Transition of the vortex lattice

The symmetry changes of the vortex lattice in borocarbide superconductors affect their pinning properties as was shown for YNi2B2C (Silhanek et al. 2001). For the field orientation // c, the reorientation transition of the vortex lattice mentioned above was found to be associated with a significant kink in the volume pinning force Fp, whereas in the basal plane (for H c) the signature of nonlocal effects is a fourfold periodicity of Fp. 

An interesting question is whether the subtle effects of non-locality and, in particular, the hexagonal-square transition of the vortex lattice would be preserved in the superconducting state of magnetic superconductors such as / Ni2B2C with R = Er and Tm. 

The elastic moduli of the vortex lattice around the transition field H j of have been analyzed within the nonlocal London model by Miranovic and Kogan (2001). In particular, the square vortex lattice was found to be soft with respect to shear displacement along the square sides [110] or [110]. 

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]. 

In addition to the hexagonal-square transition, a reorientation transition of the hexagonal vortex lattice from a state with the diagonal of the rhombic unit cell along [110] direction to [100] direction has been observed for YNi2B2C (Paul et al. 1998). Figure 51b shows that for H applied perpendicular to c the transition to a (nearly) square lattice occurs at a field of about 1 Tesla and at 0.8 Tesla a reorientation transition of the diagonal of the rhombic cell takes place (Sakata et al. 2000). 

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... 

We have studied both static and dynamic properties of the vortex systems, such as Abrikosov vortex lattice formation, vortex lattice melting, the KT transition, and the vortex glass transition, from the point of view of an analogy between our system and colloid, polymer systems [3]. Our study is based on computer simulations of two efficient model equations, recently developed by us. 

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. 

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]. 

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