近日，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。该研究于2025年9月17日发表在《美国科学院院刊》杂志上。

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。研究组推导了这类量子晶体的低能有效理论，包括具有非零陈恩数的异常霍尔晶体。

首先，研究组证明了尽管存在贝里曲率，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，这是由于平移发生器的换向。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，如弹性常数和有效质量，并将它们应用于两类模型：最近引入的λ-凝胶模型和菱形多层石墨烯（RMG）模型。在λ-凝胶模型中，他们探索了晶体几何形状变化时的能量格局，揭示了AHC在一定条件下会变得“柔软”。虽然量子化的霍尔响应保持不变，但这在晶格几何中发生了跃迁。

令人惊讶的是，贝里曲率似乎提高了有效质量，导致声子速度的降低。对于RMG中的AHC，研究组获得了声子速度和剪切刚度的估计。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，该项存在于RMG的对称设置中，并导致声子速度在相反方向上的巨大差异。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。

附：英文原文

Title: Phonons in electron crystals with Berry curvature

Author: Dong, Junkai, Sommer, Ophelia Evelyn, Soejima, Tomohiro, Parker, Daniel E., Vishwanath, Ashvin

Issue&Volume: 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, including the anomalous Hall crystal (AHC) with nonzero Chern number. First, we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, 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, and apply them to two families of models: the recently introduced λ-jellium model and a model of rhombohedral multilayer graphene (RMG). In the λ-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become “soft” under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, 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, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree–Fock calculations.

DOI: 10.1073/pnas.2515532122

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2515532122