Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators

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...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Wen-Xuan Qiu, Wu, Fengcheng
Format: Article
Language:English
Subjects:
Absorption spectra
Absorptivity
Circular polarization
Dichroism
Dipole moments
Excitons
Holes (electron deficiencies)
Insulators
Interlayers
Polarized light
Sum rules
Sums
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Summary: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 \(C\).
ISSN:2331-8422