Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity
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 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 scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of N r , E , the modulations of the coherence peak energy Δ 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, more »
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Award ID(s):
Publication Date:
NSF-PAR ID:
10229587
Journal Name:
Proceedings of the National Academy of Sciences
Volume:
117
Issue:
26
Page Range or eLocation-ID:
14805 to 14811
ISSN:
0027-8424
1. Abstract An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO 2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $${\Lambda }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}})$$ Λ P ( q ) in wavevector space. By studying strongly underdoped Bi 2 Sr 2 CaDyCu 2 O 8 at hole-density ~0.08 in the superconductivemore »
5. We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-$t′$-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative$t′$values ($t′/t=±0.2$) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The$t′<0$(hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find$t′<0$strongly suppresses superconductivity. The$t′>0$(electron-doped) regionmore »