Competition between pinning and melting in the two-dimensional vortex lattice

We discuss measurements of the ac complex conductance of a-MoGe films in the presence of a perpendicular magnetic field. The ac response of vortices in samples with weak pinning reveals an anomaly that is found to be consistent with a dislocation mediated melting in the two-dimensional vortex lattice on short length scales. However, increasing the effects of disorder on the vortex lattice by reducing the sample thickness leads to dominance of thermal-activated creep over melting. With increasing disorder, the length scale associated with the correlations in the vortex lattice is reduced and eventually the melting phenomenon disappears.