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.

7+10 pages,4+7 figures

References in corpus (28)

• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Exciton band structure of monolayer MoS2
• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Essay: Where Can Quantum Geometry Lead Us?
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Dichroic f-sum rule and the orbital magnetization of crystals
• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Programming Correlated Magnetic States via Gate Controlled Moiré Geometry
• Abelian and Non-Abelian Quantum Geometric Tensor
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Maximally Localized Wannier Orbitals, Interaction Models and Fractional Quantum Anomalous Hall Effect in Twisted Bilayer MoTe2
• Fundamental bound on topological gap
• The quantum geometric origin of capacitance in insulators
• Interaction-driven topological phase diagram of twisted bilayer MoTe${}_2$
• Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
• Gate-tunable antiferromagnetic Chern insulator in twisted bilayer transition metal dichalcogenides
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
• Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$
• Theory of topological exciton insulators and condensates in flat Chern bands
• Geometric Stiffness in Interlayer Exciton Condensates
• Berry Curvature Signatures in Chiroptical Excitonic Transitions
• Orbital Chern Insulator at $\nu =-2$ in Twisted MoTe${}_2$
• Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene

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
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• 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