The insulator and pseudogap states coalescence beneath the superconductor dome

The pseudogap effects and the expected quantum phase transitions (QPT) in cuprate materials are yet unclear in nature. A single band Tight-Binding (TB) model for the CuO planes of these materials had predicted the existence of definite pseudogap states at half-filling, after considering that a crystal symmetry breaking and non-collinear spin orientations of the single particle states are allowed. Here we show that after including hole doping in the model, a QPT which lies beneath the superconducting dome exists and is a second order one. In it, an insulator ground state (AFI), showing strong spin fluctuations at low doping, coalesce with an excited paramagnetic pseudogap (PPG) state, exhibiting a broken lattice symmetry at the critical hole density $x_{c} =$ 0$.$2. Above this value the system becomes a paramagnetic metal. The band structures and Fermi surfaces with doping are evaluated and their evolution show a close resemblance with the experimental observations, including the topological change in structure for varying hole density.