Title: Identification of multiple-flux-quanta vortices by core states in the two-band superconductor Pb

Abstract: Superconductors are of type I or II depending on whether they form an Abrikosov vortex lattice. Although bulk lead (Pb) is classified as a prototypical type-I superconductor, we observe single-flux-quantum and multiple-flux-quanta vortices in the intermediate state using mK scanning tunneling microscopy. We show that the winding number of individual vortices can be determined from the real space wave function of its Caroli-de Gennes-Matricon bound states. This generalizes the index theorem put forward by Volovik for isotropic electronic states to realistic electronic structures. In addition, the bound states due to the two superconducting bands of Pb can be separately detected. This yields strong evidence for low inter-band coupling and an independent closure of the gaps inside vortices.