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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 find 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. 

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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, 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. Universal Stripe Symmetry of Short‐Range Charge Density Waves in Cuprate Superconductors

   https://doi.org/10.1002/adma.202307515  

   Choi, Jaewon ; Li, Jiemin ; Nag, Abhishek ; Pelliciari, Jonathan ; Robarts, Hannah ; Tam, Charles C. ; Walters, Andrew ; Agrestini, Stefano ; García‐Fernández, Mirian ; Song, Dongjoon ; et al ( November 2023 , Advanced Materials)

   The omnipresence of charge density waves (CDWs) across almost all cuprate families underpins a common organizing principle. However, a longstanding debate of whether its spatial symmetry is stripe or checkerboard remains unresolved. While CDWs in lanthanum‐ and yttrium‐based cuprates possess a stripe symmetry, distinguishing these two scenarios is challenging for the short‐range CDW in bismuth‐based cuprates. Here, high‐resolution resonant inelastic x‐ray scattering is employed to uncover the spatial symmetry of the CDW in Bi₂Sr_{2 −x}La_xCuO_{6 + δ}. Across a wide range of doping and temperature, anisotropic CDW peaks with elliptical shapes are found in reciprocal space. Based on Fourier transform analysis of real‐space models, the results are interpreted as evidence of unidirectional charge stripes, hosted by mutually 90°‐rotated anisotropic domains. This work paves the way for a unified symmetry and microscopic description of CDW order in cuprates.

    

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4. Magnetic-field-sensitive charge density waves in the superconductor UTe2

   https://doi.org/10.1038/s41586-023-06005-8  

   Aishwarya, Anuva ; May-Mann, Julian ; Raghavan, Arjun ; Nie, Laimei ; Romanelli, Marisa ; Ran, Sheng ; Saha, Shanta R. ; Paglione, Johnpierre ; Butch, Nicholas P. ; Fradkin, Eduardo ; et al ( June 2023 , Nature)

   The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices1–4. However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe2 (refs. 5–8). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field Hc2. To understand the phenomenology of this unusual CDW, we construct a Ginzburg–Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe2. 

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5. 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 2 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. 

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