Superconductivity and topological Fermi surface transitions in electron-doped cuprates near optimal doping

We discuss evolution of the Fermi surface (FS) topology with doping in electron doped cuprates within the framework of a one-band Hubbard Hamiltonian, where antiferromagnetism and superconductivity are assumed to coexist in a uniform phase. In the lightly doped insulator, the FS consists of electron pockets around the $(\pi ,0)$ points. The first change in the FS topology occurs in the optimally doped region when an additional hole pocket appears at the nodal point. The second change in topology takes place in the overdoped regime ($\sim 18$) where antiferromagnetism disappears and a large $(\pi ,\pi )$-centered metallic FS is formed. Evidence for these two topological transitions is found in recent Hall effect and penetration depth experiments on Pr${}_{2-x}$Ce${}_x$CuO${}_{4-\delta }$ (PCCO) and with a number of spectroscopic measurements on Nd${}_{2-x}$Ce${}_x$CuO${}_{4-\delta }$ (NCCO).