  Starting from the single-particle Dirac Hamiltonian for charge carriers in
monolayer transition metal dichalcogenides (TMDs), we construct a four-band
Hamiltonian describing interlayer excitons consisting of an electron in one TMD
layer and a hole in the other TMD layer. An expression for the electron-hole
interaction potential is derived, taking into account the effect of the
dielectric environment above, below, and between the two TMD layers as well as
polarization effects in the transition metal layer and in the chalcogen layers
of the TMD layers. We calculate the interlayer exciton binding energy and
average in-plane interparticle distance for different TMD heterostructures. The
effect of different dielectric environments on the exciton binding energy is
investigated and a remarkable dependence on the dielectric constant of the
barrier between the two layers is found, resulting from competing effects as a
function of the in-plane and out-of-plane dielectric constants of the barrier.
The polarization effects in the chalcogen layers, which in general reduce the
exciton binding energy, can lead to an increase in binding energy in the
presence of strong substrate effects by screening the substrate. The excitonic
absorbance spectrum is calculated and we show that the interlayer exciton peak
depends linearly on a perpendicular electric field, which agrees with recent
experimental results.
