Quantitative assessment of pinning forces and the superconducting gap in   NbN thin films from complementary magnetic force microscopy and transport   measurements
  Epitaxial niobium-nitride thin films with a critical temperature of Tc=16K and a thickness of 100nm were fabricated on MgO(100) substrates by pulsed laser deposition. Low-temperature magnetic force microscopy (MFM) images of the supercurrent vortices were measured after field cooling in a magnetic field of 3mT at various temperatures. Temperature dependence of the penetration depth has been evaluated by a two-dimensional fitting of the vortex profiles in the monopole-monopole model. Its subsequent fit to a single s-wave gap function results in the superconducting gap amplitude Delta(0) = 2.9 meV = 2.1*kB*Tc, in perfect agreement with previous reports. The pinning force has been independently estimated from local depinning of individual vortices by lateral forces exerted by the MFM tip and from transport measurements. A good quantitative agreement between the two techniques shows that for low fields, B << Hc2, MFM is a powerful and reliable technique to probe the local variations of the pinning landscape. We also demonstrate that the monopole model can be successfully applied even for thin films with a thickness comparable to the penetration depth. 
T. Shapoval, H. Stopfel, S. Haindl, J. Engelmann, D. S. Inosov, B.   Holzapfel, V. Neu, L. Schultz
cond-mat.supr-con cond-mat.mtrl-sci cond-mat.str-el