  The impact of axion-like particles (ALPs) on the search of permanent electric
dipole moments (EDMs) of molecules, atoms, nuclei and nucleons is
systematically investigated. We classify first the full set of CP-violating
Jarlskog invariants emerging in the ALP effective field theory (EFT) containing
operators up to dimension-5. Then, we evaluate the leading short-distance
effects to the EDMs up to two-loop order. The high sensitivity of EDMs to
CP-violating ALP interactions is emphasised exploiting both the current and
projected experimental sensitivities.
