Cavity mediated electron-electron interactions in quantum materials

Constraining electromagnetic waves within a small region leads to enhanced vacuum field strengths, where vacuum quantum fluctuations can significantly alter the properties of 2+1D quantum materials placed inside. This introduces a powerful and flexible tuning mechanism that can be integrated into quantum devices. In this context, we explore how electron-electron interactions mediated by cavity photons may influence various phases of matter. We investigate the potential for these interactions to either weaken or enhance topological protection, as well as to modify charge orders, such as the fractionalization that gives rise to a fractional Chern insulator in moiré materials. Additionally, we discuss how such cavity-mediated interactions could provide a pathway toward realizing topological superconductivity in moire materials, opening new possibilities for quantum materials in engineered environments.