The defining characteristic of hole-doped cuprates isd-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al.,Annu. Rev. Condens. Matter Phys.11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic,d-symmetry form factor, pair density wave (PDW) state coexisting withd-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle statesNr,Eis predicted at the terminal BiO surface of Bi2Sr2CaCu2O8and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations ofNr,E, the modulations of the coherence peak energyΔpr,and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector spaceq-space. Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole densityp*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point atp* ≈ 19% occurs due to disappearance of this PDW.
Atomic-Scale Visualization of the Cuprate Pair Density Wave State
