. In the absence of Josephson coupling, the normal field component creates an Abrikosov vortex lattice normal to the layers, while the parallel component penetrates freely. For finite Josephson coupling, the vortex lattice structure may have two distinct behaviours: for moderate fields it is dominated by anisotropic London 3D currents, while in high fields the lattice has 2D character. In the 3D regime the usual core is replaced by an effective core made of 2D cores together with a region where screening is essentially 2D. Moreover, when tan θ > Γ, where θ is the field angle with respect to the normal to the layers, the effective cores are made of 2D vortices connected with pieces of Josephson vortices.