Superconductor analogy, phase transitions

The nematic to smectic A phase transition has attracted a great deal of theoretical and experimental interest because it is tire simplest example of a phase transition characterized by tire development of translational order [88]. Experiments indicate tliat tire transition can be first order or, more usually, continuous, depending on tire range of stability of tire nematic phase. In addition, tire critical behaviour tliat results from a continuous transition is fascinating and allows a test of predictions of tire renonnalization group tlieory in an accessible experimental system. In fact, this transition is analogous to tire transition from a nonnal conductor to a superconductor [89], but is more readily studied in tire liquid crystal system. 

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. 

Then, from fig.lc it is seen that SC transition onset points Tconset(H)(= Tk(H)) are at the Bloch-Gruneisen curve (dashed curve). On the other hand, such a picture is characteristic for low temperature superconductors described by s-wave BCS theory. From this analogy it may be concluded that in the cuprates the SC order parameter is of s-wave symmetry, also. Moreover, as seen from magnetic phase H-T diagram, the... 

The second family of superconducting materials is based on cation-radical salts of another donor, bis(ethylenedithio)-TTF (abbreviated BEDT-TTF or ET), which exhibit two-dimensional network mostly due to inter-stack S S interactions [100]. Another important feature of BEDT-TTF salts is their tendency to give polymorphs. For instance, (BEDT-TTF)2I3 salt affords four polymorphs (a, p, 0, and k phases), of which only the first undergoes metal-insulator transition, while the others are superconductors at ambient pressure (see Chapter 10 of this book). It is quite surprising that of all numerous BEDT-TTF structural analogs synthesized to date, only two salts of unsymmetrical derivatives, DMET [101] and MDT-TTF [102], led to superconductors. 

The fact that the positional order in this liquid crystal phase can be described by a complex order parameter just like the order parameter describing the transition from a conductor to a superconductor means that there are marty analogies between the two phenomena These are discussed at various points in the text. 

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]. 

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