Pseudogap Mott-phase in cuprate superconductors: a Hartree–Fock study with limited next-nearest-neighbor hopping

We study the pseudogap phase of cuprate superconducting systems in a Hartree–Fock approach to the Hubbard Hamiltonian with an extra competing next-nearest-neighbor hopping term of energy $$t_2$$ t 2 along the nodal directions of the sublattice Brillouin zone. A maximum pseudogap energy of 101.08 meV is obtained at the nodal points of the Fermi surface in the half-filling antiferromagnetic Mott insulating state, in good agreement with the experimental result for the La $$_2$$ 2 CuO $$_4$$ 4 compound on which our model parametrization is based. By doping the half-filled system either with holes or electrons, we observe the formation of pocket regions near the Fermi surface with low density of states at the nodes and antinodes, respectively. Remarkably, the pseudogap closes down at the critical hole and electron doping concentrations $$x_h^* = 0.20$$ x h ∗ = 0.20 and $$x_e^* = 0.17$$ x e ∗ = 0.17 , also in fine agreement with the experimental values of the cuprate systems La $$_{2-x}$$ 2 - x Sr $$_{x}$$ x CuO $$_{4}$$ 4 and Nd $$_{2-x}$$ 2 - x Ce $$_{x}$$ x CuO $$_{4}$$ 4 , which have the same CuO $$_{2}$$ 2 -plane structure at half-filling consistent with the fixing of our model parameters. By nullifying the next-nearest-neighbor hopping energy, $$t_2 = 0$$ t 2 = 0 , no pseudogap emerges. These findings suggest that limiting the electron dispersion along the nodal directions that connect contiguous Cu-sites in the same sublattice, combined with a significant on-site Coulomb repulsion, may play a relevant role to the opening of the pseudogap associated with filled or partially filled Mott states in cuprate compounds. Graphic abstract