Superexchange-induced valley splitting in two-dimensional transition metal dichalcogenides: A first-principles study for rational design

Monolayer transition metal dichalcogenides (TMDs) with spin-valley coupling are a well-studied class of twodimensional materials with potential for novel optoelectronics applications. Breaking time-reversal symmetry via an external magnetic field or supporting magnetic substrate can lift the degeneracy of the band gaps at the inequivalent K and K' high symmetry points, or valleys, in the monolayer TMD Brillouin zone, a phenomenon known as valley splitting. However, reported valley splittings thus far are modest, and a detailed structural and chemical understanding of valley splitting via magnetic substrates is lacking. Here we probe the underlying physical mechanism with a series of density functional theory (DFT) calculations of magnetic atoms with varying coverage on the surface of prototypical monolayer WSe2 and MoS2 TMDs. Near-valence band edge energies for variable magnetic atom height, lateral registry, and magnetic moment are calculated with DFT, and trends are rationalized with a model Hamiltonian with second-order spin-dependent exchange coupling. From our analysis, we demonstrate how large valley splittings may be achieved and that the valley splitting can be understood with a superexchange mechanism, which strongly depends on overlaps of TMD Bloch states at the valley extrema with the localized d states of the magnetic atom, as well as the out-of-plane component of the magnetic moment of the magnetic atom. Our calculations provide a basis for understanding prior measurements of valley splitting and suggest routes for enhancing valley splitting in future systems of interest.

Automated summary

The study investigates the physical mechanism behind valley splitting induced by magnetic atoms on the surface of monolayer TMDs, with DFT calculations evaluating the impact of different parameters of magnetic atoms on the near-valence band edge energies. It is concluded that large valley splittings can be achieved through a superexchange mechanism, depending on the overlap of TMD Bloch states with the localized d states of the magnetic atom and the out-of-plane component of the magnetic moment.