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

Abstract

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 Delta(2)/E(F), it becomes of the order of the superconducting gap Delta (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 Lambda(DOS) is between a quasiparticle state with angular momentum mu(e) = mu(0) > 1/2 and quasihole with mu(h) = -mu(0), the microwave absorption gap, Delta(dir), is between the states with mu(e) = mu(h) +/- 1. It is shown that Delta(dir) > Delta(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.