Abstract

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. The authors show that the low-frequency phonon dispersion of the AHC resembles that of the zero-field Wigner crystal, explain how elastic constants and effective mass can be extracted from microscopic models, and apply the formalism to the lambda-jellium model and rhombohedral multilayer graphene. They find that Berry curvature can soften the crystal and enhance the effective mass, identify a kineo-elastic term in the phonon effective action, and benchmark the effective theory against time-dependent Hartree-Fock calculations.

Abstract

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. The authors show that the low-frequency phonon dispersion of the AHC resembles that of the zero-field Wigner crystal, explain how elastic constants and effective mass can be extracted from microscopic models, and apply the formalism to the lambda-jellium model and rhombohedral multilayer graphene. They find that Berry curvature can soften the crystal and enhance the effective mass, identify a kineo-elastic term in the phonon effective action, and benchmark the effective theory against time-dependent Hartree-Fock calculations.

Abstract

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. The authors show that the low-frequency phonon dispersion of the AHC resembles that of the zero-field Wigner crystal, explain how elastic constants and effective mass can be extracted from microscopic models, and apply the formalism to the lambda-jellium model and rhombohedral multilayer graphene. They find that Berry curvature can soften the crystal and enhance the effective mass, identify a kineo-elastic term in the phonon effective action, and benchmark the effective theory against time-dependent Hartree-Fock calculations.

Abstract

Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. The authors show that the low-frequency phonon dispersion of the AHC resembles that of the zero-field Wigner crystal, explain how elastic constants and effective mass can be extracted from microscopic models, and apply the formalism to the lambda-jellium model and rhombohedral multilayer graphene. They find that Berry curvature can soften the crystal and enhance the effective mass, identify a kineo-elastic term in the phonon effective action, and benchmark the effective theory against time-dependent Hartree-Fock calculations.