Structural analysis of the precursor pseudogap in cuprate superconductors

We investigate the precursor pseudogap (PP) state that emerges on the lower temperature side of the pseudogap phase in cuprate superconductors based on the characteristic layer structure. The coherence among layers in the electronic state may be broken by low energy thermal interactions, whereas the coherence within the layers remains in the phase above the superconducting (SC) phase on account of strongness of the bonding. In this state, the two-electron energy gain (TEG) is also larger than that of SC state and the one-electron energy gain (OEG) is smaller than that of the SC state. We call this incoherent ensemble of in-layer states the in-layer electronic state system (IESS). The PP state is a crossover state between IESS and the normal pseudogap (NP) state, which appears on the upper temperature side, because the d-wave pairing symmetry in cuprates inverts the sign of the difference of the total electronic energy gain between the IESS and the NP state around the nodal region, even though it is positive overall. We perform our analysis at the mean field level. We show that the relationships among the SC gap, the gap of in-layer state, and the transition temperatures in the relevant phases are compatible with existing experimental data. The proposed precursor state requires pairing models to make the SC interactions three-dimensional beyond a single layer, although the precursors have in-layer properties.