Electric Dipole Moments from Axion-Like Particle Dark Matter Background

New one- and two-loop contributions to the lepton’s and nucleon’s EDM, which are induced by an axion-like particle dark matter background, are examined. These contributions include effects from CP-violating ALP interactions with photons, leptons and nucleons. The contribution to the EDM is so larger it leads to new constraints on the CP violating couplings of axion-like particles, if the axion-like particle mass is smaller than ${10}^{-11}$ eV.