Vortex lattice in presence of a tunable periodic pinning potential
  The vortex patterns stabilized by the square array of artificial pinning sites with a tunable pinning strength are studied by using a phenomenological approach in the London limit. The transitions between pinned and deformed triangular lattices are analyzed as a function of the amplitude of the vortex-pinning site interaction and the characteristic length-scale of this interaction. The critical current and different phases of vortex lattice are studied in presence of external transport current. 
W.V. Pogosov, A.L. Rakhmanov, and V.V. Moshchalkov