Superconducting Plates Research Articles

Casimir forces out of thermal equilibrium near a superconducting transition

We present a comprehensive analysis of the out-of-equilibrium Casimir pressure between two high-T_c superconducting plates, each kept at a different temperature. Two interaction regimes can be distinguished. While the zero-point energy dominates in the near field, thermal effects become important at large interplate separations causing a drop in the force’s magnitude compared with the usual thermal-equilibrium case. Our detailed calculations highlight the competing role played by propagating and evanescent modes. Moreover, as one of the plates undergoes the superconducting transition, we predict an abrupt change in the force for any plate distance, which has not been previously observed in other systems. The sensitivity of the dielectric function of the high-T_c superconductors makes them ideal systems for a possible direct measurement of the out-of-equilibrium Casimir pressure.

Casimir Effect between Superconducting Plates in the Mixed State

The Casimir effect between type-II superconducting plates in the coexisting phase of a superconducting phase and a normal phase is investigated. The dependence of the optical conductivity of the superconducting plates on the external magnetic field is described in terms of the penetration depth of the incident electromagnetic field, and the permittivity along the imaginary axis is represented by a linear combination of the permittivities for the plasma model and Drude models. The characteristic frequency in each model is determined using the force parameters for the motion of the magnetic field vortices. The Casimir force between parallel YBCO plates in the mixed state is calculated, and the dependence on the applied magnetic field and temperature is considered.

Critical states in two overlapped rectangular superconducting plates

We study vortex penetration into two-layer structures of superconducting plates under a perpendicular magnetic field. We solve the heat transport equation and the Maxwell equations with the current-voltage relation for superconductor, simultaneously, and obtain magnetic flux and current densities. We show how magnetic flux structure depends on the structure, especially distance of two-layer of superconductors.

The critical state of superconducting multilayered structures

We propose a new method for calculating the dependence of the critical current on an external magnetic field, and the distribution of this current over the layers in superconducting multilayered structures. The method is based on a numerical solution of a system of nonlinear Ginzburg–Landau equations that describe the behavior of a superconducting plate carrying a transport current in a magnetic field, provided that it does not contain Abrikosov vortices. The way in which boundary conditions in the Ginzburg–Landau theory influence the critical state of superconducting layered structures is also considered. From a mathematical point of view, application of a general boundary condition to the system of Ginzburg–Landau equations leads to a change in the order parameter along the thickness of the thin superconducting plates. The physical nature of this phenomenon is explained by the proximity effect at the superconductor–normal metal (SN) interface, which leads to the suppression of the order parameter near the SN interface. The resulting calculated dependences of the plates’ critical current on the magnetic field strength applied parallel to the layers are used to determine the critical current of multilayer structures. It is assumed that the mutual influence of superconducting layers occurs only via the magnetic field that they create.

Hybrid Magnetic Sensor Combined With a Tunnel Magnetoresistive Sensor and High-Temperature Superconducting Magnetic-Field-Focusing Plates

Magnetoresistive (MR) sensors are widely used, particularly in consumer products. However, in applications requiring extremely sensitive magnetic sensors, superconducting quantum interference devices (SQUIDs) are primarily used. In this study, we develop a hybrid magnetic sensor by combining an MR sensor with two high-temperature superconducting (HTS) plates to achieve sensitivity that lies between those of MR sensors and SQUIDs. In addition, we apply a modulation method for measuring the absolute magnetic field. A nanogranular in-gap tunnel MR sensor is installed inside the slit between the magnetic-field-focusing HTS plates, and the magnetic response is evaluated. Using the magnetic-field-focusing characteristics of the HTS plates (made from YBa2Cu3O7‐δ) and the MR sensor inside the slit between the two plates, the sensitivity and noise characteristics are improved. Adjustment of parameters, such as MR sensor height from the slit, slit width of the HTS plates, and plate size allow sensitivity control depending on the application. Moreover, the absolute magnetic response and low noise in low-frequency regions are obtained through ac modulation.

On the Effect of Boundary Conditions in the Ginzburg–Landau Theory on the Results of Calculations of the Critical State of Layered Structures

The effect of boundary conditions in the Ginzburg–Landau theory on the critical state of superconducting layered structures is studied. The method is based on the numerical solution of the Ginzburg–Landau nonlinear equations describing the behavior of a superconducting plate carrying a transport current in a magnetic field, provided the absence of vortices in it. The use of the general boundary condition for the Ginzburg–Landau system of equations leads to a change in the order parameter over the thickness of thin superconducting plates. The calculated dependences of the critical current of plates on the magnetic field applied in parallel to layers are used to determine the critical current of multilayered structures. It is assumed that the mutual influence of superconducting layers occurs only through the magnetic field induced by them.

Simulations of vortices in a star-shaped plate with an artificial pin

Although a triangular vortex lattice is stable in a bulk type-II superconductor, exotic vortex configurations are expected to appear in a small superconducting plate. Theoretical calculations on vortex structures in a star-shaped superconducting plate have been given in our preceding work. In this work, we extended our theoretical studies to the case of having an artificial pin. We performed the Ginzburg-Landau (GL) calculations systematically to compare with the pin-free case by using the finite element method. We found that a vortex tends to accommodate preferentially in an aritificial pin in the star-shaped plate. We found a systematic evolution of vortex structure with increaseing magnetic field. We compare our theoretical calculations with vortices in a star-shaped Mo80Ge20 plate with an artificial pin and without an artificial pin obtained by a scanning SQUID microscope. We reconstructed the vortex image on the sample surface by using the inverse Biot-Savart law and the Fourier transformation.

Development of Superconducting Magnetic Bearing for 300 kW Flywheel Energy Storage System

The world's largest-class flywheel energy storage system (FESS), with a 300 kW power, was established at Mt. Komekura in Yamanashi prefecture in 2015. The FESS, connected to a 1-MW megasolar plant, effectively stabilized the electrical output fluctuation of the photovoltaic (PV) power plant caused by the change in sunshine. The FESS uses a superconducting magnetic bearing (SMB) to levitate a heavy weight flywheel rotor without mechanical contact. The SMB consists of high-temperature superconducting coils (HTS coils) made of rare-Earth-Ba2Cu3Oy , superconducting tapes, and high-temperature superconducting plates (HTS plates) made of YBa2Cu3 Oy. The HTS plates in the rotor axis received the levitation forces in the magnetic field generated by the HTS coils in the stator. At first, the SMB was tested alone to check its cooling properties and to measure the levitation force. In the factory test, the SMB was confirmed to levitate the 4000-kg load, and its performance and basic reliability were verified. In the verification test, at Mt. Komekura, the FESS rotor reached a maximum of 2950 r/min, and the FESS was charged and discharged at 300 kW in the PV plant.

Size, Shape, and Impurity Effects on Transition Temperatures of Nanostructured Superconductors

We have investigated system size, shape, and nonmagnetic impurity effects on superconducting transition temperatures T c 's for nanoscaled superconducting plates using the Gor'kov equations with the finite-element method. We have considered a weak coupling superconductor to which the BCS theory is applicable. We have found that T c shows a sawtooth behavior as a function of the size and T c increases with decreasing superconductor size. Spatial distributions of superconducting order parameters abruptly change at drops in T c during the sawtooth behavior. The drops in T c and changes of distributions of order parameters are caused by retardation of the attractive interaction between electrons in the BCS theory. In addition, we have found that T c 's for rectangular plates are higher than those for square plates. Furthermore, we have found that impurity effects decrease T c 's.

Vortex Molecule in a Nanoscopic Square Superconducting Plate

Using the finite element method and solving the Bogoliubov–de Gennes equation, we have investigated magnetic field dependence of the stable vortex structures in a mesoscopic superconducting plate at low temperature ( T = 0.1 T c ). Because of the compactness of vortex configuration, there is interference between bound states around vortices and such quasi-particle structure affects the vortex configuration. Especially in two-vortices state, vortices form a molecule-like state, where bound states of each vortex form molecular orbital like bonding and anti-bonding states. The vortex configuration is different from that, which is expected from the repulsive interaction between vortices.

Scaling Solution and $n$ Dependence of the Eddy-Current Distribution in a Flat Superconductor

In this paper, we propose an approximate analytical solution of the problem of nonlinear diffusion of the current density in a high-temperature superconducting plate with current transport. It is obtained by the technique of self-similar solution. The construction of this solution highlights a characteristic time of penetration <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tp</i> whose limit for large <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> is the model of Bean. We compare our solution to the ones obtained using COMSOL multiphysics. We study the influence of variation of the magnetic induction on time penetration and the influence of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> factor on time penetration.

Critical states in thin planar type-II superconductors in a perpendicular or inclined magnetic field (Review)

The theory of the critical states of a vortex lattice in type-II superconductors is examined without any assumptions about the relative perpendicularity of the local magnetic fields and circulating currents in the sample. Such a theory has made it possible to solve a number of problems for thin films of superconductors in an external magnetic field oriented perpendicular to their surface: a theory of the shaking effect is constructed for rectangular superconducting plates and the critical states in samples with anisotropic pinning of the flux lines as well as in the presence of an order-disorder phase transition in a vortex lattice are studied. In addition, the critical states in a long superconducting strip in an inclined magnetic field are investigated.

Calculation of critical states of superconducting multilayers based on numerical solution of the Ginzburg-Landau equations for superconducting plates

The numerical method is used to analyze the critical state of superconducting multilayers. The method is based on self-consistent solutions of the Ginzburg-Landau system of nonlinear equations, which describe the behavior of a superconducting plate carrying transport current in a magnetic field, provided that there are no vortices inside the plate. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength, local magnetic field, and current distributions for multilayers in parallel magnetic fields. The mutual influence of the superconducting layers is assumed to be realized only via a magnetic field. The method makes it possible to account for the peak effect in multilayered superconductors. Our results give an alternative approach to explain different scaling laws that describe flux pinning in the two most common commercial superconductors, NbTi and ${\mathrm{Nb}}_{3}\mathrm{Sn}$. A simple method is proposed for analyzing the critical states of multilayers in magnetic fields of arbitrary strength, based on elementary transformations of the critical current-density distribution over individual layers in a zero applied magnetic field.

Penetrations and dynamics of vortices in mesoscopic superconducting plates

Nano-technologies enable us to control quantum states. Vortex states in superconductor whose dimension is order of the coherence length would be applied in electronic devices in near future. In this presentation, we report the penetration process and dynamics of vortices in mesoscopic superconducting plate with anti-dot obtained by solving the time dependent Ginzburg–Landau (TDGL) equations.As to a regular square superconducting plate with an anti-dot located at the center, for suddenly applying the field perpendicular to the plate, vortices tend to penetrate into the plate from four central points of the each square side keeping the fourfold rotational symmetry. After the penetration, we found the vortex exclusion process that residual vortices for stability of the system are expelled. For introducing external current that breaks symmetry of the system.

Quasi-particle spectrum of giant vortex states in a square nanoscopic superconducting plate

We have investigated quasi-particle structure and superconducting state of the nano-scaled superconductor under an external magnetic field using a microscopic Bogoliubov–de Gennes equation. Our results show that the giant vortex state has a peak of local density of states at the center of the vortex core in negative energy, while the singly quantized vortex has it in positive energy. This may be observable for scanning tunneling spectroscopy experiments.

Theoretical Calculation of Inductance of Flat Type Fault Current Limiter with High Tc Superconducting Plate

A flat type fault current limiter (FCL) proposed by us consists of a spiral primary winding and high Tc superconducting (HTS) plate. In order to clarify the static current-limiting performance of the flat type FCL, the magnetic field analyses were carried out for small modules of the FCL. The inductance of the FCL was calculated by analyzing the magnetic field. The magnetic field analysis suggested that a high inductance ratio might be realized by radically enlarging both the primary winding and the HTS plate, installing the high permeability material such as an iron on the FCL and stacking the FCL modules vertically in layers. It is also pointed out that the volume of the flat type FCL is smaller than that of the cylinder type FCL with same magnitude of the limiting inductance.

Quasi-particle spectrum of nano-scale superconducting plate under a magnetic field

Using the finite element method, we have solved the Bogoliubov-de Gennes equation for superconducting nano-scale plate under a magnetic field, numerically. The local density of states for these systems shows two types of the bound states inside of the superconducting energy gap. We have investigated their wave functions and identified them as the vortex bound states and the surface bound states. Under the zero external field, the surface bound states do not appear inside of the energy gap, and their energies decrease with increasing the external field.

Calculation of critical states of superconducting multilayers based on numerical solution of the Ginzburg-Landau equations for superconducting plates

Numerical methods are used to analyze the Ginzburg-Landau equations for a superconducting plate carrying transport current in a magnetic field. Critical current is calculated as a function of the applied magnetic field strength for superconducting plates with different thicknesses. The relations between the field dependence of critical current and the distributions of order parameter, magnetic field, and supercurrent in a plate are analyzed. The field-dependent critical currents computed for plates are used to determine the critical current as a function of the applied magnetic field strength and local magnetic field and current distributions for multilayers in parallel magnetic fields. The constituent superconducting layers are assumed to interact only via magnetic field. A simple method is proposed for analyzing the critical states of multilayers in magnetic fields of arbitrary strength, based on elementary transformations of the critical current-density distribution over individual layers in zero applied magnetic field. The method can be used to analyze experimental results.

Energy Minimization and Flux Domain Structure in the Intermediate State of a Type-I Superconductor

The intermediate state of a type-I superconductor involves a fine-scale mixture of normal and superconducting domains. We take the viewpoint, due to Landau, that the realizable domain patterns are (local) minima of a nonconvex variational problem. We examine the scaling law of the minimum energy and the qualitative properties of domain patterns achieving that law. Our analysis is restricted to the simplest possible case: a superconducting plate in a transverse magnetic field. Our methods include explicit geometric constructions leading to upper bounds and ansatz-free inequalities leading to lower bounds. The problem is unexpectedly rich when the applied field is near-zero or near-critical. In these regimes there are two small parameters, and the ground state patterns depend on the relation between them.

Magnetic shielding analysis of high-T/sub c/ superconducting plates by power law, flux-flow, and flux-creep models

The magnetic shielding performance of a high-T/sub c/ superconducting (HTS) plate is investigated numerically. By taking account of the crystallographic anisotropy in the shielding current density of the melt-powder-melt-growth YBa/sub 2/Cu/sub 3/O/sub x/ plate, the multiple-layer structure is introduced to modelize the HTS plate. In this case, the shielding current density is governed by the integral-differential equation of the scalar potential. In addition, the power law is used as the J-E constitutive equation for description of the characteristics of the Type-II superconductor. When the equation is descretized by using the finite element method and the weighted average method, the resulting algebraic equation is solved by using the decelerated Newton method. A numerical code for analyzing the time evolution of the shielding current density has been developed and, by use of the code, the shielding performance of HTS plates is investigated. In addition, the results obtained by using the power law, the flux-flow and the flux-creep models are compared.