Valley-selective confinement of excitons in transition metal dichalcogenides with inhomogeneous magnetic fields

Magnetized ferromagnetic disks or wires support strong inhomogeneous fields in their borders. Such magnetic fields create an effective potential, due to Zeeman and diamagnetic contributions, that can localize charge carriers. For the case of two-dimensional transition metal dichalcogenides, this potential can valley-localize excitons due to the Zeeman term, which breaks the valley symmetry. We show that the diamagnetic term is negligible when compared to the Zeeman term for monolayers of transition metal dichalcogenides. The latter is responsible for trapping excitons near the magnetized structure border with valley-dependent characteristics, in which, for one of the valleys, the exciton is confined inside the disk, while for the other, it is outside. This spatial valley separation of exciton can be probed by circularly polarized light, and moreover, we show that the inhomogeneous magnetic field magnitude, the dielectric environment, and the magnetized structure parameters can tailor the spatial separation of the exciton wavefunctions.