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We explore theoretically how the topological properties of 2D materials canbe manipulated by cavity quantum electromagnetic fields for both resonant andoff-resonant electron-photon coupling, with a focus on van der Waals moir\'esuperlattices. We investigate an electron-photon topological Chern number forthe cavity-dressed energy minibands that is well defined for any degree ofhybridization of the electron and photon states. While an off-resonant cavitymode can renormalize electronic topological phases that exist without cavitycoupling, we show that when the cavity mode is resonant to electronic minibandtransitions, new and higher electron-photon Chern numbers can emerge.

Electron-photon Chern number in cavity-embedded 2D moir\'e materials