Abstract
Understanding the origin of the pseudogap is an essential step toward elucidating the pairing mechanism in the cuprate superconductors. Recently there has been strong experimental evidence showing that $C$4 symmetry breaking occurs on the formation of the pseudogap. This form of symmetry breaking was predicted by the fluctuating bond model (FBM), an empirical model based on a strong, local coupling of electrons to the square of the planar oxygen vibrator amplitudes. In this paper we approach the FBM theory from a new direction, starting from ab initio molecular dynamics simulations. The simulations demonstrate a doping-dependent instability of the in-plane oxygens toward displacement off the Cu-O-Cu bond axis. From these results and perturbation theory we derive an improved and quantitative form of the FBM. A mean-field solution of the FBM leads to $C$4 symmetry breaking in the oxygen vibrational amplitudes and to a $d$-type pseudogap in the electronic spectrum, the features linked by recent experimental data. The phase diagram of the pseudogap derived from mean-field theory, its doping and temperature dependences, including the phase boundary ${T}^{*}$, agree well with experimental data. We extend the theory to include the long-range Coulomb interaction on the same basis as the FBM interaction. When the long-range Coulomb interaction is included in the FBM, a charge density wave (CDW) instability in the charge channel is predicted, which explains the nanoscale, rather than spatially uniform, behavior of the $C$4 symmetry breaking. Taking the CDW into account, with the theoretical $k$ dependence of the pseudogap, enables the Fermi surface arc phenomenon to be understood.
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