Destruction of Néel order in the cuprates by electron doping

Motivated by the evidence in Pr2-x Cex CuO4-y and Nd2-x Cex CuO4-y of a magnetic quantum critical point at which Néel order is destroyed, we study the evolution with doping of the T=0 quantum phases of the electron-doped cuprates. At low doping, there is a metallic Néel state with small electron Fermi pockets, and this yields a fully gapped d x2 - y2 superconductor with coexisting Néel order at low temperatures. We analyze the routes by which the spin-rotation symmetry can be restored in these metallic and superconducting states. In the metal, the loss of Néel order leads to a topologically ordered "doublon metal" across a deconfined critical point with global O(4) symmetry. In the superconductor, in addition to the conventional spin-density wave transition, we find a variety of unconventional possibilities, including transitions to a nematic superconductor and to valence-bond supersolids. Measurements of the spin-correlation length and of the anomalous dimension of the Néel order by neutron scattering or NMR should discriminate these unconventional transitions from spin-density wave theory.