Exploring Wigner crystals in two-dimensional and moiré systems: from spectroscopy to theoretical modeling

Abstract Electron correlation effects have long been a central issue in condensed matter physics, particularly with the successful development of various two-dimensional materials. Notably, recent research interest has centered on the ordered states of twisted moiré lattices, where doped low-density electrons exhibit crystallized behavior as predicted by Eugene Wigner nearly a century ago. Such correlation effects are often highly sensitive to external perturbations, including electrostatic fields or material strains. Consequently, significant challenges remain in both experimental and theoretical investigations of these correlated states. Preparing a pure moiré lattice without distortion is particularly difficult, and the computational cost of theoretical modeling for such systems grows rapidly with decreasing angles due to the increasing size of the system. In this review, we introduce recent theoretical and experimental progress regarding Wigner crystal states induced by magnetic fields and generalized Wigner crystals or Wigner molecules emerging in moiré materials, followed by a discussion of future directions in this area.