Surface-Mediated Ultrastrong Cavity Coupling of Two-Dimensional Itinerant Electrons

Engineering phases of matter in cavities requires effective light-matter coupling strengths that are on the same order of magnitude as the bare system energetics, coined the ultrastrong coupling regime. For models of itinerant electron systems, which do not have discrete energy levels, a clear definition of this regime has been lacking to date. Here, we argue that a change of the electronic mass exceeding 10% of its bare value may serve as such a definition. We propose a quantitative computational scheme for obtaining the electronic mass in relation to its bare vacuum value and show that coupling to surface polariton modes can induce such mass changes. Our results have important implications for cavity design principles that enable the engineering of electronic properties with quantum light.