Waveguiding valley excitons in monolayer transition metal dichalcogenides by dielectric interfaces in the substrate

In monolayers of semiconducting transition metal dichalcogenides, the electron-hole exchange interaction splits the exciton dispersion into a massive transverse branch and a longitudinal branch that has very light or even zero mass depending on the form of screened Coulomb interaction. The group velocity of the longitudinal branch is sensitive to the strength of electron-hole exchange, which can be engineered through the dielectric environment. Here we show that dielectric patterning of the substrate can be exploited to realize the waveguide of the exciton in the longitudinal branch in a homogeneous monolayer, leaving the massive transverse branch unaffected. At a lateral interface of different dielectric constants in the substrate, the transmission and reflection of the exciton in the longitudinal branch obey the Snell-Descartes law of optical systems, and total reflection can be exploited to realize an excitonic waveguide using two parallel interfaces. The same dielectric pattern of the substrate appears to be completely transparent for the massive transverse branch exciton, which has no interface scattering. When the monolayer is placed on a one-dimensional dielectric superlattice, the dispersion of the longitudinal branch is strongly renormalized, and the wave functions exhibit one-dimensional features, confined to either the low-dielectric or high-dielectric region. In contrast, the massive transverse branch excitons are not affected by the substrate dielectric pattern, exhibiting pristine properties as in a freestanding monolayer.