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arXiv 2412.03399cond-mat.mes-hall
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滑动电子晶体的Berry相位动力学

Berry Phase Dynamics of Sliding Electron Crystals

Yongxin Zeng, Andrew J. Millis

AI总结:

本文研究了反常霍尔晶体等新型电子晶体的滑动动力学,发现其在外场加速下的横向反常速度源于母带Berry曲率和晶体状态的伽利略非不变性,且净霍尔电导通常不量子化。

摘要:

Wigner晶体和不可公度电荷密度波等自发破缺连续平移对称性的系统,因其能够在空间中相干滑动而具有不同寻常的输运性质。最近的实验和理论研究指出,在一些具有非平凡量子几何的二维材料(例如,菱面体五层石墨烯)中,自发平移对称性破缺导致了一种拓扑非平凡的电子晶体状态,称为反常霍尔晶体,其特征是线性响应直流纵向电导率消失,而霍尔电导率不为零。在这项工作中,我们考虑系统的非平凡量子几何,对这种新型电子晶体的滑动动力学进行了理论研究。我们发现,当被外部电场加速时,晶体获得了一个横向反常速度,该速度不仅源于母带的Berry曲率,还源于晶体状态的伽利略非不变性(即具有不同动量的晶体状态不能通过简单的动量增量相联系)。我们进一步表明,晶体的加速将其内部电流从静态晶体值进行了修正,该静态值由晶体状态的Chern数决定。包括质心运动和内部电流贡献的净霍尔电导通常是不量子化的。作为一个与实验相关的例子,我们给出了菱面体五层石墨烯的数值结果,并讨论了可能的实验意义。

英文摘要:

Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a non-vanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system's nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean non-invariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

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