Theory of melted flux liquids

Novel intermediate flux states should be accessible in high-Tc superconductors, where it appears that the conventional Abrikosov flux lattice is melted over a significant portion of the (H,T) plane. We discuss the Lindemann criterion, and argue that fluctuations in a flux crystal are highly anisotropic, so that an asymptotically two-dimensional melting transition is possible as the shear modulus drops toward zero for many sample geometries and field orientations. We then describe the entangled flux liquid which arises at high-flux densities or thick samples. The statistical mechanics of this liquid is closely related to the physics of two-dimensional superfluids. The decay of vortex line correlations along the field direction is controlled by the superfluid excitation spectrum. A renormalization-group analysis shows how line wandering changes the nature of the B(H) constitutive relation near Hc1. We suggest that a heavily entangled flux liquid could exhibit a shear modulus on experimental time scales, in analogy with viscoelastic behavior in dense polymer melts.