  We studied the exciton properties in double layers of transition metal
dichalcogenides (TMDs) with a dielectric spacer between the layers. We
developed a method based on an expansion of Chebyshev polynomials to solve the
Wannier equation for the exciton. Corrections to the quasiparticle bandgap due
to the dielectric environment were also included via the exchange self-energy
calculated within a continuum model. We systematically investigated hetero
double-layer systems for TMDs with chemical compounds MX2, showing the
dependence of the inter- and intralayer excitons binding energies as a function
of the spacer width and the dielectric constant. Moreover, we discussed how the
exciton energy and its wave function, which includes the effects of the
changing bandgap, depend on the geometric system setup.
