Phase diagrams of the two-dimensional extended Hubbard model: a comprehensive functional renormalization group study

Using the singular-mode functional renormalization group method, we studied the doping-dependent phase diagram of the two-dimensional extended Hubbard model on square lattice. At half-filling, a variety of states strongly compete, including spin-density wave, charge-density wave, phase separation, as well as<i>d</i>-wave and<i>s</i>-wave superconductivity (SC). Upon electron doping, the system exhibits a strong preference for superconducting states. At slight dopings, the spin-density wave phase is strongly suppressed, and<i>d</i>-wave SC region expands into positiveU,Vregion. At moderate dopings, a region of degenerated<i>p</i>-wave superconductivities emerge for positive<i>U</i>and negative<i>V</i>. Our results demonstrate how doping tunes the dominant fluctuations, suppressing density waves and stabilizing unconventional superconducting states in two dimensions.