Since the discovery of superconductivity above 30 K by Bednorz and M\"uller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

Electronic structure of the high-temperature oxide superconductors

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

Advances in physics

http://web.mit.edu/solab/Documents/Assets/Chen-Photon%20couting%20histogram%20in%20FCS.pdf

The photon counting histogram in fluorescence fluctuation spectroscopy.

Flow behavior of a flux line in the layered superconductor 2H-${\mathrm{NbSe}}_{2}$ is studied with a magnetic field parallel to the layers in the vicinity of a pronounced peak effect. A striking crossover in the current-voltage characteristics is observed as the system enters the peak regime. The results yield a nonequilibrium phase diagram where conventional depinning of an elastic medium occurs for a rigid lattice. A defective (plastic) flow instability occurs as the lattice softens, but heals at large drives. This defective flow dominates the dynamics for a very soft lattice.

Dynamics of a disordered flux line lattice.

The magnetic flux line lattice in type II superconductors serves as a useful system in which to study condensed matter flow, as its dynamic properties are tunable. Recent studies have shown a number of puzzling phenomena associated with vortex motion, including: low-frequency noise and slow voltage oscillations; a history-dependent dynamic response, and memory of the direction, amplitude duration and frequency of the previously applied current; high vortex mobility for alternating current, but no apparent vortex motion for direct currents; and strong suppression of an a.c. response by small d.c. bias. Taken together, these phenomena are incompatible with current understanding of vortex dynamics. Here we report a generic mechanism that accounts for these observations. Our model, which is derived from investigations of the current distribution across single crystals of NbSe2, is based on a competition between the injection of a disordered vortex phase at the sample edges, and the dynamic annealing of this metastable disorder by the transport current. For an alternating current, only narrow regions near the edges are in the disordered phase, while for d.c. bias, most of the sample is in the disordered phase--preventing vortex motion because of more efficient pinning. The resulting spatial dependence of the disordered vortex system serves as an active memory of the previous history.

Dynamic instabilities and memory effects in vortex matter

tion of unperturbed OP and of its behavior in the vicinity of the transition. We have used a Corbino disk geometry (inset of Fig. 1), in which the vortices circulate in the bulk without crossing the edges, and compared it with the regular strip configuration in the same crystals. If the instability effects are a bulk phenomenon, no significant difference between the two geometries is expected; whereas if the sample edges do play a dominant role, qualitatively different behavior should be observed. This paper demonstrates that the two geometries yield a strikingly different response and, significantly, the instability effects are eliminated in the Corbino geometry. Furthermore, by preventing the edge contamination, the true bulk dynamics in the vicinity of the transition can be probed for the first time. The results suggest that the disorder-driven transition TDT is possibly a thermodynamic first-order phase transition, which shows, in addition, sharp reentrant behavior.

/pdf/instabilities-and-disorder-driven-first-order-transition-of-4n9eaa9gog.pdf

Instabilities and disorder-driven first-order transition of the vortex lattice

Dynamics of a flux-line lattice (FLL) has been studied in the anisotropic superconductor 2H-NbSe 2 , where pinning is extremely weak (critical current/depairing current ∼ 10 −6 ), the lattice is well-formed and a robust “peak effect” occurs slightly below H c2 . The strong H dependence of the rigidity of the FLL is used to explore the crossover between interaction-dominated and disorder-dominated dynamics. Three distinct types of dynamics, describing elastic flow, plastic flow and fluid flow, respectively, are observed as the lattice softens with the approach to the superconducting-to-normal phase boundary. A power-law behavior, V ∼ ( I − I c ) β , describes the I – V curves for both elastic and fluid flow (with different β) reasonably well, but not for plastic flow. The latter dominates the intermediate regime, where the peak effect occurs, and is accompanied by qualitative changes in the I – V curves related to tearing of the FLL. In this regime, a “fingerprint phenomenon” is observed in the current-dependent differential resistance describing a specific sequence of depinning of “chunks” or filaments in a given sample. At large driving forces, the disorder due to pinning is less significant, the dynamically generated defects heal and a nearly defect-free coherent motion is recovered. In some samples, the I – V curves at the onset of motion in this regime become discontinuous and hysteretic as in first-order transitions. A “non-equilibrium phase diagram” describing various regimes of dynamics is constructed. A time-averaged velocity correlation length characterizes the spatial inhomogeneity of a moving FLL and thus distinguishes between the various dynamical regimes. These dynamical phenomena are compared and contrasted with phenomena attributed to thermodynamic phase transitions in the cuprate superconductors.

Varieties of dynamics in a disordered flux-line lattice

Strong metastability and history dependence are observed in dc and pulsed transport studies of fluxline lattices in 2H-NbSe 2, leading to the identification of two distinct states of the lattice with different spatial ordering. The metastability is most pronounced upon crossing a transition line marked by a large jump in the critical current (the peak effect). Current-induced annealing of the metastable state towards the stable state is observed with a strongly current dependent annealing time, which diverges as a threshold current is approached from above. [S0031-9007(96)01054-X] In the absence of disorder the physics of a magnetic flux-line lattice (FLL) is governed by the interplay between thermal fluctuations, which favor melting, and interactions, that lead to ordering. The resulting phase diagram consists of a liquid and a solid phase with relatively simple dynamics. Quenched disorder causes the system to develop additional phases and complex dynamic effects such as pinning and irreversibility in the magnetic and electric responses. The role played by disorder and pinning in the physics of FLL in equilibrium has recently become an area of intense study [1,2]. A related but distinct topic of current interest concerns the role of motion on the spatial ordering of the FLL, the resulting dynamical transitions or crossovers that may occur, and the relation they bear to the disorder free situation [3‐7]. In this Letter we report on the existence of two distinct states of the FLL, one disordered, the other much less disordered (hereafter referred to as the ordered state), with strikingly large differences between their transport properties. As a result, the system displays a wide range of phenomena such as history dependence, metastability, current-induced annealing, and glassy relaxation. Each of these states is stable in its own sharply defined region of the (H, T ) plane and metastable elsewhere, and each can be accessed with a simple reproducible procedure. Our experiments show directly that the metastable state can be annealed into the “equilibrium” state by applying a current that depins the FLL. The annealing kinetics is found to be strongly current dependent, with the annealing time diverging as the depinning current is approached from above. The variation of these phenomena with field, temperature, and driving current provides direct access to the interplay between static and dynamic transitions and can elucidate the role of disorder in different parts of the FLL phase diagram. Our results can also be used to interpret the rich and complex history dependence studied earlier in low Tc superconducting films [8,9].

/pdf/metastability-and-glassy-behavior-of-a-driven-flux-line-1pb4d2j4dn.pdf

Mark J. Higgins

Papers

Dynamics of a disordered flux line lattice.

Dynamic instabilities and memory effects in vortex matter

Instabilities and disorder-driven first-order transition of the vortex lattice

Varieties of dynamics in a disordered flux-line lattice

Metastability and Glassy Behavior of a Driven Flux-Line Lattice.