  We study the dark excitons at the interface of sharp lateral heterostructure
of two-dimensional transition metal dichalcogenides. By introducing a
low-energy effective Hamiltonian model, we find the energy dispersion relation
of exciton and show how it depends on the onsite energy of composed materials
and their spin-orbit coupling strengths. It is shown that the effect of
geometrical structure of interface, as a deformation gauge field
(pseudo-spin-orbit coupling), should be considered in calculating the binding
energy of exciton. By discretization of real-space version of the dispersion
relation on a triangular lattice, we show that the binding energy of exciton
depends on its distance from the interface line. For exciton near the interface
the binding energy is equal to 0.36 eV, while for the exciton enough far from
the interface it is equal to 0.26 eV. Also, it has been shown that for zigzag
interface the binding energy increases by 0.34 meV in comparison with the
armchair interface due to the pseudo-spin-orbit interaction (gauge filed). The
results can be used for designing the two-dimensional lateral heterostructure
based optoelectronic devices and improving their characteristics.
