Microwave Absorption by Vortices in Superconductors with a Washboard Pinning Potential

It is well-known that a type-II superconductor, while exposed to a magnetic field B whose magnitude is between the lower and upper critical field, is penetrated by a flux-line array of Abrikosov vortices, or fluxons [1–3]. Each vortex contains one magnetic flux quantum, Φ0 = 2.07× 10−15 Wb, and the repulsive interaction between vortices makes them to arrange in a triangular lattice, with the vortex lattice parameter aL √ Φ0/B where B = |B|. A vortex is often simplified by the hard-core model [4], where the core is a cylinder of normal material with a diameter of the order of the coherence length. In this model, the magnetic field is constant in the core but decays exponentially outside the core over a distance of the order of the effective magnetic penetration depth.