Coherent long-range magnetic bound states in a superconductor

Magnetic atoms embedded in a niobium selenide superconductor are shown to give rise to a long-range coherent bound state extending tens of nanometres. The quantum coupling of fully different degrees of freedom is a challenging path towards new functionalities for quantum electronics1,2,3. Here we show that the localized classical spin of a magnetic atom immersed in a superconductor with a two-dimensional 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–NbSe2 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 phases4,5,6,7,8,9,10,11.