Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators

TL;DR

This paper theoretically links the optical absorption sum rule to quantum geometric properties like the Chern number in Chern insulators, demonstrating how excitonic responses reveal topological features in moiré materials.

Contribution

It establishes a theoretical framework connecting excitonic optical responses to quantum geometric invariants such as the Chern number in Chern insulators.

Findings

A single chiral exciton dominates the optical sum rule.

Nearly perfect magnetic circular dichroism observed in absorption spectrum.

The optical response can probe quantum geometry encoded by $K$ and $C$.

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 moir\'e superlattices.