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

The spectrum of core excitations of the Abrikosov vortex pinned by a dielectric inclusion or nanoholes the size of the coherence length is considered using the Bogoliubov-deGennes equations beyond the semiclassical approximation. While the lowest excitation, minigap, in the unpinned (or pinned by a metallic defect) vortex is of the order of Δ2/E_F, it becomes of the order of the superconducting gap Δ (E_F is Fermi energy). 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 scanning tunneling microscopy the energy gap Δ_DOS is between a quasiparticle state with angular momentum μe=μ₀>1/2 and quasihole with μh=-μ₀, the microwave absorption gap, Δ_dir, is between the states with μe=μh±1. It is shown that Δ_dir>Δ_DOS. The large minigap might play a role in magneto-transport phenomena broadly associated with the "superconductor-insulator" transition in quasi-two-dimensional systems in which small insulating inclusions are generally present.