Mixed State Of type-II Superconductors Research Articles

The mixed-state Hall conductivity of single-crystal films Nd2–xCexCuO4+δ (x = 0.14)

The magnetic-field dependencies of the longitudinal and Hall resistivity of the electron-doped compounds Nd2–xCexCuO4+δ in underdoped region (x = 0.14) were investigated. It was established experimentally a strong magnetic field dependence of the Hall conductivity, σxy(B) = C – b/B, in the region of magnetic fields corresponding to a transition from superconducting to resistive state. The observed feature can be explained with the sum of contributions of the quasiparticles and moving Abrikosov vortices into Hall effect in a mixed state of type-II superconductor.

Coherence length of magnetic field in the mixed state of type-II superconductors

Influence of impurities on coherence length Ξh in the mixed state of s-wave superconductors is investigated in framework of quasiclassical Eilenberger theory. The increasing of impurity scattering rate results in decreasing of Ξh. The obtained field dependence of Ξh for clean superconductors has a minimum and it is similar to that in Hao-Clem and Miranović-Ichioka-Machida theories for order parameter of coherence length. It is found that growing behavior of Ξh with magnetic field in dirty superconductors is different from order parameter coherence length determining by pairing potential near with vortex core. The magnetic field dependence of coherence length in normalized units, Ξh/Ξc2(B/Bc2), is nonuniversal and depends on impurity scattering potential.

Effects of nonmagnetic scatterers on the magnetic coherence length in the mixed state of type-II superconductors

Effects of nonmagnetic scatterers on the magnetic coherence length in the mixed state of type-II superconductors

On the interpretation of muon-spin-rotation experiments in the mixed state of type-II superconductors

We argue that claims about magnetic field dependence of the magnetic field penetration depth λ, which were made on the basis of muon-spin-rotation (μSR) studies of some superconductors, originate from insufficient accuracy of theoretical models employed for the data analysis. We also reanalyse some of already published experimental data and demonstrate that numerical calculations of Brandt [E.H. Brandt, Phys. Rev. B 68 (2003) 54506] may serve as a reliable and powerful tool for the analysis of μSR data collected in experiments with conventional superconductors. Furthermore, one can use this approach in order to distinguish between conventional and unconventional superconductors. It is unfortunate that these calculations have practically never been employed for the analysis of μSR data.

Thermo-magnetic refrigeration as applied to hydrogen liquefaction I. Fundamentals and type-II superconductors

Gas liquefaction utilizing the entropy transport by flux lines (FLs) in the mixed state of type-II superconductors has been proposed. Refrigerating power and the Joulian heat generated by FL current are proportional to and to the square of the superconducting (super-) current, respectively. The optimum super-current, the corresponding field strength, and the net refrigerating power ( q n ) are expressed by the elemental parameters. Introducing the well-defined FL-flow viscosity coefficient, we show that the maximum q n appears at the field with 1 9 of the upper critical field under the corresponding super-current density, and we expect the optimum refrigeration power density of about 15.8 j 0 * and 4.49 j 0 * W / m 2 (where j 0 * is the critical super-current density) for Nb 3 Ge ( T 0 = 23.2 K , B C 2 = 14.5 T at T 0 ) and MgB 2 ( T 0 = 40.0 K , B C 2 = 16 T , at T 0 ), respectively.

Quantum effects of vortex in type-II superconductors

The vortex energy of type-II superconductors in mixed state is discussed based on the assumption that vortex can undergo quantum effect. The Hamiltonian of an isolated vortex of type-II superconductors in lower magnetic fields is calculated from the elasticity of vortex within the framework of weak collective pinning theory. The results indicate that the vortex can be described using the eigenvalue of a harmonic oscillator and the eigenvalue of the vortex energy can be reduced by the action of Lorentz force of the current acting on the vortex. The quantum effects of vortices in higher magnetic fields are also studied and two particular directions of the dispersion models of the two-dimension triangular vortex lattice are given.

Scaling of the equilibrium magnetization in the mixed state of type-II superconductors

We discuss the analysis of mixed-state magnetization data of type-II superconductors using a recently developed scaling procedure. It is based on the fact that, if the Ginzburg-Landau parameter κ does not depend on temperature, the magnetic susceptibility χ(H,T) is a universal function of H/Hc2(T), leading to a simple relation between magnetizations at different temperatures. Although this scaling procedure does not provide absolute values of the upper critical field Hc2(T), its temperature variation can be established rather accurately. This provides an opportunity to validate theoretical models that are usually employed for the evaluation of Hc2(T) from equilibrium magnetization data. In the second part of the paper we apply this scaling procedure for a discussion of the notorious first order phase transition in the mixed state of high-Tc superconductors. Our analysis, based on experimental magnetization data available in the literature, shows that the shift of the magnetization accross the transition may adopt either sign, depending on the particular chosen sample. We argue that this observation is inconsistent with the interpretation that this transition always represents the melting transition of the vortex lattice.

On the interpretation of the equilibrium magnetization in the mixed state of high- Tc superconductors

We apply a recently developed scaling procedure to the analysis of equilibrium magnetization M( H) data that were obtained for Tl 2Ba 2CaCu 2O 8+ x and Bi 2Sr 2CaCu 2O 8 single crystals and were reported in the literature. The temperature dependencies of the upper critical field and the magnetic field penetration depth resulting from our analysis are distinctly different from those obtained in the original publications. We argue that theoretical models, which are usually employed for analyses of the equilibrium magnetization in the mixed state of type-II superconductors are not adequate for a quantitative description of high- T c superconductors. In addition, we demonstrate that the scaled equilibrium magnetization M( H) curve for a Tl-2212 sample reveals a pronounced kink, suggesting a phase transition in the mixed state.

Determination of the Coherence Length and the Cooper-Pair Size in Unconventional Superconductors by Tunneling Spectroscopy

The main purpose of the paper is to discuss a possibility of the determination of the values of the coherence length and the Cooper-pair size in unconventional superconductors by using tunnelling spectroscopy. In the mixed state of type-II superconductors, an applied magnetic field penetrates the superconductor in the form of vortices which form a regular lattice. In unconventional superconductors, the inner structure of a vortex core has a complex structure which is determined by the order parameter of the superconducting state and by the pairing wavefunction of the Cooper pairs. In clean superconductors, the spatial variations of the order parameter and the pairing wavefunction occur over the distances of the order of the coherence length and the Cooper-pair size, respectively. Therefore, by performing tunnelling spectroscopy along a line passing through a vortex core, one is able, in principle, to estimate the values of the coherent length and the Cooper-pair size.

Thermal conductivity and thermal Hall effect from vortex motion

In the mixed state of type-II superconductors the motion of vortices in response to an applied temperature gradient $\ensuremath{\nabla}T$ leads to a longitudinal and a transverse heat current along $\ensuremath{\nabla}T$ and $\ensuremath{\nabla}T\ifmmode\times\else\texttimes\fi{}\mathbf{B},$ respectively, where $\mathbf{B}$ is the magnetic field. We calculate the corresponding contributions to the thermal conductivity and the thermal Hall effect in terms of other thermomagnetic transport coefficients and the electrical resistivity. The vortex contribution to the thermal Hall effect may be observable in superconductors with weak pinning and small quasiparticle thermal conductivity.

Nonlinear material equation and its application in MgB 2

The nonlinear material equation and longitudinal resistivity equation of mixed state of type-II superconductors are derived starting from the free-energy functional of vortex system, in which the additional contribution due to dissipation is taken into account. Applying the longitudinal resistivity equation to transverse case we obtain an analytical expression for the Hall resistivity ρ xy . This equation fits well the recently reported experimental data of MgB 2 and successfully reproduces the empirical scaling relations for ρ xy proposed in the present paper.

Some Remarks on Vortex Matter in High-Tc Superconductors

We show that some experimentally observed features of vortex matter in high-Tc superconductors may be interpreted in simpler ways than it is usually done. In particular, we consider magnetic flux creep at low temperatures as well as the irreversibility line in the H−T phase diagram. We also discuss a new approach to the analysis of the equilibrium magnetization in the mixed state of type-II superconductors and we suggest an alternative configuration for the mixed state in magnetic fields close to the upper critical field.

Acousto-electric effect induced by transverse acoustic waves in a mixed state of type-II superconductors

A transverse ultrasonic wave should drag the vortex structure of superconductors at an acute angle with respect to the direction of wave propagation. The oscillation of the vortex density and the directed motion of the vortices give rise to a constant component of electric field in a bulk of the superconductor. The effect should be observed in all type-II superconductors above the irreversibility line.

The sign reversal and scaling relations of Hall anomaly in the mixed state type-II superconductors

We present a new model for the anomalous Hall effect in the mixed state of type-II superconductors. In this model we consider the thermally activated motion of the many body correlating vortex lattice system. The sign change of the Hall resistivity is the result of the competition between the motion of effective antivortices and the motion of the pinned vortex lattice together with the interstitial vortices. Within this model many essential experimental results for the complicated Hall effect can be explained.

De Haas–van Alphen effect in conventional and unconventional superconductors

The damping of the amplitude of the magnetization oscillations in the mixed state of type-II superconductors is found. The magnitude of the order parameter is determined self-consistently from the system of Gor'kov equations taking into consideration the electron scattering by the nonmagnetic impurities, nonuniform distribution of the order parameter and the effects of Pauli spin paramagnetism. It is shown that for the superconductors with high value of the upper critical field and small value of Fermi energy the superconducting state is gapless in broad enough mixed state region below the upper critical field. Another important consequence of the theory is that the phase transition to the mixed state of clean enough type-II ordinary superconductor is of the first order below some tricritical point temperature depending on impurities concentration. In the unconventional superconducting states where the lines of extremal cross-section of Fermi-surface by the plane perpendicular to magnetic field coincide with lines of zeros of the order parameter the amplitude of the magnetization oscillations is practically the same as in a normal state. In the superconducting phases with an other distribution of zeros the damping of dHvA oscillations corresponds qualitatively to the ordinary superconductivity. Unlike to singlet pairing for a triplet equal spin pairing the phase transition into mixed state is always of the second order.

Experimental considerations for de Haas–van Alphen studies in the mixed state

We discuss the microscopic and macroscopic factors which influence the measurement of de Haas–van Alphen oscillations in the mixed state of type-II superconductors. In particular, the effect of field inhomogeneity and macroscopic pinning of the flux lattice is analysed.

Interaction of ultrasound with vortices in type-II superconductors.

The theory of the ultrasound propagation in the mixed state of type-II superconductors is suggested which takes into account the Magnus force on vortices, the anti-Magnus force on ions, and diamagnetism of the mixed state. The acoustic Faraday effect (rotation of polarization of the transverse ultrasonic wave propagating along vortices) is shown to be linear in the Magnus force in any regime of the flux flow for wavelengths used in the ultrasound experiments now. Therefore, in contrast to previous predictions, the Faraday effect should be looked for only in clean superconductors with a large amplitude of the Magnus force.

Meissner-like response of type-II superconductors in the mixed state.

Vortex pinning and vortex cutting are included in a continuum theory for the mixed state of type-II superconductors. It is then shown that when the transport current in a field-cooled sample is increased from zero, the initial stage is always a Meissner-like surface current. In this stage the vortices remain straight, while close to the surface the field lines bend (when the current is perpendicular to the vortices) or twist (when the current is parallel to the vortices). Only when the threshold for vortex depinning or vortex cutting is reached at the surface, a critical state builds up, or, possibly, the current flow becomes resistive.

Thermal voltage noise in layered superconductors.

Thermal voltage noise in the mixed state of type-II superconductors has been calculated taking into account fluctuation modes of nonrigid vortices. It has been shown that bending of vortices leads to new effects in thermal-voltage-noise spectra at high frequencies. The power spectrum reflecting fluctuations of rigid vortices is suppressed at very low frequencies and saturates into a white spectrum at a characteristic frequency depending on the strip width. At high frequencies tilt modes of flexible vortices start to contribute to the fluctuating voltages and the power spectrum undergoes three subsequent magnitude increases, following {omega}{sup 1/2}-, {omega}{sup 2}-, and again {omega}{sup 1/2}-like behavior before becoming white again. It has been shown that for layered superconductors of a moderate anisotropy the second {omega}{sup 1/2}-like increase disappears at magnetic fields exceeding a certain threshold field corresponding to the crossover field between two-dimensional and three-dimensional vortex-lattice melting. Field dependencies of characteristic frequencies separating different regimes of spectral behavior have been evaluated and shown to be qualitatively different for low and high magnetic fields.

Magnetic oscillations and quasiparticle band structure in the mixed state of type-II superconductors.

We consider magnetic oscillations due to Landau quantization in the mixed state of type-II superconductors. Our work is based on a previously developed formalism which allows the mean-field gap equations of the Abrikosov state to be conveniently solved in a Landau-level representation. We find that the quasiparticle band structure changes qualitatively when the pairing self-energy becomes comparable to the Landau-level separation. For small pairing self-energies, Landau-level mixing due to the superconducting order is weak and magnetic oscillations survive in the superconducting state although they are damped. We find that the width of the quasiparticle Landau levels in this regime varies approximately as ${\mathrm{\ensuremath{\Delta}}}_{0}$${\mathit{n}}_{\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}1/4}$ where ${\mathrm{\ensuremath{\Delta}}}_{0}$ is proportional to the magnitude of the order parameter and ${\mathit{n}}_{\mathrm{\ensuremath{\mu}}}$ is the Landau-level index at the Fermi energy. For larger pairing self-energies, the lowest energy quasiparticle bands occur in pairs which are nearly equally spaced from each other and evolve with weakening magnetic field toward the bound states of an isolated vortex core. These bands have a weak magnetic field dependence and magnetic oscillations vanish rapidly in this regime. We discuss recent observations of the de Haas--van Alphen effect in the mixed state of several type-II superconductors in light of our results.