Helicity Modulus and Meissner Effect in a Fluctuating Type II Superconductor

The helicity modulus for a fluctuating type II superconductor is computed within the elastic medium approximation, as a probe of superconducting phase coherence and the Meissner effect in the mixed state. We argue that at the vortex line lattice melting transition, there remains superconducting coherence parallel to the applied magnetic field, provided the vortex line liquid retains a finite shear modulus at finite wavevector.