The quantum coupling of fully di erent degrees of freedom is a challenging path towards new functionalities for quantum electronics [1][2][3] . Here we show that the localized classical spin of a magnetic atom immersed in a superconductor with a twodimensional electronic band structure gives rise to a long-range coherent magnetic quantum state. We experimentally evidence coherent bound states with spatially oscillating particle-hole asymmetry extending tens of nanometres from individual iron atoms embedded in a 2H-NbSe 2 crystal. We theoretically elucidate how reduced dimensionality enhances the spatial extent of these bound states and describe their energy and spatial structure. These spatially extended magnetic states could be used as building blocks for coupling coherently distant magnetic atoms in new topological superconducting phases 4-11

Just like insulators can present topological phases characterized by Dirac edge states, superconductors can exhibit topological phases characterized by Majorana edge states. In particular, one-dimensional topological superconductors are predicted to host zero-energy Majorana fermions at their extremities. By contrast, two-dimensional superconductors have a one-dimensional boundary which would naturally lead to propagating Majorana edge states characterized by a Dirac-like dispersion. In this paper we present evidences of one-dimensional dispersive in-gap edge states surrounding a two-dimensional topological superconducting domain consisting of a monolayer of Pb covering magnetic Co–Si islands grown on Si(111). We interpret the measured dispersive in-gap states as a spatial topological transition with a gap closure. Our method could in principle be generalized to a large variety of heterostructures combining a Rashba superconductor with a magnetic layer in order to be used as a platform for engineering topological quantum phases.