Analogy with Superconductors

The SmA-TGBA, TGBc TGBa, TGBa-N , and TGBc N transitions were proved to be first-order transitions whereas they were predicted to be second-order transitions. In analogy with superconductors, it can be assumed that fluctuations cause the two latter transitions to be of first order. 

The most spectacular outcome of the analogy with superconductors is undoubtedly the identification of twist grain boundary smectic phases (TGB for short) as liquid crystal analogs of the Abrikosov flux phase in type II superconductors. The existence and structural properties of the TGB phases were first predicted theoretically by Renn and Lubensky [60] (RL) in 1988 and discovered and characterized experimentally by Goodby and coworkers shortly after [26, 61]. 

The situation with respect to Landau-type phenomenological theories is also contradictory. Drawing an analogy between the smec-tic-A phase of liquid crystals and the superconducting phase of metals, de Gennes22 23 constructed a phenomenological theory from which he concludes that the smectic-A to nematic phase transition can be second order. Halperin and Lubensky, on the other hand, have improved the analogy with superconductors and conclude that the transition will always be at least weakly first order. 

By analogy with their previous work3 on a one-dimensional superconductor with many bands, they write down the pair-pair.correlation function as... 

Gilli and Kamaye went on to build the analogy with type II superconductors into their models of filaments. Firstly they noted that the coexistence of vortices in the bulk of the superconducting volume results from the existence of small regions that make possible a partial penetration of the magnetic flux... 

Lubensky has shown that, in principle, the smectic A-cholesteric transition should always be of first order, in analogy with the behaviour of a superconductor in an external magnetic field. The relative shift of the... 

The SmA liquid crystalline phase results from the development of a one-dimensional density wave in the orientationally ordered nematic phase. The smectic wave vector q is parallel to the nematic director (along the z-axis) and the SmA order parameter i/r= i/r e is introduced by P( ) = Po[1+R6V ]- Thus the order parameter has a magnitude and a phase. This led de Gennes to point out the analogy with superfluid helium and the normal-superconductor transition in metals [7, 59]. This would than place the N-SmA transition in the three-dimensional XY universality class. However, there are two important sources of deviations from isotropic 3D-XY behavior. The first one is crossover from second-order to first-order behavior via a tricritical point due to coupling between the smectic order parameter y/ and the nematic order parameter Q. The second source of deviation from isotropic 3D-XY behavior arises from the coupling between director fluctuations and the smectic order parameter, which is intrinsically anisotropic [60-62]. 

In comparisons of muons with protons and of muonium with hydrogen atoms, pronounced quantum effects occur whenever dynamics are involved. In this way, muons have been utilized to probe a large variety of properties and materials insulators, semiconductors, metals, superconductors, insulators, gases, liquids, crystalline and amorphous solids, static and dynamic magnetic properties of all kinds, electron mobility, quantum diffusion, chemical reactivity and molecular structure and dynamics. The term adopted for the broad field of muon spin spectroscopy techniques, fiSR, emphasizes the analogy with other types of magnetic resonance for example EPR. juS represents muon spin , and R in a more general sense stands simultaneously for rotation , relaxation and resonance . 

The SmA-N transition is often encountered in liquid crystals and has been extensively studied both theoretically and experimentally. Based on the analogy with the superconductor to normal metal transition, de Gennes [19,21] classified the SmA-N transition in the isotropic three-dimensional XY universality class. Actually, however, deviation from the isotropic 3D-XY behaviour occurs to give the cross-over from second order to first order behaviour via a tricritical point due to coupling between smectic and nematic order parameters. This type of deviation has been predicted for the... 

The idea behind this solid solution is simple enough. Starting from BaBiOs, the substitution of Pb for Bi removes electrons from the system, as Pb is one element to the left of Bi in the periodic table. Obviously, electrons can also be removed from the system by substitution of K+1 for Ba2+. If we suppose that the key to the occurrence of superconductivity in BaPb 75-Bi 25Os is related to the special charge fluctuations in Bi, then, in analogy to the copper oxides, a material with solely the active component on the electronically active sites should be a better superconductor. For the Ba K BiOg solid solution, Bi is formally... 

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