Systematic investigations of the electric dipole $(E1)$ modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy $E1$ modes. We also find a universal behavior in the low-energy $E1$ modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled $E1$ peaks beyond $N=82$.
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