Comment on vortex liquid crystal in anisotropic type II superconductors.

Comment on " Vortex Liquid Crystal in Anisotropic Type II Superconductors " Recently Carlson et al. [1] tried to compose the H − T phase diagram of anisotropic superconductors based on the Lindemann criterion for melting of flux-line lattice. It is worthy to notice that the issue itself is interesting. However, their conclusion on the existence of a smectic vortex phase is unphysical for the following reasons: There is no appropriate estimate on thermal fluctuations above the " lower melting temperature " , since the basis of the elastic theory used 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.[1], 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 uniaxially anisotropic superconductors when the magnetic field is applied perpendicularly to the anisotropic axis. An idea is to suppose that one can have two Lindemann numbers in the two different directions, instead of two meltings. From the elastic theory (see references in Ref.[1]), we know that the Lindemann melting line is given by the following equation: t/ √ 1 − t = c 2 × f (b, κ, γ, Gi). This property permits us to shift the " upper melting line " in Fig. 4 of Ref.[1] to lower temperature by reducing the Lindemann number without touching the details of f (b, κ, γ, Gi) [2]. The numerical results thus obtained are shown in Fig. 1. There is a perfect collapse between the two curves when one takes c long ≃ 0.17 while fixes c short = 0.2 to the value chosen in Ref.[1]. The collapse of the two curves is expected for large κ's, namely in extremely type II superconductors, and is achieved whenever the two Lindemann numbers satisfy the fixed ratio which is revealed in our analysis. Should the " two melting lines " never collapse, there appears another possible melting scenario. One could have an intersection between these " two melting lines " , besides the ones at T = T c , H = 0 and T = 0, H = H c2. Then, the lower melting temperature should be adopted as the true one at a given magnetic field to …