Mixed State Of High-temperature Superconductors Research Articles

NOVEL VORTEX STRIPE PHASE UNDER STRONG MAGNETIC FIELD IN HIGH TEMPERATURE SUPERCONDUCTORS

The nature of vortex structure in the mixed state of high-temperature superconductors (HTS) is investigated by solving the Bogoliubov-de Gennes equations with consideration of competition between antiferromagnetic (AF) and d-wave superconductivity (DSC) orders. By varying the applied magnetic field and temperature, the geometry of vortex structure can take two different forms: conventional vortex lattice (triangular or square), or vortex stripe phases where all the order parameters including spin density wave, charge density wave and superconducting order exhibit stripe-like behavior. This novel vortex stripe phases may show up at low temperature and adjacent to upper critical field H c2 Phase diagram of temperature dependence of H c2 will be presented. Our results may shed light on the understanding of the low-temperature H c2 anomalies in some HTS. New experiments are proposed to test our predictions.

Competing order in the mixed state of high-temperature superconductors

We examine the low-temperature behavior of the mixed state of a layered superconductor in the vicinity of a quantum critical point separating a pure superconducting phase from a phase in which a competing order coexists with superconductivity. At zero temperature, we find that there is an avoided critical point in the sense that the phase boundary in the limit $\stackrel{\ensuremath{\rightarrow}}{B}0$ does not connect to the $B=0$ critical point. Consequently, there exists a quasi-one-dimensional (1D) regime of the phase diagram, in which the competing order is largely confined to 1D ``halos'' about each vortex core, and in which interactions between neighboring vortices, although relevant at low temperature, are relatively weak.

The interpretation of magnetisation and entropy jumps in the mixed state of high-temperature superconductors

In the high-temperature superconductor BSCCO, local measurements of magnetic field at the surface of a crystal in the mixed state show sharp changes as a function of applied field or temperature. These `jumps' have been interpreted as signs of a first-order flux lattice melting (or sublimation) transition. We show that if `intermediate state' effects are accounted for, a first-order transition leads to a sharp jump in the global magnetisation only in the case of samples that are significantly non-ellipsoidal in shape. We also investigate the relationship between a jump in magnetisation, M, and the associated change in the B-field immediately above the crystal surface and show that Δ M is expected to be twice Δ B/ μ 0. In addition, we emphasise that the Clausius–Clapeyron relationship between magnetisation jump and entropy jump should involve the local H-field, not the B-field or the applied H-field. Re-interpreting some published experimental data, considering these factors, leads to the conclusion that the entropy change can be as much as 4.0 k B per flux line per layer, compared with less than 2 k B previously reported for this data, and that a similar factor should be applied to other measurements, where the entropy change can now be as high as 14 k B per flux line per layer. We show that part of this entropy can be attributed to the cores of the extra flux lines introduced into the sample by the transition, and that a considerable amount of the remainder may be associated with changes in the microscopic degrees of freedom. We present and analyse new experimental data on local field jumps and global magnetisation measurements, and find that they agree with the above. We also show that these data are consistent with the boundary region between the liquid and solid phases having a width of around 20 flux line spacings at a field of 10 mT.

Nature of the low-field transition in the mixed state of high-temperature superconductors

We have numerically studied the statics and dynamics of a model three-dimensional (3D) vortex lattice at low magnetic fields. For the statics we use a frustrated 3D $\mathrm{XY}$ model on a stacked triangular lattice. We model the dynamics as a coupled network of overdamped resistively shunted Josephson junctions with Langevin noise. At low fields, there is a weakly first-order phase transition, at which the vortex lattice melts into a line liquid. Phase coherence parallel to the field persists until a sharp crossover, conceivably a phase transition, near ${T}_{\mathcal{l}}>{T}_{m}$ which develops at the same temperature as an infinite vortex tangle. The calculated flux flow resistivity in various geometries near ${T=T}_{\mathcal{l}}$ closely resembles experiment. The local density of field induced vortices increases sharply near ${T}_{\mathcal{l}},$ corresponding to the experimentally observed magnetization jump. We discuss the nature of a possible transition or crossover at ${T}_{\mathcal{l}}$(B) which is distinct from flux lattice melting.

Twin-boundary effect on the Hall conductivity in high-Tcsuperconducting thin films

The pinning influence on the Hall conductivity in the mixed state of high-temperature superconductors is still experimentally and theoretically controversial. In this work, the effect of twin-boundary pinning on the Hall conductivity is studied, with particular emphasis on the high-field results. The longitudinal and Hall resistivities were measured in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} and YbBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} thin films, up to 18 T: a signature due to the pinning of the vortices in the twin boundaries is clearly visible in the longitudinal resistivity {rho}{sub xx} and in the Hall resistivity {rho}{sub xy}, but disappears when the Hall conductivity {sigma}{sub xy}{congruent}{rho}{sub xy}/{rho}{sub xx}{sup 2} is computed. However, at lower temperatures, a minimum of d{sigma}{sub xy}/dT is proved to be a weak signature of the twin-boundary pinning. These results are confirmed by similar measurements done on one sample rotated 16{degree} away from the magnetic field direction. {copyright} {ital 1997} {ital The American Physical Society}

Vortex-lattice phase transitions in Bi2Sr2CaCu2 O8 crystals with different oxygen stoichiometry.

The vortex-lattice phase transitions in Bi 2Sr2CaCu2O8 crystals with various oxygen stoichiometry are studied using local magnetization measurements. Three new findings are reported: The first-order phase transition line at elevated temperatures shifts upward for more isotropic overdoped samples. At lower temperatures another sharp transition is observed that results in enhanced bulk pinning in the second magnetization peak region. The two lines merge at a multicritical point at intermediate temperatures forming apparently a continuous phase transition line that is anisotropy dependent. PACS numbers: 74.60.Ec, 74.60.Ge, 74.60.Jg, 74.72.Hs The mixed state of high-temperature superconductors (HTSC) has a very complicated phase diagram. The nature of the different vortex phases and the thermodynamic transitions between them are of fundamental interest, and are the subject of substantial recent theoretical and experimental efforts [1 ‐ 10]. It is generally accepted that the high anisotropy plays a crucial role in the richness of the phase diagram of HTSC. Nevertheless, a systematic study of the anisotropy effects is quite complicated and was limited so far by the lack of a well defined phase boundary that could be monitored as a function of the anisotropy. A recent advance in local measurements has revealed a sharp step in magnetization due to a first-order vortex-lattice phase transition in Bi2Sr2CaCu2O8 (BSCCO) crystals [10]. Such a clearly defined fundamental transition is thus a natural candidate for an investigation of the anisotropy effects in HTSC, and this paper presents a first study in this direction. Another intriguing feature of the phase diagram of many HTSC crystals, and BSCCO in particular, is the anomalous second magnetization peak at lower temperatures. The associated increase of magnetization with magnetic field has been attributed to surface barrier effects [11], crossover from surface barrier to bulk pinning [12], sample inhomogeneities [13], dynamic effects [14], and 3D to 2D transitions [15‐ 17]. Our local measurements indicate that a very abrupt upturn in the bulk critical current occurs at the onset of the second peak in BSCCO. We postulate that this behavior is triggered by an underlying thermodynamic phase transition of the flux-line lattice. Furthermore, for the different anisotropy crystals the two phase transition lines are found to form, apparently, one continuous transition line that changes from first to possibly second order at

Flux dynamics and c-axis resistive dissipation in the mixed state of high-temperature superconductors The case of (La 1− xSr x) 2CuO 4

We take the single-crystalline (La 1− x Sr x ) 2CuO 4 system ( x = 0.068) as an example to study flux dynamics in the mixed state of high- T c superconductors by systematically measuring its c-axis resistivity, ϱ c , as a function of temperature, magnetic-field intensity and magnetic-field orientation with respect to the ab-plane. We firstly show the experimental evidence that excludes the contribution of Lorentz force driven flux motion to the c-axis resistive dissipation. Furthermore, we argue that neither the vortex dynamics for conventional anisotropic superconductors nor the two-dimensional pancake vortices model is appropriate for the present system. We then demonstrate the difficulty of the previously considered Lorentz force free dissipation models in explaining the present experimental observations. Finally, a phenomenological model is introduced, in which the phase slippage model developed by Ambegaokar and Halperin is extended to the case of the c-axis resistivity by taking into account the following two main features: (1) the intrinsic layered structures along the c-axis, and (2) the irreversibility line, T irr( H), corresponding to a vortex glass-liquid transition. To show the advantages of the present model, we compare the model with the experimental ϱ c ( T, H) data for H|| C, which gives excellent agreement in almost the whole transition region (five decades).

Galvanomagnetic and thermomagnetic phenomena in the mixed state of high-temperature superconductors

The thermomagnetic phenomena in the mixed state of high-{Tc} superconductors are investigated in terms of the phenomenological three-fluid (superconductive and no rmal quasiparticles, and Abrikosov vortices) model. General relations are found between the various transport coefficients which are valid for the entire transition superconductive state {yields} mixed state {yields} normal state.

Thermal diffusion of quasiparticles and vortices in high-temperature superconductors

In the mixed state of high-temperature superconductors (HTSC) vortex motion under the influence of the Lorentz force of an applied transport or shielding current has been studied in a large number of experiments. Recently, an increasing amount of work has concentrated also on the transport effects due to the thermal force acting on the quasiparticles and vortices in an applied temperature gradient, resulting in the Nernst and Seebeck effect. We summarize the highlights of these latter experiments. In particular, we address the following subjects: origin of the Seebeck effect in the mixed state, transport entropy of the vortex structure in strongly anisotropic HTSC's, Hall contribution to the Nernst and Seebeck effect, and measurements in the fluctuation regime. From the temperature dependence of the transport energy of the vortices the slope ϑ H c2/ϑ T near T c, the coherence length and the Ginzburg-Landau parameter can be determined.

Galvanomagnetic and thermomagnetic phenomena in the mixed state of high-temperature superconductors

The thermomagnetic phenomena in the mixed state of high- T c superconductors are investigated in terms of a phenomenological three-fluid (superconductive and normal quasiparticles, and Abrikosov vortices) model. We have found quite general relations between various transport coefficients which are valid for the whole transition (superconductive state-mixed state-normal state).

Mixed state of high-temperature superconductors

Mixed state of high-temperature superconductors

Anomalous Hall effect in the mixed state of high-temperature superconductors

The Hall effect in the mixed state of high- T c superconductors (HTSC) is of an anomalous nature: near the transition there is a range of temperatures and of magnetic fields where the sign of the Hall effect is opposite to that in the normal state. The universality of the phenomenon in question is indicative of its connection with some general properties of the mixed state of type-II superconductors, namely, with peculiarities of motion of magnetic flux vortex lines (vortices) in these superconductors. This work puts forward a model accounting for a number of vortex motion specific features and providing a possibility to obtain the characteristics of the anomalous Hall effect. The work is based on the phenomenologically generalized results of Bardeen-Stephen and Nozieres-Vinen, supplemented with an allowance for a new mechanism of vortex “friction” associated with Andreev electron reflection on the interface between the normal core and the superconducting periphery of a vortex. Within the framework of the model suggested, magnetic field (and temperature) dependences of the longitudinal and Hall resistances of a mixed state superconductor have been calculated at temperatures nearing T c. At certain quite realistic parameters which define the forces acting on the vortices, there is a range of magnetic fields and temperatures where the sign of the Hall effect is opposite to that in the normal state. The lower limit of this range is the irreversibility line and the upper critical field.

Thermal diffusion of quasiparticles and flux quanta in the mixed state of high-temperature superconductors

In the mixed state of the copper-oxide superconductors the motion of the vortex structure due to a temperature gradient generates the Nernst and Seebeck effect. The first effect is essentially the result of the thermal force acting directly on the vortex lines. The second effect is primarily due to the thermal diffusion of quasiparticles which is compensated by a backflow supercurrent. In the mixed state both effects exist over the same temperature range over which the electric resistivity remains finite.

Thermoelectric and Thermomagnetic Effects in High-Temperature Superconductors

ABSTRACTIn the mixed state of high-temperature superconductors the dominant part of the Seebeck and Nernst effect is due to the thermal diffusion of quasiparticles and vortices, respectively. Our understanding of the Seebeck effect is based on the two-fluid counterflow model of Ginzburg and its extension to the mixed state with the presence of vortices. From the Nernst effect the transport entropy of the vortices is obtained. We summarize the recent thermoelectric and thermomagnetic experiments, paying also attention to the role of the Magnus force (Hall effect) and to the thermal fluctuation effects near TC.