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 establish a quantum geometric limit for the directional nonreciprocity of thin-film thermal emitters in the far-field regime. We demonstrate that the frequency-integrated contrast between emissivity and absorptivity is bounded solely by the quantum weight of the electronic ground state. This result reveals an intrinsic tradeoff: achieving a broad nonreciprocal window requires materials with 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.