Probing correlated states with plasmonic origami

Understanding the nature of strongly correlated states in flat-band materials (such as moir\'e heterostructures) is at the forefront of both experimental and theoretical pursuits. While magnetotransport, scanning probe, and optical techniques are often very successful in investigating the properties of the underlying order, the exact nature of the ground state often remains unknown. Here we propose to leverage strong light-matter coupling present in the flat-band systems to gain insight through dynamical dielectric response into the structure of the many-body ground state. We argue that due to the enlargement of the effective lattice of the system arising from correlations, conventional long-range plasmon becomes ``folded'' to yield a multiband plasmon spectrum. We detail several mechanisms through which the structure of the plasmon spectrum and that of the dynamical dielectric response is susceptible to the underlying order revealing valued insights such as the interaction-driven band gaps, spin-structure, and the order periodicity.