Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity

Abstract

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., Annual Review of Condensed Matter Physics 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 N(r,E) is predicted at the terminal BiO surface of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ and compared with high-precision electronic visualization experiments using spectroscopic imaging STM. The PDW+DSC model predictions include the intra-unit-cell structure and periodic modulations of N(r,E), the modulations of the coherence peak energy ${\Delta }_p$ (r), 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 Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ 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.

References in corpus (15)

• Theory of Intertwined Orders in High Temperature Superconductors
• A `checkerboard' electronic crystal state in lightly hole-doped Ca_{2-x}Na_{x}CuO_{2}Cl_{2}
• An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
• Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La(1.875)Ba(0.125)CuO(4)
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Dynamical layer decoupling in a stripe-ordered, high T_c superconductor
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Visualizing the Energy-gap Modulations of the Cuprate Pair Density Wave State
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Charge ordering in superconducting copper oxides
• Spectral signatures of modulated d-wave superconducting phases
• Universality of scanning tunneling microscopy in cuprate superconductors
• Density Waves Cause Sub-Gap Structures but no Pseudogap in Superconducting Cuprates

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• Identification of a Nematic Pair Density Wave State in Bi2Sr2CaCu2O8+x
• Microscopic mechanism for fluctuating pair density wave
• Two-dimensional superconducting fluctuations associated with charge density wave stripes in La${}_{1.87}$Sr${}_{0.13}$Cu${}_{0.99}$Fe${}_{0.01}$O${}_4$
• Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase
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• Electronic Theory for Scanning Tunneling Microscopy Spectra in Infinite-Layer Nickelate Superconductors
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• Monte Carlo study of cuprate superconductors in a four-band $d$-$p$ model: Role of orbital degrees of freedom
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
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