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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 »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.« less

laminar two-phase mixing layer at supercritical pressure

Background: We investigated the association between reproductive risk factors and breast cancer subtype in Black women. On the basis of the previous literature, we hypothesized that the relative prevalence of specific breast cancer subtypes might differ according to reproductive factors. Methods: We conducted a pooled analysis of 2,188 (591 premenopausal, 1,597 postmenopausal) Black women with a primary diagnosis of breast cancer from four studies in the southeastern United States. Breast cancers were classified by clinical subtype. Case-only polytomous logistic regression models were used to estimate ORs and 95% confidence intervals (CI) for HER2+ and triple-negative breast cancer (TNBC) status inmore »relation to estrogen receptor–positive (ER+)/HER2− status (referent) for reproductive risk factors. Results: Relative to women who had ER+/HER2− tumors, women who were age 19–24 years at first birth (OR, 1.78; 95% CI, 1.22–2.59) were more likely to have TNBC. Parous women were less likely to be diagnosed with HER2+ breast cancer and more likely to be diagnosed with TNBC relative to ER+/HER2− breast cancer. Postmenopausal parous women who breastfed were less likely to have TNBC [OR, 0.65 (95% CI, 0.43–0.99)]. Conclusions: This large pooled study of Black women with breast cancer revealed etiologic heterogeneity among breast cancer subtypes. Impact: Black parous women who do not breastfeed are more likely to be diagnosed with TNBC, which has a worse prognosis, than with ER+/HER2− breast cancer.« less

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_k^{\alpha }$, for all momentakon the Fermi surface of every bandα. While there are a variety of techniques for determining$$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$$\mid {\Delta }_k^{\alpha }\mid$, no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_k^{\alpha }$. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting allk-space regions where$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_k^{\alpha }$has the same or opposite sign. But use of a single isolated impuritymore »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 single-atom scattering in FeSe where s_±energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$${\Delta }_k^{\alpha }$of opposite sign.

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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 atmore »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, 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.« less