Dielectric function in WSe2

We develop a Hartree-Fock numerical method for computing the band structure of a two-dimensional Wigner crystal in an electron gas at zero temperature. The ground state is assumed to be fully spin-polarized. Single-particle excitation spectra are evaluated in spin-conserving channel. As an application, we use the developed code to compute the static dielectric function epsilon(q,0) of a Wigner-crystal state formed in a two-dimensional transition-metal dichalcogenide, specifically monolayer WSe2. The dielectric response is obtained from the Hartree-Fock band structure and eigenfunctions through a static Lindhard-type polarizability. The method provides a theoretical tool for investigating screening, band-structure reconstruction, and interaction effects in low-density two-dimensional systems, with possible relevance for future experimental studies.