Triangular lattice exciton model

We present a minimalistic equilateral triangular lattice model, from which we derive electron and exciton band structures for semiconducting transition-metal dichalcogenides. With explicit consideration of the exchange interaction, this model is appropriate across the spectrum from Wannier to Frenkel excitons. The single-particle contributions are obtained from a nearest-neighbor tight-binding model parameterized using the effective mass and spin-orbit coupling. The solutions to the characteristic equation, computed in direct space, are in qualitative agreement with first-principles calculations and highlight the inadequacy of the two-dimensional hydrogen model to describe the lowest-energy exciton bands. The model confirms the lack of subshell degeneracy and shows that the A-B exciton split depends on the electrostatic environment as well as the spin-orbit interaction.