卡西米尔排斥的量子几何界限
Quantum-geometric bounds on Casimir repulsion
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中文总结 AI 辅助
本文推导二维板间卡西米尔力的量子几何界限，发现饱和几何界限的平坦陈带可扩大卡西米尔排斥窗口，为观测排斥提出新优化策略。
中文摘要 AI 辅助
量子几何张量已被证明可限定材料的能隙、光吸收和介电 susceptibility。本文在长距离极限下推导了二维板间卡西米尔力的大小和符号的新量子几何界限。这些界限限制了此前认为的增加板的陈数以最大化排斥的益处，并为金属板更强的吸引力提供了量子几何起源，无论其陈数如何。这些界限使我们推断，饱和几何界限的平坦陈带（包括朗道能级和莫尔平带）扩大了卡西米尔排斥存在的窗口，并使排斥转变发生在更小、更具实验相关性的距离。我们推导了如扭曲MoTe₂等材料平台的估计值。本研究表明，量子几何界限对排斥性卡西米尔力的约束超出了已知定理，并提出了观测排斥的新优化策略。
英文摘要
The quantum geometric tensor has been shown to bound the gap, optical absorption, and dielectric susceptibilities of materials. Here we derive new quantum-geometric bounds on the magnitude and sign of the Casimir force between two-dimensional plates in the long-distance limit. These bounds limit the previously attributed benefit of increasing the plate's Chern number to maximize repulsion, and give a quantum geometric origin to the stronger attractive force of metallic plates, regardless of their Chern number. These bounds allow us to infer that flat Chern bands that saturate geometric bounds, including Landau levels and moiré flat bands, enlarge the window where Casimir repulsion exists and bring the repulsive crossover to smaller, more experimentally relevant distances. We derive estimates for material platforms such as twisted MoTe$_2$. Our work shows that quantum-geometric bounds constrain repulsive Casimir forces beyond previously known theorems, and suggests new optimization strategies to observe repulsion.
