Anharmonicity of flux lattices and thermal fluctuations in layered superconductors

Abstract

We study elasticity of a perpendicular flux lattice in a layered superconductor with Josephson coupling between layers. We find that for flux displacements \ensuremath{\rho} the energy contains ${\ensuremath{\rho}}^{2}\mathrm{ln}\ensuremath{\rho}$ terms, so that elastic constants cannot be strictly defined. Instead we define effective elastic constants by a thermal average. The tilt moduli have terms $\ensuremath{\sim}\mathrm{ln}T$ which for ${\ensuremath{\lambda}}_{J}\ensuremath{\ll}a,$ where ${\ensuremath{\lambda}}_{J}$ is the Josephson length and $a$ is the flux-line spacing, lead to $〈{\ensuremath{\rho}}^{2}〉\ensuremath{\sim}T/|\mathrm{ln}T|.$ The expansion parameter indicates that the dominant low-temperature phase transition is either layer decoupling at high fields $({\ensuremath{\lambda}}_{J}\ensuremath{\gg}a)$ or melting at low fields $({\ensuremath{\lambda}}_{J}\ensuremath{\ll}a).$