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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 2more »Free, publiclyaccessible full text available December 1, 2022

Abstract Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energygap
, for all momenta$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$k on the Fermi surface of every bandα . While there are a variety of techniques for determining , no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha $$ $\mid {\Delta}_{k}^{\alpha}\mid $ . Recently, however, a technique based on phaseresolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single nonmagnetic impurity atom, was introduced. In principle, energyresolved and phaseresolved Fourier analysis of these images identifies wavevectors connecting all$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$k space regions where has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$ it generates to the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$ determined from singleatom scattering in FeSe where s_{±}energygap symmetry is established. Finally, to exemplify utility, we use the multiatom technique on LiFeAs and find scattering interference between the holelike and electronlike pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$ of opposite sign.$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta}_{k}^{\alpha}$ 
Chargedensity waves (CDWs) are a ubiquitous form of electron density modulation in cuprate superconductors. Unveiling the nature of quasistatic CDWs and their dynamical excitations is crucial for understanding their origin––similar to the study of antiferromagnetism in cuprates. However, dynamical CDW excitations remain largely unexplored due to the limited availability of suitable experimental probes. Here, using resonant inelastic Xray scattering, we observe dynamical CDW excitations in Bi2Sr2LaCuO6+δ (Bi2201) superconductors through its interference with the lattice. The distinct anomalies of the bondbuckling and the bondstretching phonons allow us to draw a clear picture of funnelshaped dynamical CDW excitations in Bi2201. Our results of the interplay between CDWs and the phonon anomalies shed light on the nature of CDWs in cuprates.

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,more »

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electronpair density wave (PDW). To search for evidence of a fieldinduced PDW, we visualized modulations in the density of electronic states N ( r ) within the halo surrounding Bi 2 Sr 2 CaCu 2 O 8 vortex cores. We detected numerous phenomena predicted for a fieldinduced PDW, including two sets of particlehole symmetric N ( r ) modulations with wave vectors Q P and 2 Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary fieldinduced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO 2 unitcell periodicity and coexisting with its secondary CDWs.