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Bound states in superconductors are expected to exhibit a spatially resolvedelectron-hole asymmetry which is the hallmark of their quantum nature. Thisasymmetry manifests as oscillations at the Fermi wavelength, which is usuallytiny and thus washed out by thermal broadening or by scattering at defects.Here we demonstrate theoretically and confirm experimentally that, when coupledto magnetic impurities, bound states in a vortex core exhibit an emergent axialelectron-hole asymmetry on a much longer scale, set by the coherence length. Westudy vortices in 2H-NbSe$_2$ and in 2H-NbSe$_{1.8}$S_{0.2}$ with magneticimpurities, characterizing these with detailed Hubbard-corrected densityfunctional calculations. We find that the induced electron-hole imbalancedepends on the band character of the superconducting material. Our results openinteresting prospects for the study of coupled superconducting bound states.

Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors