Quantum Vortex Core and Missing Pseudogap in the Multiband BCS-BEC Crossover Superconductor FeSe

FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein condensation crossover regime where the superconducting gap size and the superconducting transition temperature T_{c} are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above T_{c} may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was not detected. These apparently conflicting observations may be related to the multiband nature of FeSe.