Continuum Photonic Axion Insulators

Here, I study the conditions for realizing an axion topology in a homogeneous inversion-symmetric electromagnetic continuum, in the absence of a crystalline lattice. I introduce a continuum inversion invariant expressed solely in terms of the spectral properties of the material response in the zero- and infinite-wave-vector limits. Surprisingly, it is found that standard gyrotropic-type material responses are strongly constrained and, under fairly general conditions, cannot open an axion gap within first-order perturbation theory. Based on an analogy between the effective response of crystalline photonic axion insulators and the optical response of centrosymmetric altermagnets, a class of spatially dispersive odd magnetoelectric couplings that can open an axion gap is identified. These findings suggest an interesting hierarchy of nonreciprocal mechanisms in electromagnetic continua: while uniform gyrotropy relates to Chern phases, odd magnetoelectric coupling relates to axion phases.