 Award ID(s):
 1664842
 NSFPAR ID:
 10112673
 Date Published:
 Journal Name:
 Science
 Volume:
 364
 Issue:
 6444
 ISSN:
 00368075
 Page Range / eLocation ID:
 976 to 980
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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null (Ed.)The defining characteristic of holedoped 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 strongcoupling meanfield theory of cuprates, to model the atomicscale electronic structure of an eightunitcell 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 highprecision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunitcell 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 scatteringwavevector space q  space . Consistency between all these predictions and the corresponding experiments indicates that lightly holedoped 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 symmetrybreaking 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.more » « less

Abstract An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electrondensity 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 realspace, 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 holedensity ~0.08 in the superconductive phase, we detect the 8 a 0 periodic $${\Delta }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{r}}}}}})$$ Δ P ( r ) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature $$\Lambda ({{{{{\boldsymbol{q}}}}}})$$ Λ ( q ) that is predicted specifically for the temperature dependence of an 8 a 0 periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d wave superconductivity to a pure PDW state in the Bi 2 Sr 2 CaDyCu 2 O 8 pseudogap phase.more » « less

We review the physics of pairdensity wave (PDW) superconductors. We begin with a macroscopic description that emphasizes order induced by PDW states, such as chargedensity wave, and discuss related vestigial states that emerge as a consequence of partial melting of the PDW order. We review and critically discuss the mounting experimental evidence for such PDW order in the cuprate superconductors, the status of the theoretical microscopic description of such order, and the current debate on whether the PDW is a mother order or another competing order in the cuprates. In addition, we give an overview of the weak coupling version of PDW order, Fulde–Ferrell–Larkin–Ovchinnikov states, in the context of cold atom systems, unconventional superconductors, and noncentrosymmetric and Weyl materials.more » « less

The CuO 2 antiferromagnetic insulator is transformed by holedoping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic densityofstates D ( E ) for energies  E  < Δ * , where Δ * is the PG energy. Unanticipated brokensymmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite Q densitywave (DW) state and a Q = 0 nematic (NE) state. Sublatticephaseresolved imaging of electronic structure allows the doping and energy dependence of these distinct brokensymmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy Δ * . Moreover, no new energygap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermisurface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energygap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi 2 Sr 2 CaCu 2 O 8 .more » « less

Abstract A pairdensitywave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a densitymatrix renormalizationgroup (DMRG) study of an effective
t J V model, which is equivalent to the HolsteinHubbard model in a strongcoupling limit, on long two, four, and sixleg triangular cylinders. While a state with longrange PDW order is precluded in one dimension, we find strong quasilongrange PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of timereversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around theK and points in the Brillouin zone can be identified. We conclude that the state is valleypolarized and that the PDW arises from intrapocket pairing with an incommensurate center of mass momentum. In the twoleg case, the exponential decay of spin correlations and the measured central charge$${K}^{\prime}$$ ${K}^{\prime}$c ≈ 1 are consistent with an unusual realization of a LutherEmery liquid.