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Scanning tunneling experiments on single crystals of superconductingFeTe$_{0.55}$Se$_{0.45}$ have recently provided evidence for discrete energylevels inside vortices. Although predicted long ago, such levels are seldomresolved due to extrinsic (temperature, instrumentation) and intrinsic(quasiparticle scattering) limitations. We study a microscopic multiband modelwith parameters appropriate for FeTe$_{0.55}$Se$_{0.45}$. We confirm theexistence of well-separated bound states and show that the chemical disorderdue to random occupation of the chalcogen site does not affect significantlythe vortex-core electronic structure. We further analyze the vortex boundstates by projecting the local density of states on angular-momentumeigenstates. A rather complex pattern of bound states emerges from themultiband and mixed electron-hole nature of the normal-state carriers. Thecharacter of the vortex states changes from hole-like with negative angularmomentum at low energy to electron-like with positive angular momentum athigher energy within the superconducting gap. We show that disorder in thearrangement of vortices most likely explains the differences foundexperimentally when comparing different vortices.

Signatures of nodeless multiband superconductivity and particle-hole crossover in the vortex cores of FeTe$_{0.55}$Se$_{0.45}$