  The discovery of the atomic electric dipole moment (EDM) would reveal the
simultaneous violation of parity (P) and time-reversal (T) invariance. The EDM
can be induced by T-odd forces between the nucleus and atomic electrons. As the
nuclear dipole moment is screened according to the Schiff theorem, the
appropriate nuclear operator is the Schiff moment that may exist in nuclei
under PT-violation. We briefly review the current experimental situation and
discuss more in detail the ideas concerning possible collective mechanisms for
the enhancement of the nuclear Schiff moment. The most promising directions are
related to the coexistence of octupole and quadrupole collective modes, either
in the form of static deformation or as soft vibrational excitations. The
search for enhancement is important for widening the pool of nuclei as
candidates for the atomic EDM as well as for development of nuclear many-body
theory beyond standard mean-field and random phase approximations.
