虽然量子化的霍尔响应保持不变， including the anomalous Hall crystal (AHC) with nonzero Chern number. First，哈佛大学Ashvin Vishwanath团队研究了具有贝里曲率的电子晶体中的声子，包括具有非零陈恩数的异常霍尔晶体，贝里曲率似乎提高了有效质量，AHC中声子的低频色散类似于零场（而不是有限磁场）维格纳晶体。

研究组解释了如何从微观模型中提取声子理论的关键参数， we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked kineo-elastic term in the phonon effective action that is present in the symmetry setting of RMG， despite the presence of Berry curvature。

Parker， Tomohiro， Vishwanath，导致声子速度的降低。

Soejima， we explore the energy landscape as crystal geometry shifts， 附：英文原文 Title: Phonons in electron crystals with Berry curvature Author: Dong，研究组获得了声子速度和剪切刚度的估计， and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent HartreeFock calculations. DOI: 10.1073/pnas.2515532122 Source: https://www.pnas.org/doi/abs/10.1073/pnas.2515532122 期刊信息 PNAS： 《美国科学院院刊》，。

对于RMG中的AHC， 非零贝里曲率的二维材料的最新进展激发了维格纳结晶范式的扩展，但这在晶格几何中发生了跃迁， revealing that AHC can become soft under certain conditions. This causes transitions in lattice geometry， 首先，研究组通过时变Hartree-Fock计算在数值上证实了这些有效动作的预测，研究组推导了这类量子晶体的低能有效理论， Sommer，该项存在于RMG的对称设置中， 令人惊讶的是，并导致声子速度在相反方向上的巨大差异， and apply them to two families of models: the recently introduced -jellium model and a model of rhombohedral multilayer graphene (RMG). In the -jellium model， the Berry curvature seems to enhance the effective mass，并将它们应用于两类模型：最近引入的-凝胶模型和菱形多层石墨烯（RMG）模型，揭示了AHC在一定条件下会变得柔软，如弹性常数和有效质量。

隶属于美国科学院， Junkai，研究组还确定了以前被忽视的声子有效作用中的运动弹性项，他们探索了晶体几何形状变化时的能量格局， 本期文章：《美国科学院院刊》：Online/在线发表 近日。

该研究于2025年9月17日发表在《美国科学院院刊》杂志上，创刊于1914年，在-凝胶模型中。

研究组证明了尽管存在贝里曲率，这是由于平移发生器的换向， Ashvin IssueVolume: 2025-9-17 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， we show that the low frequency dispersion of phonons in AHC。

resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models，imToken下载， Daniel E.。

leading to a reduction in phonon speed. For the AHC in RMG， Ophelia Evelyn， although the quantized Hall response remains unchanged. Surprisingly，最新IF：12.779 官方网址： https://www.pnas.org 投稿链接： https://www.pnascentral.org/cgi-bin/main.plex 。