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Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

To study the melting transition of a vortex crystal (or cluster) consisting of a small number of vortices confined in a mesoscopic-scale superconductor, $c$-axis magnetoresistance in the highly anisotropic high-${T}_{\mathrm{c}}$ superconductor ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+y}$ (Bi2212) has been measured using a triangle-shaped stack of intrinsic Josephson junctions, which was trimmed out from a single-crystal flake of Bi2212 via a double-sided etching process using a focused ion beam. We observed oscillations of the melting transition line, in which the oscillating part of the melting temperature has sharp peaks when the number of vortices $N$ exactly coincides with the triangular number $n(n+1)/2$ ($n$ is an integer number), at least for $Nl50$. This is in contrast to the case of square shapes where the enhancements appeared as broad peaks around $N={n}^{2}$. Furthermore, the field ranges of the $N$-vortex state expand at the triangular numbers of $N$, suggesting that the triangular number of vortices has a more stable configuration than the others. Numerical studies on the configuration of vortices in a triangle shape show that geometrical matching with no defect structures is realized at the triangular numbers, whereas an edge dislocation often appears in the other nonmatching cases. The degree of suppression of the melting temperatures at nonmatching numbers is reasonably consistent with the value estimated from the increase in free energy with the introduction of an edge dislocation.

A theoretical calculation for the superconducting transition temperature of the hole-doped cuprate is performed based on supercurrent generation by the spin-twisting itinerant motion of electrons. The superconducting transition temperature, T c , is determined by a numerical simulation as the stabilization temperature of the coherence-length-sized loop currents, “spin-vortex-induced loop currents (SVILCs),” generated by the spin-twisting itinerant motion of electrons. The simulation indicates that the stabilization of the SVILCs occurs in two steps; when temperature is decreased from room temperature, first, the phase where the sum of the winding numbers of the SVILCs is zero appears; with further decrease of the temperature, the phase where the winding numbers of the SVILCs are fixed appears. We identify the latter to the superconducting phase, and the former to the temperature below which the Kerr rotation is observed. The calculated T c value is close to the experimental value around the optimal doping. It scales as ${{t^{2}} \over U}$ in a similar manner to the antiferromagnetic spin-fluctuation, where t is the nearest neighbor transfer integral and U is the on-site Coulomb repulsion parameter. The calculated T c disagrees in the underdoped and overdoped regions. These disagreements are explained as due to the reduction of T c by the quantum criticality arising from the two quantum critical points at the lowest and highest ends of the hole density x of the superconducting phase, where the former corresponds to the percolation threshold of the spin-vortices, and the latter to the spin-vortex formation-destruction critical point.

We report on the scanning tunneling microscopy (STM) and spectroscopy (STS) study on a newly discovered superconductor, Ir 1 − x Pt x Te 2 . We previously found that the sample which shows superconductivity forms so called “patchwork structure (PS)”. To obtain the spatial evolution of electronic structure on the PS, we performed STM/STS measurements on the PS. STS measurements revealed that an averaged spectrum shows the same energy asymmetry as that in the low temperature phase in the parent material, IrTe 2 . Furthermore, the spectrum at the trough on the PS is more asymmetric than that at the crest. This tendency is similar to that observed on the supermodulation in the low temperature phase in IrTe 2 .

Based on a new supercurrent generation mechanism proposed for the cuprate superconductivity (as reported by Koizumi (J. Supercond. Nov. Magn. 24:1997, 2011); Hidekata and Koizumi (J. Supercond. Nov. Magn. 24:2253, 2011); Koizumi et al. (J. Supercond. Nov. Magn. 27:121, 2014); Koizumi et al. (J. Supercond. Nov. Magn. 2014), we re-derive the ac Josephson effect including the current flow through the leads connected to the Josephson junction and the impressed electromotive force. It is noted that the actual experimental boundary condition where the Josephson frequency 2e V 0/h (h is Planck’s constant, e is the absolute value of electron charge, and V 0 is the dc voltage across the Josephson junction) is measured differently from the one assumed by Josephson, and 2e V 0/h is obtained by the electron tunneling instead of the Cooper pair tunneling. It is also indicated that the standard textbook description for the Josephson relation, “if a dc voltage V 0 is applied, the time-variation of ϕ occurs” (as reported by Feynman et al. (1965); Ashcroft and Mermin (1976); Kittel (1986); Tinkham (1996) (ϕ is related to the tunneling current as J s = J c sinϕ) should be rephrased, “if the time-variation of ϕ is introduced, a voltage difference V 0 appears.” We show that by adding the Rashba spin-orbit interaction to the Bardeen, Cooper, and Schrieffer (BCS) Hamiltonian, the spin-twisting itinerant motion of electrons is stabilized in the BCS superconductors; thus, it is suggested that the present, new supercurrent generation mechanism is also relevant to the BCS superconductors, i.e., the true origin of the supercurrent generation in the BCS superconductors may also be the spin-twisting itinerant motion of electrons.

We propose a novel supercurrent generation mechanism in the cuprate. The supercurrent is generated as a collection of the spin-vortex-induced loop currents created with the doped holes at their centers. A quartet of the spin-vortices with width 4a (a is the lattice constant of the CuO2 plane) is the stable unit of the spin-vortices, and an assembly of them creates a network channel for the supercurrent flow. A macroscopic supercurrent flows when they cover the whole CuO2 plane. The Ginzburg-Landau macroscopic wave function formalism is also derived from the present supercurrent generation mechanism.

We have measured the magnetic field effect of THz radiation emitted from a mesa structure fabricated from high-quality high-transition temperature ( T c ) superconductor single crystalline Bi 2 Sr 2 CaCu 2 O 8+δ using a newly developed measurement system in magnetic fields up to 6 T. The results show that the THz radiation was strongly suppressed in magnetic fields with a considerable anisotropy: about 20 Oe magnetic field is sufficient for the total suppression of the THz radiation for the field being parallel to the c -axis, while for the field being parallel to the ab -plane the radiation has first a slight hump at about 50 Oe, then has a sudden drop at about 150 Oe, and shows a step-wise structure between about 200 and 300 Oe before the intensity diminishes completely below the detection sensitivity limit at about 450 Oe. These characteristic features are discussed in comparison with recent theoretical works.

Recent developments of coherent terahertz (THz) oscillators based on the intrinsic Josephson junctions (IJJs) in mesas of the high temperature superconductor Bi2Sr2CaCu2O8+δ are reviewed. Experimental and theoretical studies of the emission from equilateral, right-angled isosceles, and acute isosceles triangular mesas are compared with those obtained from rectangular, square, and disk mesas, in order to determine the role of the mesa geometry. The superconducting properties and emission frequency f spectra are presented for a variety of triangular mesa geometries. Analytic and finite difference time domain numerical calculations of the emissions from the internal electromagnetic (EM) cavity modes of triangular mesas are compared with experiment. The experimental f always satisfies the ac Josephson relation, and its narrow linewidth arises from the synchronized emissions from many IJJs. For some mesa geometries, f also strongly locks onto an EM cavity mode frequency, enhancing the emission’s stability and output power. For other geometries, such cavity mode locking is weak, and f is highly tunable.

In this study, we investigate numerically the terahertz radiation from the mesa-structured intrinsic Josephson junctions (IJJs). The Sine–Gordon equation for inside of the mesa, and the Maxwell equation for outside of the mesa, are solved simultaneously. We consider the influence of a hot spot in the mesa where jc locally decreases, and calculate the radiation power as a function of the voltage. We observe strong radiation when the ac Josephson frequency satisfies the cavity resonance condition. For this strong radiation from the IJJs mesa, we calculate the radiation patterns. The radiation patterns reflect the existence of two types of internal modes: a uniform background mode and a cavity resonance mode. Furthermore, the radiation patterns are strongly affected by the diffraction at substrate edges., The 8th International Symposium on Intrinsic Josephson Effects and Plasma Oscillations in High-Tc Superconductors (PLASMA 2012)

We report on intense and coherent terahertz (THz) electromagnetic (EM) waves emitted from equilateral triangular mesa structures of the intrinsic Josephson junctions (IJJs) in single crystalline high-Tc superconducting Bi2Sr2CaCu2O8+δ. The focused ion beam milling technique is used for mesa fabrication. THz radiation is observed when the emission frequency is in the vicinity of the primary cavity resonance frequency determined by the mesa geometry. We also investigated numerically the THz radiation from such mesas using the finite difference time domain method. We found an apparent EM mode similar to the known TM(1, 0) = TM(0, 1) cavity mode during the THz emission.

An attempt has been made to improve THz radiation characteristics emitted from mesas made from Bi2Sr2CaCu2O8+δ single crystals in order to achieve an ultimate goal of high frequency quantum device applications, named here as the Quantum Terahertz Electronics (QTE). Among many requirements to be fulfilled and necessary for the development, we here made an effort to generate more intense radiation using a stand-alone type of mesa. Some characteristic features are described.

The persistent current generation in the cuprate is theoretically investigated based on the spin-vortex superconductivity theory. We present a way to impose the single-valued condition on wave functions and clarify the appearance of a vector potential and the persistent current generation by it when the spin-vortices are created by the conduction electrons. We attribute the reason for the very high superconducting transition temperature in the cuprate to the enhanced stability of the spin-vortices by the strong hole–lattice interaction.

To investigate vortex states in exfoliated Bi2Sr2CaCu2O8+y high-Tc superconductor with and without micro-hole arrays, the in-plane resistance in the vortex states has been measured. In exploration of vortex-lattice melting transition in pristine films, signs of the transition have been successfully found in the films as thin as a few hundred nm. A comparison of irreversibility lines in both samples indicates that influence of artificial micro holes is masked at low temperatures due to the native residual pinnings.

In this study, we have numerically investigated the radiation from two separated mesa-structured intrinsic Josephson junctions(IJJs)whichareelectricallyconnectedinseries.Wehavecalculatedelectromagneticfield insideandoutside of IJJs simultaneously using two dimensional model. The radiation power has been calculated as a function of the distance between two mesas. We have observed the oscillation of the radiation power with respect to the distance coming from the change of electromagnetic interaction between the mesas. In particular, at the distances where the electromagnetic standing waves appear in the interspace between the mesas, the radiation powers become larger than twicethe poweremitted by oneisolatedmesa. We have also calculatedthe radiationpatternsemitted by two mesas and found thattheradiation patterns greatly changewith the distances.

We present a thermal analysis of a patterned mesa on a Bi2Sr2CaCu2O8 (Bi2212) single crystal that is based on tunneling characteristics of the c-axis stack of ~800 intrinsic Josephson junctions in the mesa. Despite the large mesa volume (e.g., 40x300x1.2 micron3) and power dissipation that result in selfheating and backbending of the current-voltage curve (I-V), there are accessible bias conditions for which significant polarized THz-wave emission can be observed. We estimate the mesa temperature by equating the quasiparticle resistance, Rqp(T), to the ratio V/I over the entire I-V including the backbending region. These temperatures are used to predict the unpolarized black-body radiation reaching our bolometer and there is substantial agreement over the entire I-V. As such, backbending results from the particular Rqp(T) for Bi2212, as first discussed by Fenton, rather than a significant suppression of the energy gap. This model also correctly predicts the observed disappearance of backbending above ~60 K., 4 pages, 2008 Applied Superconductivity Conference

Recently, in relation to the THz wave emission, there arises much attention in studies of the electromagnetic waves excited in the intrinsic Josephson junctions (IJJs) of high T c superconductors. We investigate by numerical simulation the electromagnetic wave emission from the in-phase IJJs without an applied magnetic field. Due to the boundary condition of the electromagnetic field at the edges of the junctions, large intensity of the emitted power is obtained, when the anti-nodes of the standing waves in the inside induction field coincides with the boundary edge, As the result, we have an oscillatory increase of the emitted power with a decreasing bias current in the in-phase IJJs, and the maximum emitted power is obtained near the retrapping point. In the longer in-phase junctions, solitonic (vortex–anti-vortex) phase motions are also excited when certain conditions are satisfied. We discuss also those effects on the emitted power.

The vortex-lattice melting transition of a limited number of vortices confined in mesoscopic square superconductors was studied by $c$-axis resistance measurements using stacks of intrinsic Josephson junctions in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+y}$. In contrast to the melting transition in bulk crystals, we have first found a clear oscillatory behavior in the field dependence of the melting temperature in small samples of $5--10\text{ }\text{ }\ensuremath{\mu}m$ square. The periods of the oscillations roughly obey the regularity of the matching conditions of square vortex lattices surrounded by a square boundary and the melting temperatures are enhanced around the vortex number of ${i}^{2}$ (where $i$ is an integer). The results suggest that a confinement effect by the square boundary stabilizes square lattice structures which are realized around ${i}^{2}$ vortex number even in competition with the favorable Abrikosov triangular lattice in the bulk.

Continuous terahertz electromagnetic waves have new applications in scientific and industrial fields such as medicine and information technology. Cuprate high-temperature superconductors have a layer structure, and form a naturally multi-connected Josephson junction system called intrinsic Josephson junction (IJJ). In IJJ, there appears a new excitation called the Josephson plasma. Its frequency is in the region of terahertz inside the superconducting energy gap. The excited plasma wave is converted into an electromagnetic wave at sample surfaces. Therefore the IJJ has a great potential to generate terahertz continuous wave. Here we report the results of simulations to find the optimum condition for obtaining the strongest emission power of the terahertz waves. The simulations were carried out using our theory. Since the simulation uses very large-sized coupled nonlinear equations therefore difficult to compute, we used the fastest supercomputer named as Earth Simulator. We found that the quite intense continuous terahertz coherent wave is emitted from a small sample with high-energy efficiency.

Superconducting quantum interference devices (SQUIDs) can be used to detect the signals of nuclear quadrupole resonance (NQR). The NQR frequencies of some interesting materials are in the order of MHz. However, the sensitivity of a high-Tc SQUID is normally not enough to detect the weak NQR signals. To improve the sensitivity of a high-Tc SQUID at MHz frequency, we used a transformer made of normal copper wire. The transformer was composed of a pickup coil, an input coil and a capacitor. The pickup coil was used to detect the magnetic field; the input coil was used to couple the field to the SQUID; and the capacitor was used to create a resonant frequency. By using the normal metal transformer, the magnetic field resolution of the high-Tc dc SQUID was improved by about 38.8 times (from 220 to 5.67 fT Hz−1/2) at 954 kHz.

Josephson vortex lattice in narrow Bi-2212 intrinsic Josephson junctions have been studied. Formation of rectangular Josephson vortex lattice is expected in narrow width due to the edge effect. Current–voltage (I–V) characteristics were measured as a function of the magnetic field applied parallel to their a–b planes. Maximum zero bias current (IC,branch) and flux-flow voltage were measured. We observed that the IC,branch monotonically decreased with magnetic field up to 0.6 T. Above 0.6 T, IC,branch showed an enhancement, accompanied by an enhancement of flux-flow voltage thus flux-flow speed, up to 1.0 T. This result indicates a change in the configuration of vortex lattices from triangular to other structure (possibly rectangular) by the edge effect in which configuration both the flux-flow voltage and IC,branch are enhanced due to an increase in the maximum velocity of the vortex lattice.

Continuous coherent terahertz waves have various kinds of application such as biology and information science. One of the hurdles for technical advancements in the terahertz region of electromagnetic wave is development of sources for intense and continuous coherent and frequency tunable terahertz waves. Therefore, we investigate a mechanism for emitting the terahertz waves by using high T c superconductors. High T c superconductors form naturally stacked Josephson junctions. In the junctions there appears an excitation called Josephson plasma, the frequency of which is in the range of terahertz. The frequency appears inside the superconducting main energy gap and the Landau damping is weak. Therefore, if the Josephson plasma is excited in someway, the excited plasma decays by emitting an electromagnetic wave. When an external current and a magnetic field are applied to the sample, fluxon flow induces a voltage. The voltage creates oscillation current through the Josephson effect, and the current excites the Josephson plasma waves with terahertz frequencies. In the present work we perform simulation of terahertz emission using Earth Simulator. We used the parameters corresponding to Bi 2 Sr 2 CaCu 2 O 8+ δ and obtained the following results. The sample itself works as a cavity, and the input energy given by an external current is stored in a form of standing wave of the Josephson plasma. A part of the energy is emitted as terahertz waves. The emitting electromagnetic wave is continuous coherent terahertz waves with the power of an order of 1000 W/cm 2 . The frequency is tunable by changing the applied current.

c-axis micro-bridges of La/sub 2-x/Sr/sub x/CuO/sub 4/ (LSCO) single crystals were fabricated by the focused-ion-beam (FIB) etching method. Small rectangular LSCO pieces were fabricated by cutting and grinding single crystals of underdoped LSCO of x=0.09. The size of LSCO single crystals between electrodes was cut to (5-20)/spl times/40 /spl mu/m/sup 2/ in the ab-plane by using the FIB etching method. The junction resistance exhibited clear two-step structures corresponding to the superconducting transition of two different components of crystal structure. Superconductor-insulator-superconductor (SIS) like-branch structures on I-V curves of the LSCO stacks were observed for the first time. The branch structures show voltage jumps of several tens mV in the range of 2 K to 5 K with temperature dependence. When the temperature is changed from 2 K to 5 K, the critical current around zero bias regions splits into a few small voltage jumps with intervals of several mV in the range of 1 mV to 3 mV.

After a brief description of the double-sided fabrication process, we give an example to show that a quite large array of intrinsic Josephson junctions (IJJs) can be made by superconductively connecting 256 stacks of junctions together. Each of these stacks contains only 40 junctions which prevents problems causing by heating. We present a detailed discussion on a new structure we have developed in which an extra electrode can be fabricated in the middle of an array by a slight modification of the double-sided process. Using this middle electrode, we can determine further information on the physical processes inside the stack than is possible without such an electrode. Finally we shall discuss terahertz generation in IJJs when an external magnetic field is applied perpendicular to the width of the junctions.

Oscillations of Josephson vortex-flow resistance have been studied in narrow (L/spl sim/2-4/spl lambda//sub J/) Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8+/spl delta// intrinsic Josephson junctions as a function of magnetic field applied parallel to junction edges. Lengths of junctions fabricated are /spl sim/1 /spl mu/m in order to enhance pinning effects of Josephson vortex lattice to the junction edges and thus to enhance formation of rectangular vortex lattice which would lead an in-phase mode of the junctions as a necessary condition for the THz generator application. The observed Josephson vortex flow resistance showed a periodic oscillation with a period (H/sub p/) corresponding to one flux quantum enters per junction, namely, corresponding to the rectangular vortex lattice. Observed strong oscillation was a result of collective behavior of the entry and escape of vortices in a form of rectangular vortex lattice. Peaks in the oscillations were found at the fields H=nH/sub p/, here n shows an integer number. Here, Josephson vortex lattice flow speed shows a local maximum. With this magnetic field, outermost vortex rows geometrically match to the edges of junctions. Contrary to this, a minimum of flow speed, namely pinned state of the vortex lattice, was observed at H=(n+1/2)H/sub p/.

Charge dynamics in the two-dimensional Hubbard model is investigated by quantum Monte Carlo simulations. We find that dielectric function ϵ ( q , ω ) becomes negative at finite frequencies for U / t =4 with hole density δ =0.15. Numerical results indicate that vertex corrections enhance charge fluctuations and that this enhancement is important for overscreening. Based on the numerical results, we briefly discuss phonon softening which is observed by X-ray and neutron inelastic scattering experiments.

Cross-whisker intrinsic Josephson junction has been developed as a probe of symmetry of the superconducting order parameter. Two B2212 single crystal whiskers were connected on a MgO substrate at their c -plane with various crossing angles. Angular dependence of the critical current densities showed d-wave-like 4-fold symmetry. However, the angular dependence was much stronger than that of the conventional d x 2 − y 2 -wave. The critical current density of the cross-whisker junction with cross-angle α =45° was not completely zero. Shapiro steps and Fraunhofer pattern were clearly observed in 45° twisted cross-whisker junctions. It is suggested that the superconducting gap exists even at nodal direction.

When phonons strongly mix with electron charge fluctuations with low frequencies, the phonon mediated attractive interaction between electrons is strongly enhanced. The occurrence of the mixing has been indicated by the neutron scattering experimental results that the dispersion of the in-plane Cu–O bond-stretching mode in the high Tc cuprate superconductors is strongly softened near the zone boundary. We propose that the phonon mediated attractive interaction strongly enhanced by the vibronic effect can form a basis for the phonon mechanism of high temperature superconductivity. With the Eliashberg theory and with the electronic structure determined by ARPES and the electronic dielectric function obtained by the softened dispersion of the in-pane Cu–O stretching mode, we calculated the transition temperature and the order parameter at the transition temperature. The order parameter is of the d(x2-y2) symmetry and the transition temperature is well in excess of 100 K.

As a test of the superconducting order parameter, we have developed an intrinsic Josephson junction by the name of cross-whisker junction. This junction was made using two Bi 2 Sr 2 CaCu 2 O 8+d single crystal whiskers. Two whiskers were connected at their c planes with various cross-angles. Angular dependence of the critical current densities shows d-wave-like fourfold-suminetry. However, the angular dependence is much stronger than that of the conventional d x 2 -y 2 wave. The Jc shows its smallest value around 45 deg, which suggests that the Josephson penetration depth becomes longer. We have successfully observed a Fraunhofer pattern in the cross-whisker junction with cross-angle 45 deg.

We studied the DC current-driven vortex state of a Bi 2 Sr 2 CaCu 2 O 8+ δ model in the presence of pointlike disorder via a Monte Carlo simulation. We found that the vortex drift velocity v as a function of temperature T drastically changes twice at a depinning ( T dp ) and a melting ( T m ) temperature, as is consistent with our two-stage melting scenario. At the low field region, whereas v remains almost zero for T T dp , it rapidly grows for T dp T T m and the Bragg peak intensity survives for T T m . We thus give numerical evidence that a moving Bragg glass phase exists for the intermediate temperature regime of T dp T T m .

The recent neutron scattering experiments in high T c superconductors show that the frequencies of the LO phonon of a stretching mode is strongly softened and the frequencies of the LO and TO phonons are inverted in certain wave number and frequency regions. This fact suggests that the electronic dielectric function becomes negative (over-screening effect) due to the correlation effect in these regions, and the Coulomb interaction in the LO phonon is screened. In this case, the theory suggests that the attractive interaction mediated by optical phonons is highly enhanced. This fact will be a capable mechanism of high T c superconductivity. A characteristic of the electronic energy band in cuprate superconductors is that there appear the flat bands just below the Fermi level along the k x and k y axes due to the correlation effect. This feature has been observed by the angle-resolved photoemissions. From both the above effects, we predict that the symmetry of the order parameter is of the d x 2 − y 2 wave and the superconduting transition temperature can exceeds 200 K.

Contacting the c planes of two Bi2212 whiskers we made cross-whiskers junctions with intrinsic Josephson junction nature. The cross-angle dependence of the critical current has a fourfold symmetry and therefore the symmetry of the superconducting order parameter is d-wave like. However, the angular dependence is much stronger than that of the conventional d-wave. Recently, neutron scattering experiments in cuprate superconductors showed the occurrence of very large charge fluctuations with relatively low frequencies along the q x and q y axes. Taking account of this fact, we calculated the superconducting order parameter originating from the Coulomb channel and obtained the d-wave like order parameter whose structure is consistent with the present experiments.

High-Tc cuprate superconductors like Bi 2 Sr 2 CaCu 2 O 8+ y (Bi-2212) show very large anisotropy in the electrical conduction. Inside the CuO 2 plan the conduction looks like that in good metals, while the block layers located between CuO 2 planes behave like insulating barriers. Thus, neighboring CuO 2 layers are linked by the Josephson coupling in superconducting states, and the Bi-2212 single crystal can be regarded as a natural serial array of Josephson junctions along the c-axis. It has been found out that in such a system a unique excitation mode called the collective Josephson plasma exists. The mode collectively oscillates along the c-axis, while it propagates along any direction ranged from the ab -plane to the c-axis. If the mode can be coherently excited, the system should be very useful as a device generating strong electromagnetic wave emission. In this paper we review a theoretical framework describing the Josephson plasma modes. The Josephson vortex penetrates into the sample under the magnetic field parallel to the CuO 2 plane and it moves along the ab -plane under an external current parallel to the c-axis. In the vortex flow state, the vortex speed can reach and exceed the propagating velocities of the Josephson plasma modes due to very weak dissipation. Then, the vortices strongly couple with the plasma modes and change their flowing lattice configurations into patterns dependent on the interacting plasma mode profiles. Among many expected flow patterns, we pay attention to a special state resonating with a plasma mode in-phase along the c-axis because all junctions synchronize in such a state. Large-scale numerical simulations by Machida et al. confirmed that the special state characterized by the rectangular lattice stably appears in a wide range of I–V characteristics. In this paper, we report their recent simulation results.

We perform numerical simulations solving the coupled sine-Gordon equation for intrinsic Josephson junction and the Maxwell equation for the wave guide attached at a neighbor of junction sites in order to simulate actual emission process of electromagnetic wave caused by the Josephson vortex flow. The simulation results reveal that the power of emitted electromagnetic waves becomes the maximum at the highest resonant voltage estimated from the dispersion relations of the Josephson plasma modes of the system and the flowing vortex configuration is almost complete rectangular lattice at the maximum point.

We numerically examine a possible vortex-matter phase diagram of Bi 2 Sr 2 CaCu 2 O 8+ δ in the presence of dense pointlike defects, by using a Monte Carlo simulation based on the Lawrence–Doniach model. Distinct phases of the Bragg glass, vortex glass, and pancake vortex gas, together with a depinning line within the glass phases, manifest themselves on the field ( B )-temperature ( T ) plane. While the locations of these phase boundaries are sensitive to pointlike pinning energy U p ( T ), we phenomenologically obtain a universal B – T phase diagram depending on a single parameter U p ( T ). We also discuss the relevance of numerical simulation to recent experiments.

In order to make clear a correlation between mesoscopic ferromagnetic cluster and the colossal magnetoresistance in perovskite based manganites, the systems (La 1- x Tb x ) 2/3 Ca 1/3 MnO 3 with x ...

The Josephson plasma wave emerging in layered HTSC is a very unique collective excitation which is assigned to a composite wave of the Josephson current and the electromagnetic field. Single crystals of layered HTSC correspond to multi-stacked Josephson junction arrays and the Josephson plasma oscillations are collectively excited over all junctions, that is, the crystals as a whole respond to AC electromagnetic perturbations. Experimentally, the Josephson plasma excitations have been observed by the optical reflectivity and the microwave resonant absorption. On the other hand, theoretically, the nature of the Josephson plasma waves and related electromagnetic behaviors can be studied using the equations for the superconducting phase. First, we point out that the measurements of the plasma resonance provide a useful tool to study the nature and stateof the vortices in HTSC since the Josephson plasma strongly interacts with the vortices. Second, we illustrate some related in intriguing electromagnetic behaviors including the interaction with the Josephson vortex, for example, a Cherenkov like radiation of the Josephson plasma. Finally, we suggest a way to excite the Josephson plasma effectively, that is, we show that a superradiation of the Josephson plasma is theoretically possible.

Large scale Monte Carlo simulations are performed in order to clarify thermodynamic properties of interlayer Josephson vortices in high-T c superconductors. In weakly/highly anisotropic systems, the normal to superconducting phase transition is first/second order. The critical anisotropy parameter is originated from the intrinsic pinning effect of the layered structure, and depends on the strength of the magnetic field.

A critical value in the product of the anisotropy parameter and the magnetic field is observed in interlayer Josephson-vortex systems by extensive Monte Carlo simulations. Below (above) this critical value the thermodynamic phase transition between the normal and the superconducting states upon temperature sweeping is first (second) order. It is discussed that the origin of this tricritical point is the highly anisotropic layered structure of high- ${T}_{c}$ superconductors.

The structure and dynamics of a single Josephson vortex and the collective dynamics of Josephson vortices in highly anisotropic High- T c superconductors (HTSCs) are briefly reported on the basis of the numerical simulation results. The Josephson vortex has a peculiar variation scale for the tunneling current in contrast to Abrikosov vortex. In the presence of a transport current along the c -axis, the single Josephson vortex excites wake-like electromagnetic fields behind the vortex center due to the Cherenkov radiation, while a mass of Josephson vortices move with flow lattice structures depending on the current strength. It is shown that the moving vortex lattice structures are strongly affected by the interaction with the transverse Josephson plasma modes.

The purpose of this paper is to present microscopic theory for intrinsic Josephson junctions and provide proper model equations describing macroscopic longitudinal and transverse dynamics in intrinsic Josephson junctions. We start with BCS functional integral formalism and clarify that fluctuations around the Josephson relation have an important role in low-energy fluctuations when the superconducting layer thickness is decreased to atomic scale comparable to the charge screening length. Intrinsic Josephson junctions completely fulfill such condition, in which the longitudinal plasma excitation mode propagating along the stacking direction is proved to exist. On the other hand, we derive the most basic dynamical equations for the superconducting phase and charge based on Euler–Lagrange equations obtained from effective action and show that the equations can be reduced to the phenomenological coupled Sine–Gordon equation and Koyama–Tachiki model under proper approximations considering two typical experimental situations.

In order to clarify the ``superradiant'' conditions for the moving Josephson vortices to excite in-phase AC electromagnetic fields over all junctions, we perform large scale simulations of realistic dimensions for intrinsic Josephson junctions under the layer parallel magnetic field. Three clear step-like structures in the I-V curve are observed above a certain high field ($H > 1T$ in the present simulations), at which we find structural transitions in the moving flux-line lattice. The Josephson vortex flow states are accordingly classified into four regions (region I $\sim $ IV with increasing current), in each of which the power spectrum for the electric field oscillations at the sample edge are measured and typical snapshots for Josephson vortex configurations are displayed. Among the four regions, especially in the region III, an in-phase rectangular vortex lattice flow state emerges and the power spectrum shows remarkably sharp peak structure, i.e., superradiant state. Comparison of the simulation results with an eigenmode analysis for the transverse propagating Josephson plasma oscillations reveals that the resonances between Josephson vortex flow states and some of the eigenmodes are responsible for the clear flux lattice structural transitions. Furthermore, the theoretical analysis clarifies that the width of the superradiant state region in the I-V characteristics enlarges with decreasing both the superconducting and insulating layer thickness., 8 pages, Revtex, 7 figures; figure arrangements improved. no changes in text

We demonstrate that both microwave resonant absorptions and multiple-branch structures in the $I\ensuremath{-}V$ characteristics observed in intrinsic Josephson junctions are caused by the dynamical breaking of the charge neutrality inside the atomic-scale superconducting layers. The Lagrangian for the time-dependent Lawrence-Doniach model incorporating the charge neutrality breaking effect is proposed. On the basis of the Lagrangian, the longitudinal collective Josephson plasma mode is proved to exist. The branching behaviors in the $I\ensuremath{-}V$ curves are almost completely reproduced by careful numerical simulations for the model equation derived from the Lagrangian.

The effects of applied current on the vortex-lines dynamics in heavy-ion-irradiated ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ are studied through Monte Carlo simulation. From the analysis of current-voltage characteristics, we find a clear peak effect in the critical current density, prominent near the melting transition of the vortex solid, when the magnetic field is increased toward the matching field. The peak field corresponds to a fractional $(\ensuremath{\approx}1/3)$ filling factor of the vortices to columnar defects. This enhanced vortex pinning occurs simultaneously with a rapid change in the interlayer-coupling nature of the current-driven vortex state. In addition, numerical results on current-driven moving vortex lines could also explain other anomalies obtained from the recent Josephson plasma measurements.

The mechanism of the flux-line-lattice (FLL) melting in anisotropic high-T_c superconductors in ${\bf B}\parallel {\bf \hat{c}}$ is clarified by Monte Carlo simulations of the 3D frustrated XY model. The percentage of entangled flux lines abruptly changes at the melting temperature T_m, while no sharp change can be found in the number and size distribution of vortex loops around T_m. Therefore, the origin of this melting transition is the entanglement of flux lines. Scaling behaviors of physical quantities are consistent with the above mechanism of the FLL melting. The Lindemann number is also evaluated without any phenomenological arguments., Comment: 10 pages, 5 Postscript figures, RevTeX; changed content and figures, Phys. Rev. B Rapid Commun. in press