Microscopic structure of the vortex cores in granular niobium: A coherent quantum puzzle

Abstract

When macroscopic quantum condensates -- superconductors, superfluids, cold atoms and ions, polaritons etc. -- are put in rotation, a quantum vortex lattice forms inside. In homogeneous type-II superconductors, each vortex has a tiny core where the superconducting gap $Δ(r)$ is known to smoothly vanish towards the core centre on the scale of the coherence length $ξ$. The cores host quantized quasiparticle energy levels known as Caroli-de Gennes-Matricon (CdGM) bound states [Caroli {\it et al.,} Phys. Lett. v. 9, 307 (1964)]. In pure materials, the spectrum of the low-lying CdGM states has the characteristic level spacing $\sim Δ_0^2/E_F$, where $E_F$ is the Fermi energy and $Δ_0$ is the bulk gap. In disordered ones, the CdGM states shift and broaden due to scattering. Here, we show, both experimentally and theoretically, that the situation is completely different in granular Nb films, which are commonly used in superconducting electronics. In these films, in which the grains are smaller than $ξ$, the gap $Δ$ in the quasiparticle spectrum reduces towards the vortex core centres by discrete jumps at the grain boundaries. The bound states adapt to the local environment and appear at unexpectedly high energies. Both $Δ(r)$ and bound states form a puzzle-like spatial structure of the core, elements of which are whole grains. Our discovery shakes up the established understanding of the quantum vortex and encourages a reconsideration of the vortex motion and pinning mechanisms in granular superconductors.