Chiral anomaly in a (1+1)-dimensional Floquet system under high-frequency electric fields

We investigate the chiral anomaly in a Floquet system under a time-periodic electric field in (1+1) dimensions. Using the van~Vleck high-frequency expansion, we analytically calculate the chiral current and the pseudo-scalar condensate for massless/massive fermions and how they are balanced with the topological charge. In the high-frequency limit, we find that finite-mass effects are suppressed and the topological charge is dominated by the chirality production. Our calculations show that the information about the chiral anomaly is stored not in the static Floquet Hamiltonian but in the periodic kick operator. The computational steps are useful as the theoretical foundation for higher-dimensional generalization.