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1. Generic character of charge and spin density waves in superconducting cuprates

   https://doi.org/10.1073/pnas.2119429119  

   Lee, Sangjun ; Huang, Edwin W. ; Johnson, Thomas A. ; Guo, Xuefei ; Husain, Ali A. ; Mitrano, Matteo ; Lu, Kannan ; Zakrzewski, Alexander V. ; de la Peña, Gilberto A. ; Peng, Yingying ; et al ( April 2022 , Proceedings of the National Academy of Sciences)

   Charge density waves (CDWs) have been observed in nearly all families of copper-oxide superconductors. But the behavior of these phases across different families has been perplexing. In La-based cuprates, the CDW wavevector is an increasing function of doping, exhibiting the so-called Yamada behavior, while in Y- and Bi-based materials the behavior is the opposite. Here, we report a combined resonant soft X-ray scattering (RSXS) and neutron scattering study of charge and spin density waves in isotopically enriched La 1.8 − x Eu 0.2 Sr x CuO 4 over a range of doping 0.07 ≤ x ≤ 0.20 . We findmore »that the CDW amplitude is temperature independent and develops well above experimentally accessible temperatures. Further, the CDW wavevector shows a nonmonotonic temperature dependence, exhibiting Yamada behavior at low temperature with a sudden change occurring near the spin ordering temperature. We describe these observations using a Landau–Ginzburg theory for an incommensurate CDW in a metallic system with a finite charge compressibility and spin-CDW coupling. Extrapolating to high temperature, where the CDW amplitude is small and spin order is absent, our analysis predicts a decreasing wavevector with doping, similar to Y and Bi cuprates. Our study suggests that CDW order in all families of cuprates forms by a common mechanism.« less
2. Distinction between pristine and disorder-perturbed charge density waves in ZrTe3

   https://doi.org/10.1038/s41467-019-13813-y  

   Yue, Li ; Xue, Shangjie ; Li, Jiarui ; Hu, Wen ; Barbour, Andi ; Zheng, Feipeng ; Wang, Lichen ; Feng, Ji ; Wilkins, Stuart B. ; Mazzoli, Claudio ; et al ( January 2020 , Nature Communications)

   Charge density waves (CDWs) in the cuprate high-temperature superconductors have evoked much interest, yet their typical short-range nature has raised questions regarding the role of disorder. Here we report a resonant X-ray diffraction study of ZrTe$${}_{3}$$${}_3$, a model CDW system, with focus on the influence of disorder. Near the CDW transition temperature, we observe two independent signals that arise concomitantly, only to become clearly separated in momentum while developing very different correlation lengths in the well-ordered state that is reached at a distinctly lower temperature. Anomalously slow dynamics of mesoscopic charge domains are further found near the transition temperature,more »in spite of the expected strong thermal fluctuations. Our observations signify the presence of distinct experimental fingerprints of pristine and disorder-perturbed CDWs. We discuss the latter also in the context of Friedel oscillations, which we argue might promote CDW formation via a self-amplifying process.

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3. Magnetic field–induced pair density wave state in the cuprate vortex halo

   https://doi.org/10.1126/science.aat1773  

   Edkins, S. D. ; Kostin, A. ; Fujita, K. ; Mackenzie, A. P. ; Eisaki, H. ; Uchida, S. ; Sachdev, Subir ; Lawler, Michael J. ; Kim, E.-A. ; Séamus Davis, J. C. ; et al ( June 2019 , Science)

   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 electron-pair density wave (PDW). To search for evidence of a field-induced 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 field-induced PDW, including two sets of particle-hole symmetric N ( r ) modulations with wave vectors Q P and 2more »Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO 2 unit-cell periodicity and coexisting with its secondary CDWs.« less
4. Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides

   https://doi.org/DOI: 10.1103/PhysRevB.98.205153  

   Mazumdar, S. ( October 2018 , Physical review. B, Condensed matter)

   We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity Cu2+ -> Cu1+ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the T' compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and BaBiO3. The unusuallymore »high ionization energy of the closed shell Cu1+ ion, taken together with the dopingdriven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small d-p electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive O2- ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell Cu1+ ions, in the doped state. The model thus gives microscopic justification for the two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional T' crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of O1- -Cu l(1+)-O1- spin singlets that coexists with broken rotational C-4 symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit twodimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and ihid. 93, 205111 (2016)]. We posit that a similar valence transition, Ir4+ -> Ir3+, occurs upon electron doping Sr2IrO4. We make testable experimental predictions in cuprates including superoxygenated La2CuO4+delta and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable.« less
5. Two-dimensional charge order stabilized in clean polytype heterostructures

   https://doi.org/10.1038/s41467-021-27947-5  

   Sung, Suk Hyun ; Schnitzer, Noah ; Novakov, Steve ; El Baggari, Ismail ; Luo, Xiangpeng ; Gim, Jiseok ; Vu, Nguyen M. ; Li, Zidong ; Brintlinger, Todd H. ; Liu, Yu ; et al ( December 2022 , Nature Communications)

   Abstract Compelling evidence suggests distinct correlated electron behavior may exist only in clean 2D materials such as 1T-TaS 2 . Unfortunately, experiment and theory suggest that extrinsic disorder in free standing 2D layers disrupts correlation-driven quantum behavior. Here we demonstrate a route to realizing fragile 2D quantum states through endotaxial polytype engineering of van der Waals materials. The true isolation of 2D charge density waves (CDWs) between metallic layers stabilizes commensurate long-range order and lifts the coupling between neighboring CDW layers to restore mirror symmetries via interlayer CDW twinning. The twinned-commensurate charge density wave (tC-CDW) reported herein has a singlemore »metal–insulator phase transition at ~350 K as measured structurally and electronically. Fast in-situ transmission electron microscopy and scanned nanobeam diffraction map the formation of tC-CDWs. This work introduces endotaxial polytype engineering of van der Waals materials to access latent 2D ground states distinct from conventional 2D fabrication.« less