Origin of the pseudogap in high-temperature cuprate superconductors

Cuprate high-temperature superconductors exhibit a pseudogap in the normal state that decreases monotonically with increasing hole doping and closes at x ≈ 0.19 holes per planar CuO₂ while the superconducting doping range is 0.05 < x < 0.27 with optimal T_c at x ≈ 0.16. Using ab initio quantum calculations at the level that leads to accurate band gaps, we found that four-Cu-site plaquettes are created in the vicinity of dopants. At x ≈ 0.05, the plaquettes percolate, so that the Cu d_{x 2y2}/O p_ω orbitals inside the plaquettes now form a band of states along the percolating swath. This leads to metallic conductivity and, below T_c, to superconductivity. Plaquettes disconnected from the percolating swath are found to have degenerate states at the Fermi level that split and lead to the pseudogap. The pseudogap can be calculated by simply counting the spatial distribution of isolated plaquettes, leading to an excellent fit to experiment. This provides strong evidence in favor of inhomogeneous plaquettes in cuprates.