Lorentz Microscopy Observation of Unconventional Behaviors of Vortices in High-T c Superconductors

Vortices in high-T _c superconductors have been predicted to behave in unconventional manners that reflect the layered structure of the materials. Our newly developed 1-MV field-emission electron microscope has opened the way to enable individual vortices to be observed inside high-T _c superconducting thin films. This makes it possible to investigate the inner structures of vortices, such as those trapped along tilted columnar defects and those of chain vortices that are formed when a magnetic field is obliquely applied with respect to the normal of the layer plane of the materials.     

Hall Tunneling of Vortices in Superclean Superconductors

We discuss the main features of Hall tunneling of pancake vortices in superclean high-T _c superconductors. The general formalism for the calculation of the lifetime of a vortex pinned in a metastable configuration is described. The results are applied to the problem of quantum tunneling of a pancake vortex from a columnar defect in the limit of a small driving current.     

Comments on the Force on Pinned Vortices in Superconductors

The question of the nature of the force, usually referred to as the “Lorentz force” experienced by vortices in superconductors has arosen new attention in the last years. This paper contains some observations that may help understand the nature of this force, at least for stationary, pinned vortices. One observation is that the force is not proportional to the electromagnetic coupling constant, i.e. the electric charge. This points to the importance of kinematical analysis in discussing it. A second observation refers to the fact that in the London limit, kinetic energy dominates over magnetic energy in the formation energy of a vortex. We give an exact derivation of the force using the London model. We indicate that in the Ginzburg–Landau theory the same result obtains. Our derivation shows also the origin of additional forces experienced by the vortex near the sample surface.     

Vortices with Fractional Flux Quanta in Multi-Band Superconductors

In superconductors with three or more components, time-reversal symmetry may be broken when the inter-component couplings are repulsive, leading to a superconducting state with twofold degeneracy. When prepared carefully, there is a stable domain wall on a constriction which connects two bulks in states with opposite chiralities. Applying external magnetic field, vortices in different components dissociate with each other, resulting in a ribbon shape distribution of magnetic field at the domain wall.     

Vortices in Hubbard Superconductors: A Bogoliubov-de Gennes Approach

Based on the Bogoliubov-de Gennes formalism, we study vortices with quantum magnetic fluxes in two-dimensional supercells, when an external magnetic field (B) is applied to s-, d-, and anisotropic s-wave superconductors. This study is carried out by using a generalized Hubbard model including negative U and V, as well as a nearest-neighbor correlated hopping interaction (Δt). The self-consistent calculation of the superconducting gap (Δ) shows the formation of vortices in real space, whose structure depends on the electron-electron interaction. Furthermore, the supercell averaged Δ as a function of B reveals qualitatively different behaviors for the three analyzed pairing interactions. Finally, the results suggest that the d-wave superconducting states have larger second critical magnetic fields than those corresponding to isotropic and anisotropic s-wave ones.     

Dynamical Phase Diagram of Driven Vortices in High-T c Superconductors

Large-scale simulations on the current-driven three-dimensional frustrated anisotropic XY model with resistively-shunted junction dynamics have been performed to study the dynamical phase diagram in high-T _c superconductors. With the decrease of the current, a moving smectic is found between a moving Bragg glass and a moving liquid at high temperatures. The first-order phase transition between the moving Bragg glass and the moving smectic is clarified. At low temperatures, the moving Bragg glass can crossover to the (creeping) Bragg glass directly. Interestingly, at very high currents, the moving Bragg glass is replaced by a highly disordered phase due to the activation of vortices and anti-vortices.     

Quantized Vortices and Diamagnetic Precursor to the Meissner State in High-T c Superconductors

We report the magnetic imaging for underdoped and optimally-dopedLa_2–x Sr _x CuO₄ (LSCO) thin films on single substrates and nearly optimallydoped YBa₂Cu₃O_7–x (YBCO) thin films on tricrystal substrates in the temperature range both below and above T _c using scanning SQUID microscopy. Below T _c, clear integer- and half-integer quantized vortices were observable. Above T _c, however, the inhomogeneous diamagnetic domains appeared. The local diamagnetic domains that led to the Meissner state were found in the broad temperature range for underdoped samples and in the narrow limited temperature range for optimally-doped samples. The results provide evidence that local diamagnetic domains are closely related to the pseudogap state. The continuous connection of the domain state above T _c with the state of a half-integer vortex at the tricritical point in the YBCO film below T _c also indicates that the diamagnetic domains are also closely related to the occurrence of d_x ^{2-y 2}-wave superconductivity.     

Spontaneous Generation of Single Vortices and Anti-Vortices in Superconductors with Restricted Geometries

We study the nucleation of vortices in a thin (thickness ≪ penetration depth) mesoscopic superconducting disc in an applied magnetic field perpendicular to the disc (i.e., parallel to the axis of the disc). We write down an expression for the free energy of the system with an arbitrary number of vortices and anti-vortices at finite (non-zero) temperatures. For a given applied field, we minimize the free energy to find the optimal position of the vortices and anti-vortices (the configuration which minimizes the energy). We show that, whereas at zero temperature anti-vortices do not nucleate, anti-vortices do penetrate the disc at finite temperatures. We also calculate the magnetization of the disc as a function of the applied field and hence determine the different configurations possible in which a fixed number of fluxoids can penetrate the disc.     

Recent advances in Lorentz microscopy

Lorentz transmission electron microscopy (LTEM) has evolved from a qualitative magnetic domain observation technique to a quantitative technique for the determination of the magnetization state of a sample. In this review article, we describe recent developments in techniques and imaging modes, including the use of spherical aberration correction to improve the spatial resolution of LTEM into the single nanometer range, and novel in situ observation modes. We review recent advances in the modeling of the wave optical magnetic phase shift as well as in the area of phase reconstruction by means of the Transport of Intensity Equation (TIE) approach, and discuss vector field electron tomography, which has emerged as a powerful tool for the 3D reconstruction of magnetization configurations. We conclude this review with a brief overview of recent LTEM applications.     

Josephson Vortices in Weakly-Coupled Superconductors as Topological Solitons of the Sine-Gordon Equations for Phase Differences

No Heading We present a mathematically rigorous solution of the problem of magnetic properties of weakly-coupled superconducting multilayers with an arbitrary number N 2 of superconducting layers in external parallel magnetic fields H > 0. By minimizing a relevant Gibbs free-energy functional, we show that the equilibrium vortex structure is given by a new class of soliton solutions: namely, topological solitons of a system of N – 1 coupled static sine-Gordon equations for the phase differences in a finite spatial interval I = [–L,L]. A complete classification of the new soliton solutions is presented. For N = 2, 3, and N = , exact, closed-form analytical expressions are derived. The special case L = , H = 0 is considered separately. Non-soliton solutions are also analyzed: they are shown to be saddle points of the Gibbs free-energy functional. A comparison with the experiment is drawn.PACS numbers: 03.75.Lm, 05.45.Yv     

Noise-Assisted Microwave Up-conversion by Vortices in Thin-Film Superconductors with a dc-Biased Washboard Pinning Potential

So far the main theoretical basis for understanding and optimization of the microwave properties of vortices in type II superconductors has been relying upon the Coffey–Clem (CC) approach for the linear impedance at nonzero temperature. However, the CC model does not account for the non-linear response and the possibility to control it by changing the value of the dc transport current in a superconducting sample. For this reason, we have exactly solved the Langevin equation for the two-dimensional non-linear vortex dynamics in a dc bias-tilted cosine pinning potential in the presence of an ac current of arbitrary amplitude and frequency ω and have, thereby, substantially generalized the CC results. In this work we analyze the behavior of the non-linear response on kω-frequency in a wide range of dc and ac current densities, ω, and temperature. The kω-response is found to depend strongly on all these parameters, as exemplified for the third-harmonic (k=3) transformation coefficient Z ₃. The parametric window for the most enhanced up-conversion is presented. The predicted effects can be experimentally verified in thin-film superconductors with some pinning potential of the washboard type.     

Direct Observation and Interpretation of Carrier Dynamics of Molecular Magnetic Superconductors

The temperature-dependent time-resolved reflectance spectra of the organic superconductors (OSs) κ- and λ-(BETS)₂MCl₄ (M=Fe, Ga) and κ-(ET)₂Cu[N(CN)₂]Br are reported. The π electrons of the organic molecules (BETS or ET) are responsible for the electrical conduction in these salts, while only the Fe-containing salts have localized spins on the d electrons in the Fe atoms (S=5/2) with π–d interaction. Analysis of the spectra provided the relaxation time τ of the carriers, as well as information concerning the number of carriers at the Fermi energy N(E _F). The carrier dynamics were classified in terms of high-T _C and low-T _C OSs. In these salts, the results indicate that (1) the electron-phonon interaction is important in the occurrence and stability of the superconducting phase, and (2) electron correlation can be related to the enhancement of T _C.     

Interaction between the Ferromagnetic Dots and Vortices: Numerical Calculation and Experimental Results

Enhancing the pinning force in high-T _c superconductors can be achieved by externally introduced periodic magnetic dots. We numerically calculate the interaction between ferromagnetic dots and vortices in high-T _c superconductors. The London equation is used to generate two-dimensional vortex lattice. In the matching condition, we calculate the attraction force between magnetic dots and vortices. It is found that in an ideal condition, the pinning force of the magnetic dot reaches 2.5×10⁻¹¹ N that is more than one order magnitude stronger than the intrinsic pinning force in YBa₂Cu₃O₇ thin films. In the experimental side, we use a novel nano-technique to deposit periodic submicron Ni dots on YBa₂Cu₃O₇ thin films. The current versus voltage characteristics of an YBa₂Cu₃O₇ thin film strip with uniform Ni dots are measured at various temperatures and magnetic fields. They are compared with the current versus voltage characteristics of a bare YBa₂Cu₃O₇ thin film strip without magnetic dots. It is found the critical current value of the strip with Ni dots reduces with a much slower pace as the magnetic field strength increases in comparison with the value of the bare sample.     

Recent Results in the Mie Theory

Abstract

The Hart-Montroll (HM) method of analytical summing of the Mie series is reconsidered. The HM scattering amplitude is corrected for the low values of the diffraction parameter kR. The question of unitarity violation is discussed and solved. It is stressed that non-Rayleigh polarization may be obtained only by developing the approximation beyond that of HM.     

Measurement of Velocity Fields of Nonstationary Air Vortices by Anemometry Using Particle Images

Measurement Techniques - We consider aspects of using the method of anemometry on particle images to measure the velocity fields of nonstationary air vortices. To prevent the loss of a cross-pair...     

Photoemission Experiments on High-Tc Superconductors: Recent Progress and Some Open Questions

We summarize some of the main results on photoemission spectroscopy in the field of high-T _c superconductivity, beginning with a discussion of several open questions. We then briefly analyze our experiments that illustrate the role of doping and of intentionally introduced disorder (by electron bombardment) in Bi₂Sr₂CaCu₂O_8+x single crystals.     

局部高亮干扰文本图像的二值化方法研究

本文提出一种新的基于Curvelet变换的文本图像二值化处理方法,以消除文本图像中局部高亮度区域对二值化图像质量的影响.首先对具有局部高亮度区域干扰的原始文本图像进行Curvelet变换,得到图像在曲波域的Curvelet系数集;然后根据各Curvelet系数所表征的图像特征,对Curvelet系数进行非线性增强,以优化文本图像的直方图分布;对增强的Curvelet系数集进行反变换,得到直方图优化后的时域图像,进而应用Otsu方法实现文本图像二值化.应用本文方法对具有带状及点状局部高亮度区域的文本图像进行二值化处理,并采用ABBYYFineReaderl0对二值图像进行OCR识别.实验结果表明,通过本文提出的处理方法所得到的二值化图像,其字符的OCR识别准确率最高可达94.81％,优于其他四种典型的图像二值化处理方法.     

Effect of Dissipation on Quantum Tunneling of Vortices in Tl2Ba2Ca2Cu3O10+δSuperconductors

The temperature and magnetic field dependence of the magnetic relaxation rate has been investigated at low temperatures (1.8 < T < 10 K) on two Tl₂Ba₂Ca₂Cu₃O_10+δ samples (epitaxial thin film and sintered pellet). The temperature dependence gives evidence of a crossover in the mechanism of vortex motion, from classical thermal activation to quantum tunneling as temperature decreases. The field dependence of the relaxation rate indicates a crossover in the dimensionality of vortices, from three-dimensional flux lines to two-dimensional pancake vortices as field increases. For the thin film, the temperature dependence of the rate has been fitted to the theoretically predicted expressions for finite-temperature enhancement of the quantum rate in different regimes of dissipation. In spite of the similarity of the fits, the estimate of the ratio of Hall to viscous drag terms in the equation of motion indicates that quantum tunneling in this system occurs in an intermediate dissipative regime, where both terms contribute to the motion of vortices.