Two-dimensional (2D) van der Waals materials are a promising platform for exciton state engineering. In this paper, we study the properties of excitons in 2D group VI transition metal dichalcogenide semiconductors that are modified by a periodic electrostatic potential through the quadratic Stark effect. Using a model that retains only center-of-mass and valley degrees of freedom, we find that electrostatic potentials can drive optical valley splitting up to $\sim 10\mathrm{meV}$ and induce valley-selective exciton dispersion. We explain why both properties are sensitive to the rotational symmetry of the electrostatic trapping potential using a combination of numerical results and analytical approximations. An important consequence of valley splitting is that the lowest exciton band is nondegenerate and has a linear dispersion around $\mathit{\gamma }$ that is expected to suppress thermal excitations, allowing true Bose condensation and superfluidity of excitons in two space dimensions.

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• Excitons
• Twistronics
• Valley degrees of freedom
• Valleytronics
• Ferroelectrics
• Layered semiconductors
• Transition metals
• Exact solutions for many-body systems
• Numerical techniques