  Unlike the hole-doped cuprates, both nodal and nodeless superconductivity
(SC) are observed in the electron-doped cuprates. To understand these two types
of SC states, we propose a unified theory by considering the two-dimensional
t-J model in proximity to an antiferromagnetic (AF) long-range ordering state.
Within the slave-boson mean-field approximation, the d-wave pairing symmetry is
still the most energetically favorable even in the presence of the external AF
field. In the nodal phase, it is found that the nodes carry vorticity and are
protected by the adjoint symmetry of time-reversal and one unit lattice
translation. Robust edge modes are obtained, suggesting the nodal d-wave SC
being a topological weak-pairing phase. As decreasing the doping concentration
or increasing the AF field, the nodes with opposite vorticity annihilate and
the nodeless strong-pairing phase emerges. The topological phase transition is
characterized by a critical point with anisotropic Bogoliubov quasiparticles,
and a universal understanding is thus established for all electron-doped
cuprates.
