Various ordered states in a 2D interacting electron system close to an electronic topological transition

We consider a 2D electron system on a square lattice with hopping beyond nearest neighbors. The existence of the quantum critical point associated with an electronic topological transition in the noninteracting system results in density wave (DW) and high-temperature d-wave superconducting (dSC) instabilities in the presence of an exchange interaction J. We analyse different DW ordering such as isotropic Spin DW (SDW), d-wave SDW, isotropic Charge DW (CDW) and d-wave CDW. The coexistence of dSC and SDW orders leads necessarily to the existence of a third order which is a π triplet superconducting (PTS) order. A new phase diagram with a mixed phase of SDW, dSC and PTS order is found. The theory is applied to high- T_c cuprates.