Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

Significance By making a variety of quantitative comparisons between electronic visualization experiments and a theory describing coexisting pair density wave and superconductive states in cuprates, we find striking correspondence throughout. Our model can thus explain the microscopic origins of many key atomic-scale phenomena of the cuprate broken-symmetry state. These observations are consistent with the possibility that a short-range pair density wave (PDW) state coexists with superconductivity below a critical hole density in Bi2Sr2CaCu2O8, that the charge density wave modulations in cuprates are a consequence of the PDW state, that the cuprate pseudogap is the antinodal gap of the PDW, and that the critical point in the cuprate phase diagram occurs due to disappearance of the PDW.
The defining characteristic of hole-doped cuprates is d-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 with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states Nr,E is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and 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 of Nr,E, the modulations of the coherence peak energy Δpr, and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space q-space. Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, 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 at p* ≈ 19% occurs due to disappearance of this PDW.