Quantum geometric limit for hemispherically averaged nonreciprocity in thin-film thermal emitters

Nonreciprocal thermal emitters that violate Kirchhoff’s law offer a path to surpass efficiency limits in energy conversion, yet their fundamental physical bounds remain unexplored. Here we derive a materials-intrinsic upper bound on the frequency-integrated, hemispherically averaged nonreciprocity of an ultra-thin, self-supporting film in vacuum in the far field. The derivation combines the generalized Kirchhoff’s law, passivity-based absorption bounds for a 2D sheet, and the Onishi–Fu log-frequency sum rule. The resulting inequality links the achievable nonreciprocal contrast–bandwidth product to the electronic quantum weight of the electronic ground state. It reveals a fundamental tradeoff: opening a broadband nonreciprocal window requires a large quantum weight. Quantified through case studies of excitonic and massive Dirac thin films, this limit provides a materials-first guideline for designing next-generation thermal photonic devices.