DATA: 09/05/2025.
HORÁRIO: 10h.
LOCAL: Auditório do CCE.

ABSTRACT:
Recent discoveries of fractional Chern-insulator (FCI) states in moiré transition-metal dichalcogenides and rhombohedral multilayer graphene have opened a new arena for exploring strongly correlated topological matter in flat bands. In this talk I will weave together two complementary stories that reveal how FCIs respond—or fail to respond—to electromagnetic probes: First, I will discuss the long-wavelength density–density correlations of ideal flat-band FCIs. By combining Stillinger–Lovett perfect-screening arguments with the vanishing intraband matrix elements of the current operator, I show that the low-energy collective modes inside a single Chern band are anomalously dark: they have negligible dipole moment, and therefore couple only weakly to light. The surviving interband response is fixed by the quantum geometry of the Chern band, providing a direct link between Berry curvature fluctuations and optical weight. Second, I will examine what happens when the same FCI (or its Landau-level cousin, a fractional quantum Hall state) is exposed to a (residual) moiré-periodic lattice in graphene/hBN or twisted MoTe₂. Using a single-mode approximation supplemented by Monte-Carlo evaluation of three-point correlation functions, we study an effective Hamiltonian for neutral excitations and show how the magnetoroton dispersion is folded into bands. The periodic potential both redistributes oscillator strength into the terahertz window and drives a soft-mode instability toward a charge-density-wave phase at a critical potential strength. Together, these results highlight how the interplay between band geometry, interactions, and moiré potentials shapes the neutral excitation spectrum of fractional Chern insulators and related fractional quantum Hall phases in moiré materials.