Dynamic chiral magnetic effect and Faraday rotation in macroscopically disordered helical metals

We develop an effective medium theory for electromagnetic wave propagation through gapless non-uniform systems with dynamic chiral magnetic effect. The theory allows to calculate macroscopic-disorder-induced corrections to the values of optical, as well as chiral magnetic conductivities. In particular, we show that spatial fluctuations of optical conductivity induce corrections to the effective value of the chiral magnetic conductivity. Experimentally, these corrections can be observed as sharp features in the Faraday rotation angle near frequencies that correspond to the bulk plasmon resonances of a material. Such features are not expected to be present in single crystal samples.