  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.

Mesoscale and Nanoscale Physics