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

For a clean high-T$_c$ 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 $C_{44}$ of a vortex lattice and vortex liquid. The vortex contribution to $C_{44}$ can be expressed in terms of the squared $c$-axis Josephson plasmon frequency $\omega_{pl}^2$. The transverse component of the field has very little effect on the position of the melting curve.