平带Chern带中位移电流随超晶格周期的幂律增长
Power-law growth of shift current with superlattice period in flat Chern bands
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中文总结 AI 辅助
本研究证明位移电流与回旋位移成正比，提出普适标度律，并在莫尔平带中验证，发现积分权重随周期线性增长、峰值立方增长。
中文摘要 AI 辅助
量子几何在拓扑量子材料中支配着广泛的物理可观测量。在其理想极限下，量子几何为不断增长的可观测量类别提供了精确的界限和分析结果。然而，对于位移电流而言，一个类似的框架仍然难以捉摸，因为它依赖于多个能带之间的几何关系。在这项工作中，我们证明了位移电流与回旋位移（由朗道能级混合引起的回旋中心的位移）成正比。这一机制产生了一个普适的标度律：积分权重和峰值幅度分别按 $l^{i+1-n}$ 和 $l^{2i+1-n}$ 标度，其中 $l$ 是磁长度或莫尔周期，$n$ 是破坏对称性微扰的动量阶数，$\Delta E \propto l^{-i}$ 是能级间距。我们在均匀磁场下精确可解的chiral-$N$朗道能级以及薛定谔和狄拉克莫尔天文学晶体中验证了该标度律，这些晶体捕捉了扭曲MoTe$_2$和扭曲双层石墨烯的平Chern带。对于具有畸变天文学纹理的薛定谔平带，积分权重随莫尔周期线性增长，而共振峰则三次方增长。
英文摘要
Quantum geometry governs a wide array of physical observables in topological quantum materials. In its ideal limit, quantum geometry yields exact bounds and analytical results for a growing class of observables. However, a comparable framework for the shift current remains elusive because it depends on geometric relations between multiple bands. In this work, we show that the shift current is proportional to the cyclotron shift, the displacement of the cyclotron center induced by Landau-level mixing. This mechanism yields a universal scaling law: the integrated weight and the peak magnitude scale as $l^{i+1-n}$ and $l^{2i+1-n}$ in the magnetic length or moiré period $l$, where $n$ is the momentum order of the symmetry-breaking perturbation and $ΔE \propto l^{-i}$ is the level spacing. We verify the scaling law in exactly solvable chiral-$N$ Landau levels under a uniform magnetic field and in Schrödinger and Dirac moiré skyrmion crystals, which capture the flat Chern bands of twisted MoTe$_2$ and twisted bilayer graphene. For a Schrödinger flat band with a distorted skyrmion texture, the integrated weight grows linearly with the moiré period and the resonant peak grows cubically.
发表机构
- University of Tennessee（田纳西大学）
- Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
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