Statics and Dynamics of Generalized Wigner Molecular Crystals and Moiré Systems

Recently, Wigner molecular crystals have been observed in moiré systems where multiple charges are trapped in each potential minimum [1]. This system can be modeled as charged particles on a triangular substrate at fillings of N = 1, 2, 3, and higher. The Wigner molecular crystal states have both positional and orientational order, analogous to molecular crystals. Here, we study the charge ordering of Wigner molecular crystals at integer fillings of two or higher, as well as at fractional fillings, building upon our previous work for fillings of N < 1.0 [2]. We find that the system can be described in terms of n-mer-like states, and that at fractional fillings, a superlattice ordering of multiple coexisting n-mer states can appear. As a function of temperature, we show that the n-mer states can lose orientational but not positional ordering, and that at higher temperatures, the lattice melts. For incommensurate fillings, there can be localized thermal hopping of soliton-like degrees of freedom. We demonstrate that this system should have interesting dynamical states as a function of external drive, with a pinned polarized state in which the orientation of the n-mers follows the direction of the driving field, as well as multiple-step depinning processes at higher drives.

[1] H. Li et al, "Wigner molecular crystals from multielectron moiré artificial atoms," Science 385, 86 (2024).

[2] C. Reichhardt and C.J.O. Reichhardt, "Depinning, melting, and sliding of generalized Wigner crystals in moiré systems," Phys. Rev. Res. 7, 013155 (2025)