  In a type II superconductor in a moderate magnetic field, the superconductor
to normal state transition may be described as a phase transition in which the
vortex lattice melts into a liquid. In a biaxial superconductor, or even a
uniaxial superconductor with magnetic field oriented perpendicular to the
symmetry axis, the vortices acquire elongated cross sections and interactions.
Systems of anisotropic, interacting constituents generally exhibit liquid
crystalline phases. We examine the possibility of a two step melting in
homogeneous type II superconductors with anisotropic superfluid stiffness from
a vortex lattice into first a vortex smectic and then a vortex nematic at high
temperature and magnetic field. We find that fluctuations of the ordered phase
favor an instability to an intermediate smectic-A in the absence of intrinsic
pinning.
