Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators

Abstract

We theoretically derive the sum rule for the negative first moment of the absorptive optical conductivity with excitonic effects and establish its connection to the quantum weight $K$ and Chern number $C$ of the ground state. Applying this framework, we investigate the excitonic optical response of the Chern insulator at hole filling factor $\nu =1$ in twisted bilayer MoTe${}_2$. A single chiral exciton state, which selectively absorbs circularly polarized light of a specific handedness, dominates the optical sum rule. The chiral exciton state comprises two types of interlayer electron-hole transitions, which cancel out the total out-of-plane dipole moment. The absorption spectrum shows nearly perfect magnetic circular dichroism, which can be attributed to the nearly saturated bound $K\ge |C|$ of the Chern insulator under study. Our work illustrates the potential of using excitonic optical responses to probe quantum geometry encoded by $K$ and $C$ of Chern insulators in moiré superlattices.

arXiv comment7+10 pages,4+7 figures

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Cited by in corpus (8)

• Quantum weight: A fundamental property of quantum many-body systems
• Observation of Ferromagnetic Phase in the Second Moiré Band of Twisted MoTe2
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
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• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Distinct topological excitonic insulators characterized by quantum geometry