Large valley (orbital) polarization near a magnetic impurity in monolayer NbSe₂: Green's Function and density-functional studies

We show that a magnetic impurity in the monolayer transition metal dichalcogenides (TMDs) such as 2H-NbSe₂ induces a valley (orbital) polarization in its vicinity in addition to the standard spin polarization of the electron gas due to the coupled spin-valley physics. There is a site-dependent occupancy difference between the angular momentum orbitals, L₊ - L_-, where L_± ≡ ¦x²- y² >± i ¦xy >, which is large close to the impurity site, but diminishes away from it, similar to the Friedel oscillation. The spin/orbital polarization is studied from the impurity Green's function method using the low-energy k.p Hamiltonian (valley orbital model) as well as from density-functional calculations. Such magnetic-impurity-induced orbital polarization should exist to a varying degree in any crystal with spin-orbit coupling, but is especially large in non-centrosymmetric crystals such as the monolayer TMDs. To our knowledge, this is the first time that an orbital polarization has been predicted near an impurity in any system. Our results should be readily accessible for experimental study using conventional and spin polarized scanning tunneling microscopy as well as optical experiments with polarized light.