Surface melting of the vortex lattice
  We discuss the effect of an (ab)-surface on the melting transition of the pancake-vortex lattice in a layered superconductor within a density functional theory approach. Both discontinuous and continuous surface melting are predicted for this system, although the latter scenario occupies the major part of the low-field phase diagram. The formation of a quasi-liquid layer below the bulk melting temperature inhibits the appearance of a superheated solid phase, yielding an asymmetric hysteretic behavior which has been seen in experiments. 
A. De Col, G.I. Menon, V.B. Geshkenbein, and G. Blatter