Charged vortex structure in high-temperature superconductors

By using a model Hamiltonian with competing antiferromagnetic (AFM) spin density wave (SDW) and d-wave superconductivity orders, the effect of next-nearest-neighbour (nnn) hopping on spin and charge structures in high-temperature superconductors is investigated at finite temperatures. For an optimally doped sample, we find that the AFM order magnitude in the vortex core is firstly enhanced and then suppressed, accompanied with a ``positively → negatively → positively" charged vortex structure transition with increasing nnn hopping strength, which implies that the AFM order is unnecessarily bounded to an electron-rich vortex core. In addition, a charge ordering pattern with four negatively charged peaks localized in a small region is also found around the vortex core centre without net charge. Recent scanning-tunneling-microscopy experimental observations of the checkerboard structure are hopefully understood.     

Direct observation of the scaling relation between density of states and pairing gap in a dirty superconductor

Theories and experiments on dirty superconductors are complex but important in terms of both theoretical fundamentals and practical applications. These activities are even more challenging when magnetic fields are present because the field distribution, electron density of states, and superconducting pairing potentials become nonuniform. Here, we present tunneling microspectroscopic experiments on Nb C single crystals and demonstrate that Nb C is a homogeneous dirty superconductor. When applying magnetic fields to the samples, we found that the zero-energy local density of states and the pairing energy gap followed the explicit scaling relation proposed by de Gennes for homogeneous dirty superconductors in high magnetic fields. More significantly, our experimental findings indicate that the validity of the scaling relation extends to magnetic field strengths far below the upper critical field, calling for a new nonperturbative understanding of this fundamental property in dirty superconductors. On the practical side, we used the observed scaling relation to derive a simple and straightforward experimental scheme for estimating the superconducting coherence length of a dirty superconductor in magnetic fields.     

欠掺杂高温超导体中的涡旋电荷结构相变

利用平均场t-t′-U-V-V_c模型,通过自洽求解Bogoliubov-de Gennes方程,研究了高温超导体中涡旋结构的相变.发现增大原位排斥势U,自旋密度波、电荷密度波以及d波序参量由棋盘结构转变为条纹结构.模型哈密顿量中引入合适强度的长程库仑势后,欠掺杂高温超导体样品中也可以出现二维或者棋盘结构,结果与文献报道的扫描隧道显微镜实验结果一致. 关键词： 高温超导 涡旋结构 长程库仑势     

Anomalous Josephson vortex solutions in Josephson junctions with multiple tunneling channels

We construct a theory for Josephson junction with multiple tunneling channels. We focus on two situations, i.e., a heterotic junction composed of two-gap-superconductor, insulator, and one-gap-superconductor, and a grain-boundary junction formed by two identical multi-gap superconductors. Then, we show that the magnetic field distribution of the Josephson vortex for ±s-wave superconductivity is much more enlarged than that for s-wave without sign change between the order parameters. We display such anomalous vortices and suggest how to evaluate the enlargement.     

高温超导体磁通动力学和混合态相图(II)

文章简要介绍了高温超导体磁通动力学和混合态物理在过去十余年的发展.高温超导体由于其自身的一些特点,使得它与常规超导体相比较拥有极其丰富的相图,磁通动力学也表现出了非常丰富的研究内容,很多新的概念被提出,新的现象被观察到.比如说涡旋玻璃态,集体钉扎和蠕动,磁通格子的一级和二级熔化相变,布拉格玻璃,峰值效应,二维涡旋饼态,Josephson 磁通运动等等,均是在高温超导体发现之后提出来的新的概念或新发现的现象.有些研究结果目前尚无定论,如关于涡旋玻璃态存在与否的争论至今仍然在进行,但是这些研究内容无疑会大大促进超导物理的发展.高温超导体磁通动力学纷繁复杂的研究内容可以归结为三个相互关联的数字：Ginzburg数(Tc/H2cεζ3)2/2,量子电阻Qu=(e2/)(ρn/εζ),和临界电流的比值jc/j0,这里ζ是相干长度,Hc是热力学临界磁场,ε是有效质量的各向异性度,ρn是正常态电阻率,jc是零温临界电流,j0是拆对临界电流.对于高温超导体前两个数值（Ginzburg数和量子电阻）很大,而临界电流比值较小,因此导致有强的热涨落和量子涨落,以及很强的磁通运动行为（对应小的实测临界电流）.磁通动力学的研究从更深层次影响超导体的临界电流问题和强电应用的发展,最后简要地介绍了这方面的情况.     

Supercooling across first-order phase transitions in vortex matter

Hysteresis in cycling through first-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature T or magnetic field H (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in H-T space, and will be larger when T is lowered at constant H compared to the case when H is lowered at constant T. We discuss the effect of isothermal field variations on metastable supercooled states produced by field-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.     

磁通格子的有序-无序相变和反向熔化

考虑了无序钉扎、热涨落和磁通互作用, 用Monte Carlo分子动力学模拟方法研究二维磁通格子在无序钉扎强度和温度空间的相图, 以及由布拉格玻璃相到非晶磁通玻璃相和到磁通液体相的有序-无序相变.为了决定磁通格子的序，计算了静态结构因子和磁通格子位形的有限尺寸指数.计算结果表明，Bragg玻璃相在低温的无序磁通玻璃相和高温的磁通液体相之间 , 表现出磁通格子的反向熔化行为.分析后认为，这一反向熔化行为起因于磁通之间互作用的温度效应. 关键词： Ⅱ类超导体 磁通格子 相图 结构因子 反向熔化     

Quasi-particle structure around a single vortex in high-Tc superconductors

For analyzing the checker-board like modulation of the local density of states (LDOS) around a vortex observed in the slightly overdoped Bi₂Sr₂CaCu₂O_x, we examined the effect of pseudogap state of high-T_c superconductors to the LDOS around the vortex. We first derived the Bogoliubov-de Gennes equation for d-wave superconductivity (d-SC) in the presence of d-spin density wave (d-SDW). Using the Fourier–Bessel expansion, we solved this equation for a single vortex state, numerically. We found that the peak of the bound states around E = 0 becomes small and modulation of the LDOS is observed for larger d-SDW order parameter.     

Experimental distinction between giant vortex and multivortex states in mesoscopic superconducting squares

We study the distinction between giant vortex states and multivortex states in a thin mesoscopic superconducting square by using the temperature dependence of the vortex expulsion fields. We find that the results agree well with those obtained from the multiple-small-tunnel-junction method, indicating that the distinction by the temperature dependence of the vortex expulsion fields is applicable to superconducting squares.     

二维激子极化激元凝聚中涡旋叠加态稳态及动力学特性研究

利用分步Crank-Nicolson方案的虚时和实时有限差分方法求解耗散系统的Gross-Pitaevskii(GP)方程,研究了二维激子极化激元凝聚(exciton-polariton condensates)体系中正反涡旋叠加态的稳态结构并直观地验证这种稳态结构在半导体微腔旋转下的稳定性和动力学特性.通过虚时和实时演化相结合的方法求解出几种角动量情况下所对应的稳定涡旋叠加态.然后利用实时演化方法研究在半导体微腔旋转的情况下,正反涡旋叠加态的稳定性及其旋转角速率和半导体微腔旋转角速率之间的定量关系.最后研究了单涡旋态在半导体微腔旋转时形成涡旋阵列的动力学过程,并给出了泵浦光宽度和增益项对涡旋阵列结构的影响.研究表明,系统的泵浦,损耗和增益对稳定性和动力学特性有重要影响.     

Symmetric behavior of vortex states of superconducting networks in a magnetic field

We present magnetic field dependence of phase transition temperature and vortex configuration of superconducting networks based on theoretical study. The applied magnetic field is called “filling field” that is defined by applied magnetic flux (in unit of the flux quantum) per unit loop of the superconducting network. If a superconducting network is composed of very thin wires whose thicknesses are less than coherence length, the de Gennes–Alexander (dGA) theory is applicable. We have already shown that field dependences of transition temperature curves have symmetric behavior about the filling field of 1/2 by solving the dGA equation numerically in square lattices, honeycomb lattices, cubic lattices and those with randomly lack of wires networks. Many experimental studies also show the symmetric behavior. In this paper, we make an explicit theoretical explanation of symmetric behaviors of superconducting network respect to the applied field.     

On the correspondence between a screw dislocation in gradient elasticity and a regularized vortex

We show the correspondence between a screw dislocation in gradient elasticity and a regularized vortex. The effective Burgers vector, nonsingular distortion and stress fields of a screw dislocation and the effective circulation, smoothed velocity and momentum of a vortex are given and discussed.     

Quantum vortex strings: A review

The quantum worldsheet dynamics of vortex strings contains information about the 4d non-Abelian gauge theory in which the string lives. Here I tell this story. The string worldsheet theory is typically some variant of the CP^N-1 sigma-model, describing the orientation of the string in a U(N) gauge group. Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories have been known since the 1970s. The vortex string provides a quantitative link between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning parameters, the CP^N-1 sigma-model can be coaxed to flow to an interacting conformal fixed point which is related to the 4d Argyres-Douglas fixed point. For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical supersymmetry breaking and, more interestingly, supersymmetry restoration, in a way which captures the physics of Seiberg’s quantum deformed moduli space.     

高温超导体磁通钉扎和磁通动力学研究简介

ψ=ψ0eiφ行为用统一的波函数进行描述,其相位φ在宏观尺度上是相同的.当磁场低于一定值的时候,在超Φ0=h/2e保证最大的界面面积,降低系统能量.该最小的磁通束被称为磁通量子,其磁通量是(h为普朗克超导态是一个宏观量子相干态,其载流子是库珀对.在没有外加磁场和电流的时候,这些库珀对的运动导体的边界处穿透深度内会出现一...     

多个子玻色-爱因斯坦凝聚气体膨胀叠加形成的量子涡旋现象研究

基于二维模型,研究了多个子玻色-爱因斯坦凝聚气体在谐振势阱内膨胀叠加形成的量子涡旋现象.运用传播子方法,分析了对称分布的三个子玻色-爱因斯坦凝聚气体膨胀叠加形成宏观量子涡旋的物理过程,得到量子涡旋随时间演化的规律;发现涡旋核分布在谐振势阱内出现振荡;涡旋与反涡旋随时间演化而相互转变,并对这些现象进行了物理分析.     

Isotropic-to-nematic transition in melt of polydisperse semi-flexible homopolymers

The isotropic-to-nematic phase transition in a melt of semi-flexible homopolymers with length polydispersity have been considered within the Landau–de Gennes approach. The number of monomer units in chain is assumed to be a random variable distributed by the Schulz–Zimm distribution; the stiffness of macromolecules has been taken into account within discrete worm-like chain model. It was found that increase of polydispersity yields the increase of the temperature of the isotropic–nematic transition.     

无序二维约瑟夫森结阵列中磁场引起的涡旋玻璃态相变

采用电阻阻错结的无序二维约瑟夫森结阵列模型,数值研究超导薄膜中垂直磁场引起的涡旋运动.通过分析磁场激发产生的涡旋度Ne及低频电压噪声S₀的变化特性,得到如下结论：在无序超导体中固定温度不变,随着磁场的减弱涡旋液态经过准有序的布拉格相,涡旋玻璃相重新进入到低磁场下的钉扎稀磁液相. 由于在涡旋玻璃相中,电流驱动下的噪声值表现出一个峰,表明系统处于无序与有序相互竞争的亚稳态,并且临界电流应有峰值效应. 计算得到噪声值的变化与Okuma等得到的无序超导Mo_xSi_1-x膜实验现象一致,并能解释磁场降低引起的重新进入钉扎的稀磁液相行为. 关键词： 约瑟夫森结阵列 磁通玻璃 重新进入 峰值效应     

Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.     

Jackiw-Pi模型的新涡旋解

运用φ映射拓扑流理论研究了Jackiw-Pi模型中的自对偶方程，得到一个静态的自对偶解满足带有δ函数项的刘维尔方程, 从而得到了一个完整的带有拓扑信息的涡旋解,自然给出了磁通量子化.     

Topological aspect of vortex lines in two-dimensional Gross—Pitaevskii theory

Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.