Origin of the Pseudogap in High-Temperature Cuprate Superconductors

Computational details Calculations to compute the pseudogap (PG) from Equation 1 were performed by averaging 100 ensembles of 2,500 x 2,500 lattices. Four-site plaquettes were randomly doped up to x = 0.187, then three-site plaquettes up to x = 0.226, followed by two-site plaquettes to x = 0.271, and finally one-site plaquettes were doped until no d spins remained at x = 0.317. The details of the doping methodology are described in the manuscript. The PG was determined for each isolated plaquette along with the average. The average value is the PG observed in bulk measurements (neutron, ARPES, specific heat, etc). STM sees an inhomogenous distribution of PG values. We find the standard deviation of the PG is approximately constant with doping and ~ 15 meV, in agreement with the STM value of ~ 10-20 meV. Calculations to determine the doping values 0.187, 0.226, 0.271, and 0.317 at the boundaries of plaquette doping of four, three, two, and one undoped Cu d spins were determined by generating a ensemble of 1,000 doped lattices of size 1,000 x 1,000 using a linear scaling percolation algorithm.