莫尔材料中的光-物质耦合和量子几何
Light-matter coupling and quantum geometry in moiré materials
摘要：
量子几何学被认为是量子材料物理学的重要组成部分，特别是平带系统，如莫尔材料。另一方面，光和物质之间的耦合在各个学科中都非常重要，特别是对于Floquet和固体的腔体工程。在这里，我们提出了光-物质耦合和布洛赫波函数的量子几何之间的基本关系，特别关注平带和莫尔材料，其中电子动能的猝灭可以允许人们比在高色散系统中更容易达到强光-物质耦合的极限。我们表明，尽管事实上，平坦的带消失的带速度和曲率，光耦合到他们通过几何贡献。具体来说，带内量子度规允许平带内的抗磁耦合;带间贝瑞连接支配平带和色散带之间的偶极矩阵元。我们在两个代表性的模型系统中说明了这些效应：（i）具有单个平带的量子链，以及（ii）扭曲双层石墨烯的紧束缚模型。对于（i），我们通过证明平带内的非零抗磁光物质耦合来强调量子几何的重要性。对于（ii），我们探讨了各种光-物质耦合矩阵元素的扭曲角依赖性。此外，在对应于几乎平坦能带的魔角处，尽管费米速度几乎为零，但在圆偏振光的照射下，我们显示了Floquet拓扑能隙开口。我们讨论了这些发现如何为基于光物质耦合的平带和莫尔材料中的电子特性控制提供基本的设计原理和工具。
英文摘要：
Quantum geometry has been identified as an important ingredient for the physics of quantum materials and especially of flat-band systems, such as moiré materials. On the other hand, the coupling between light and matter is of key importance across disciplines and especially for Floquet and cavity engineering of solids. Here we present fundamental relations between light-matter coupling and quantum geometry of Bloch wave functions, with a particular focus on flat-band and moiré materials, in which the quenching of the electronic kinetic energy could allow one to reach the limit of strong light-matter coupling more easily than in highly dispersive systems. We show that, despite the fact that flat bands have vanishing band velocities and curvatures, light couples to them via geometric contributions. Specifically, the intra-band quantum metric allows diamagnetic coupling inside a flat band; the inter-band Berry connection governs dipole matrix elements between flat and dispersive bands. We illustrate these effects in two representative model systems: (i) a sawtooth quantum chain with a single flat band, and (ii) a tight-binding model for twisted bilayer graphene. For (i) we highlight the importance of quantum geometry by demonstrating a nonvanishing diamagnetic light-matter coupling inside the flat band. For (ii) we explore the twist-angle dependence of various light-matter coupling matrix elements. Furthermore, at the magic angle corresponding to almost flat bands, we show a Floquet-topological gap opening under irradiation with circularly polarized light despite the nearly vanishing Fermi velocity. We discuss how these findings provide fundamental design principles and tools for light-matter-coupling-based control of emergent electronic properties in flat-band and moiré materials.
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