Vortex lattice phase

In addition to the vortex lattice occupying the main part of the H-T-phase diagram of borocarbide superconductors, several other vortex phases have been identified in the nonmagnetic borocarbides. Mun et al. (1996) found, by transport measurements on YNi2B2C,... 

An influence of finite dimensions of multilayered nanostmctures on superconducting phase nucleation and vortex mobility is studied both experimentally and theoretically. Resistive characteristics are observed to be sensitive to the geometrical symmetry of samples. For multilayers with the symmetry plane in the superconducting layer the resistive transitions are widely spread with respect to the samples with the symmetry plane in normal layers. This result is explained by the joint action of Lorentz and pinning forces on the nascent vortex lattice. 

The development of patterns is not necessarily a manifestation of a nonequilibrium process. A spatially non-uniform state can correspond to the minimum of the free-energy functional of a system in thermodynamic equihbrium, as Abrikosov vortex lattices, stripe ferromagnetic phases and periodic diblock-copolymer phases mentioned above. In the latter, a hnear chain molecule of a diblock-copolymer consists of two blocks, say, A and B. Above the critical temperature Tc, there is a mixture of both types of blocks. Below Tc, the copolymer melt undergoes phase separation that leads to the formation of A-rich and B-rich microdomains. In the bulk, these microdomains typically have the shape of lamellae, hexagonally ordered cylinders or body-centered cubic (bee) ordered spheres. On the surface, one again observes stripes or hexagonally ordered spots. 

In condensed matter physics, the effects of disorder, defects, and impurities are relevant for many materials properties hence their understanding is of utmost importance. The effects of randomness and disorder can be dramatic and have been investigated for a variety of systems covering a wide field of complex phenomena [109]. Examples include the pinning of an Abrikosov flux vortex lattice by impurities in superconductors [110], disorder in Ising magnets [111], superfluid transitions of He in a porous medium [112], and phase transitions in randomly confined smectic liquid crystals [113, 114]. 

Next came the likewise phenomenological Ginzburg-Landau theory of superconductivity, based on the Landau theory of a second-order phase transition (see also Appendix B) that predicted the coherence length and penetration depth as two characteristic parameters of a superconductor (Ginzburg and Landau, 1950). Based on this theory, Abrikosov derived the notion that the magnetic field penetrates type II superconductors in quantized flux tubes, commonly in the form of a hexagonal network (Abrikosov, 1957). The existence of this vortex lattice was... 

Twist grain boundary (TGB) phase Shubnikov phase / Abrikosov vortex lattice... 

Renn and Lubensky proposed a model for the analogue of the vortex lattice [43] for the N -SmA transition [42]. Simultaneously and independently such a phase was discovered by direct observation, supported by X-ray analysis as well as freeze-fracture, by Goodby et al. [44] between the isotropic liquid and a SmC phase. The first TGBA phase found to exist between N and SmA was studied in a dynamic experiment [45]. In the Renn-Lubensky model, uniform sheets of SmA of extent separated by parallel planes of screw dislocations, twist relative to each other [46]. 

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