Comment on ”Vortex Liquid Crystal in Anisotropic Type II Superconductors” The suppression of superconductivity in type II superconductors

Comment on " Vortex Liquid Crystal in Anisotropic Type II Superconductors " The suppression of superconductivity in type II superconductors is associated with the melting transition of the lattice of flux quanta [1, 2, 3]. Most melting phenomena in Nature are thermodynamic first-order phase transitions. An analytic description of melting is thus difficult since there is no good handle, such as the diverging quantities in a second-order phase transition, for us to explore. A reasonable, phenomenological argument goes back to Lindemann [4], in which a criterion is set on the averaged displacements of objects under concerned, so that one expects a meling transition when they become larger than a portion, Lindemann number, of the inter-object distance. The Lindemann criterion has been successful in many cases, and specifically for melting of flux-line lattice in type II superconductors. Nevertheless, one should keep in mind that Lindemann's argument is a phenomenology, and cannot tell whether the melting is a first-order transition or not. Furthermore, Lindemann's argument applies only to the solid side of the melting transition. In order to use it, one needs knowledge about the solid, and thus should restrain oneself from going beyond the melting line. Recently Carlson et al. tried to use the Lindemann criterion for melting of flux-line lattice in anisotropic super-conductors [5]. It is worthy to notice that the issue itself is interesting and has not been addressed satisfactorily yet. However, the conclusion on the existence of a smectic vortex phase in the anisotropic superconductors drawn from Lindemann's argument by the authors is unphysical. The reason of the mistake is clear: There is no appropriate estimate on the thermal fluctuations above the " lower melting temperature " in a given magnetic field, since the basis of the elastic theory [6] adopted by the authors, namely the lattice structure, disappears already; One therefore cannot argue even the existence of the intermediate phase, such as smectic in Fig. 1 of Ref.[5], above the " lower melting temperature " , not only its melting as noticed by the authors. It is interesting to ask if one can draw useful information from a Lindemann-type argument for melting phenomena in anisotropic superconductors. An idea, which looks more physical than claiming the existence of intermediate phase above lattice, is to suppose that one can have different Lindemann numbers in different directions for anisotropic superconductors. Then one can lower the " upper melting line " …