Electron crystallization in weakly doped semiconductors from first principles

The Wigner crystal, a long-sought prototypical phase of an interacting electron gas, has recently been observed in doped two-dimensional semiconductors via scanning tunneling microscopy measurements, marking a new chapter in the study of correlated electron systems in low-dimensional materials. Although nearly a century has passed since Eugene Wigner first proposed the concept of the Wigner crystal, understanding Wigner crystallization from first principles remains elusive due to strong electron correlations and the long-wavelength nature of the phenomenon. Here, we investigate electron crystallization in doped two-dimensional semiconductors using a generalized Kohn-Sham (GKS) density functional theory (DFT) approach. By adopting the Bloch electron basis, we efficiently perform GKS-DFT calculations for excess charge carriers. We study the Γ-valley of hole-doped bilayer MoSe₂ and examine the energy competition between the uniform hole liquid phase and the hole crystal phase across various doping regimes. We discuss possible connections to previous measurements.