Origin of Matching Effect in Anti-dot Array of Superconducting NbN Thin Films

We investigate the origin of matching effect observed in disordered superconducting NbN thin films with periodic array of holes. In addition to the periodic variation in the electrical resistance just above the superconducting transition temperature, Tc0, we find pronounced periodic variations with magnetic field in all dynamical quantities which can be influenced by flux-line motion under an external drive such as the magnetic shielding response and the critical current which survive in some samples down to temperatures as low as 0.09Tc0. In contrast, the superconducting energy gap, D which is a true thermodynamic quantity does not show any periodic variation with magnetic fields for the same films. Our results show that commensurate pinning of the flux line lattice driven by vortex-vortex interaction is the dominant mechanism for the observed matching effects in these superconducting anti-dot films rather than Little-Parks like quantum interference effect.