Tilt Modulus and Angle-Dependent Flux Lattice Melting in the Lowest Landau Level Approximation

For a clean high-Tc superconductor, we analyze the Lawrence-Doniach free energy in a tilted magnetic field within the lowest Landau level (LLL) approximation. The free energy maps onto that of a strictly c-axis field, but with a reduced interlayer coupling. We use this result to calculate the tilt modulus C44 of a vortex lattice and vortex liquid. The vortex contribution to C44 can be expressed in terms of the squared c-axis Josephson plasmon frequency ω2 pl. The transverse component of the field has very little effect on the position of the melting curve.