Waveguiding valley excitons in a homogeneous monolayer through dielectric-patterning of substrate*

In monolayers of the semiconducting transition metal dichalcogenides, the electron-hole exchange in an exciton couples exciton's valley pseudospin and centre-of-mass momentum. It 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. Here we show that dielectric patterning of the substrate can be exploited to realize waveguide of the exciton in the longitudinal branch, leaving the massive transverse branch unaffected. At a lateral interface of different dielectric constant in the substrate, the longitudinal branch exciton's transmission and reflection obey the Snell-Descartes law of optical system. This dielectric heterostructure appears transparent to the transverse branch exciton. When placing the monolayer on a one-dimensional dielectric superlattice, the dispersion of the longitudinal branch exciton is changed signicantly, and the wavefunctions exhibit one-dimensional features. In contrast, the massive transverse branch excitons are not affected by the substrate dielectric pattern.