Comment on "Axion induced oscillating electric dipole moments"

In the recent work [Phys. Rev. D 91, 111702(R) (2015)], C. Hill concludes that the axion electromagnetic anomaly induces an oscillating electron electric dipole moment of frequency $m_a$ and strength $\sim 10^{-32}~e$ cm, in the limit $v/c \to 0$ for the axion field. Here, we demonstrate that a proper treatment of this problem in the lowest order yields $\textit{no}$ electric dipole moment of the electron in the same limit. Instead, oscillating electric dipole moments of atoms and molecules are produced by different mechanisms.