Massless Mode in Abrikosov Flux Lattice. II. Elastic Modes and Superconducting Order

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Abstract
We reexamine harmonic fluctuation theory of Abrikosov flux lattice previously developed on the basis of Landau level expansion of the order parameter. We explicitly show that, as far as fluctuations of flux density are taken into account, the usual elastic theory is nicely derived in the case with fluctuations of lowest two Landau levels, and that superconducting long range order (or gauge invariant phase coherence) is absent in 3D flux lattice. It is pointed out that these results are also obtained according to other frameworks based on the elastic theory. The resulting expression of elastic free energy becomes complicated when other higher Landau levels are taken into account. Nevertheless we can show that the superconducting long range order is lost even in such a general case. The relevance of these results to high T c superconductors is briefly discussed.