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1. Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

   https://doi.org/10.1073/pnas.2002429117  

   Choubey, Peayush ; Joo, Sang Hyun ; Fujita, K. ; Du, Zengyi ; Edkins, S. D. ; Hamidian, M. H. ; Eisaki, H. ; Uchida, S. ; Mackenzie, A. P. ; Lee, Jinho ; et al ( June 2020 , Proceedings of the National Academy of Sciences)

   null (Ed.)

   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, 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. 

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2. Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

   https://doi.org/10.1038/s41467-021-26028-x  

   Wang, Shuqiu ; Choubey, Peayush ; Chong, Yi Xue ; Chen, Weijiong ; Ren, Wangping ; Eisaki, H. ; Uchida, S. ; Hirschfeld, Peter J. ; Davis, J. C. ( December 2021 , Nature Communications)

   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 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. 

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3. Weyl Fermions and broken symmetry phases of laterally confined 3 He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

    

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4. Evidence for a vestigial nematic state in the cuprate pseudogap phase

   https://doi.org/10.1073/pnas.1821454116  

   Mukhopadhyay, Sourin ; Sharma, Rahul ; Kim, Chung Koo ; Edkins, Stephen D. ; Hamidian, Mohammad H. ; Eisaki, Hiroshi ; Uchida, Shin-ichi ; Kim, Eun-Ah ; Lawler, Michael J. ; Mackenzie, Andrew P. ; et al ( July 2019 , Proceedings of the National Academy of Sciences)

   The CuO 2 antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D ( E ) for energies | E | < Δ * , where Δ * is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite- Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry 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 energy-gap 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 Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap 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 . 

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5. Water Quenched and Acceptor‐Doped Textured Piezoelectric Ceramics for Off‐Resonance and On‐Resonance Devices

   https://doi.org/10.1002/smll.202204454  

   Leng, Haoyang ; Wang, Yu U. ; Yan, Yongke ; Karan, Sumanta Kumar ; Wang, Ke ; Li, Xiaotian ; Fanton, Mark ; Fox, Joshua J. ; Priya, Shashank ( November 2022 , Small)

   Piezoelectric materials should simultaneously possess the soft properties (high piezoelectric coefficient,d₃₃; high voltage coefficient,g₃₃; high electromechanical coupling factor,k) and hard properties (high mechanical quality factor,Q_m; low dielectric loss, tan δ) along with wide operation temperature (e.g., high rhombohedral–tetragonal phase transition temperatureT_r–t) for covering off‐resonance (figure of merit (FOM),d₃₃ ×g₃₃) and on‐resonance (FOM,Q_m ×k²) applications. However, achieving hard and soft piezoelectric properties simultaneously along with high transition temperature is quite challenging since these properties are inversely related to each other. Here, through a synergistic design strategy of combining composition/phase selection, crystallographic texturing, defect engineering, and water quenching technique, <001> textured 2 mol% MnO₂doped 0.19PIN‐0.445PSN‐0.365PT ceramics exhibiting giant FOM values ofQ_m × (227–261) along with highd₃₃ ×g₃₃(28–35 × 10⁻¹²m²N⁻¹), low tan δ (0.3–0.39%) and highT_r–tof 140–190 °C, which is far beyond the performance of the state‐of‐the‐art piezoelectric materials, are fabricated. Further, a novel water quenching (WQ) room temperature poling technique, which results in enhanced piezoelectricity of textured MnO₂doped PIN‐PSN‐PT ceramics, is reported. Based upon the experiments and phase‐field modeling, the enhanced piezoelectricity is explained in terms of the quenching‐induced rhombohedral phase formation. These findings will have tremendous impact on development of high performance off‐resonance and on‐resonance piezoelectric devices with high stability.

    

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