Anti-commutative dynamical magneto-electric response in certain solid state materials

Axion field induced topological magneto-electric response has attracted lots of attentions since it was first proposed by Qi et al. in 2008. Here we find a new type of anti-commutative magneto-electric response \beta^{\xi}(\omega), which can induce a dynamical magneto-electric current driven by a time-varying magnetic field. Unlike the Chern-Simons Axion term, this magneto-electric response term is gauge-independent and non-quantized, and manifests in the systems breaking the symmetries of the time-reversal, inversion and mirror. In particular, we propose the antiferromagnetic material Mn_{2}Bi_{2}Te_{5} as a material candidate to observe dynamical magneto-electric current, in which a large magneto-electric response term \beta^{\xi}(\omega) originates from band inversion.