Anharmonicity of flux lattices and thermal fluctuations in layered superconductors

We study elasticity of a perpendicular flux lattice in a layered superconductor with Josephson coupling between layers. We find that for flux displacements ρ the energy contains (Formula presented) terms, so that elastic constants cannot be strictly defined. Instead we define effective elastic constants by a thermal average. The tilt moduli have terms (Formula presented) which for (Formula presented) where (Formula presented) is the Josephson length and (Formula presented) is the flux-line spacing, lead to (Formula presented) The expansion parameter indicates that the dominant low-temperature phase transition is either layer decoupling at high fields (Formula presented) or melting at low fields (Formula presented).