Spectroscopy of phonon-coupled integer and fractional Chern insulators: emergence of polarons and chirality deficit of graviton mode

Strong electron-phonon coupling can destabilize both Chern insulators (CIs) and fractional Chern insulators (FCIs) in favor of charge order, but whether the instabilities in CI and FCI share a common microscopic mechanism remains unclear. In this paper, we address this question by studying a flat-ba