Valley-driven orbital polarization induced by a magnetic impurity in monolayer ${\mathrm{NbSe}}_2$

Due to the coupled spin-valley physics, monolayer 2D transition metal dichalcogenides (TMDs) show many unusual electronic and transport properties. Here, we show that a magnetic impurity in the metallic TMDs such as the $2H\text{−}{\mathrm{NbSe}}_2$ induces a large orbital polarization in its neighborhood with a Friedel type oscillation, in addition to the usual spin polarization. We study the orbital polarization, hitherto unexplored for any impurity system, using the impurity Green's function approach as well as tight-binding and density functional methods. Concrete results are presented for the Mn substitutional impurity in ${\mathrm{NbSe}}_2$ from density-functional calculations. The orbital polarization here is due to the orbital moment imbalance between the $K/K^{\prime }$ valleys, which is driven by the impurity-induced spin imbalance. Our work demonstrates the Friedel oscillation for the first time in the orbital channel. Our results should be readily accessible for experimental study using techniques such as the spin polarized scanning tunneling microscopy.