Microwave absorption in the cores of the Abrikosov vortices pinned by artificial insulator inclusion

The spectrum of core excitations of the Abrikosov vortex pinned by a dielectric inclusion or nanoholes of the size of the coherence length is considered using the Bogoliubov-deGennes equations beyond the semiclassical approximation. While the lowest excitation, mini-gap, in the unpinned (or pinned by a metallic defect) vortex is of the order of ^Δ2/ ^F, it becomes of the order of the superconducting gap Δ. The reconstruction of the quasiparticle excitations' spectrum has a significant impact on optical properties and on the tunneling density of states. We calculate the absorption amplitude and point out that, while in STM the energy gap ^ΔDOS is between a quasiparticles state with angular momentum ^μe= ^μs>1/2 and quasi-hole with ^μh=- ^μs the microwave absorption gap, ^Δdir is between states with ^μe= ^μh+1. It is shown that ^Δdir> ^ΔDOS. The large mini-gap might play a role in magneto-transport phenomena broadly associated with the "superconductor-insulator" transition in quasi 2D systems in which small insulating inclusions are generally present.