Hong-Chen Jiang, Thomas P. Devereaux, Steven A. Kivelson
{"title":"Competition between charge-density-wave and superconducting orders on eight-leg square Hubbard cylinders","authors":"Hong-Chen Jiang, Thomas P. Devereaux, Steven A. Kivelson","doi":"10.1038/s41535-026-00910-7","DOIUrl":"https://doi.org/10.1038/s41535-026-00910-7","url":null,"abstract":"The issue of whether d-wave superconductivity (SC) occurs in the square-lattice Hubbard model with U of order of the bandwidth has been one of the most debated issues to emerge from the study of high temperature SC. Here, we report variational results on eight-leg cylinders with next-nearest-neighbor hopping in the range −0.5t≤t′≤0.25t-0.5tle t^{prime} le 0.25t with U = 8t and 12t and doped hole concentrations δ = 1/12 and 1/8. For t′≤0t^{prime} le 0, the ground-state appears to be a charge-density wave (CDW) of one sort or another with SC correlations that are extremely short-ranged. In contrast, in some cases, the local magnetic order has a correlation length greater than half the cylinder width - suggestive that magnetic order might also arise in the 2D limit. For t′>0t^{prime},>,0, our results depend more strongly on boundary conditions (periodic vs antiperiodic), making it still harder to correctly guess whether SC or CDW correlations dominate in the 2D limit. These results were obtained employing matrix-product states with bond dimensions large enough that energy differences as small as 10−3t per site can be resolved.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"13 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kinga Jasiewicz, Paweł Wójcik, Michał P. Nowak, Michał Zegrodnik
{"title":"Interplay between altermagnetism and superconductivity in two dimensions: intertwined symmetries and singlet-triplet mixing","authors":"Kinga Jasiewicz, Paweł Wójcik, Michał P. Nowak, Michał Zegrodnik","doi":"10.1038/s41535-026-00898-0","DOIUrl":"https://doi.org/10.1038/s41535-026-00898-0","url":null,"abstract":"We study the interplay between altermagnetism and unconventional superconductivity for two-dimensional square- and triangular-lattice systems. Our approach is based on an effective single particle Hamiltonian which mimics the alternating spin splitting of the <italic>d</italic>-<italic>wave</italic> and <italic>i</italic>-<italic>wave</italic> altermagnetic state. By supplementing the model with intersite pairing term we characterize the principal features of the coexistent altermagnetic-superconducting state as well as the possibility of inducing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Our calculations show that the subtle interplay between the symmetries of the superconducting and altermagnetic order parameters as well as the shape/size of the Fermi surface lead to various types of anisotropic behaviors of the resultant non-zero momentum pairing, which has not been possible in the originally proposed FFLO state. Moreover, additional pairing symmetries appear leading to multi-component order parameter with singlet-triplet mixing. We discuss our result in the context of possible applications like, e.g., the superconducting diode.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"64 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Daniel Kaplan, Pavel A. Volkov, Jennifer Coulter, Shiwei Zhang, Premala Chandra
{"title":"Spatiotemporal order and parametric instabilities from first-principles","authors":"Daniel Kaplan, Pavel A. Volkov, Jennifer Coulter, Shiwei Zhang, Premala Chandra","doi":"10.1038/s41535-025-00829-5","DOIUrl":"https://doi.org/10.1038/s41535-025-00829-5","url":null,"abstract":"Shaping crystal structure with light is an enduring goal of physics and materials engineering. Here we present calculations in candidate materials selected by symmetry that allow light-induced spatiotemporal parametric instabilities. We demonstrate a theoretical framework that includes a complete symmetry analysis of phonon modes that contribute to parametric instabilities across all non-centrosymmetric point groups, a detailed survey of the materials landscape and finally the computation of nonlinear couplings from first principles. We then showcase detailed results for chiral crystals, ferroelectrics, and layered van der Waals materials. Our results pave the way towards realizing designer time-crystalline order in quantum materials, detectable with time-resolved diffractive probes.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"63 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lara Pätzold, Anna Sandberg, Henrik Schilling, Hlynur Gretarsson, Enrico Bergamasco, Marco Magnaterra, Petra Becker, Paul H. M. van Loosdrecht, Jeroen van den Brink, Maria Hermanns, Markus Grüninger
{"title":"Between Mott and cluster Mott: spin-orbit entangled dimer singlets in Ba3CeRu2O9","authors":"Lara Pätzold, Anna Sandberg, Henrik Schilling, Hlynur Gretarsson, Enrico Bergamasco, Marco Magnaterra, Petra Becker, Paul H. M. van Loosdrecht, Jeroen van den Brink, Maria Hermanns, Markus Grüninger","doi":"10.1038/s41535-026-00909-0","DOIUrl":"https://doi.org/10.1038/s41535-026-00909-0","url":null,"abstract":"The hexagonal 4<italic>d</italic> ruthenates Ba<sub>3</sub><italic>M</italic>Ru<sub>2</sub>O<sub>9</sub> host structural dimers and exhibit a delicate balance of competing interactions. Hund’s coupling, trigonal crystal-field splitting, and hopping for <italic>a</italic><sub>1<italic>g</italic></sub> and <inline-formula><alternatives><mml:math><mml:msubsup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mi>π</mml:mi></mml:mrow></mml:msubsup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${e}_{g}^{pi }$$end{document}</tex-math></alternatives></inline-formula> orbitals all fall within a narrow energy window. This yields a series of possible ground states, ranging from the localized Mott limit with (anti-)ferromagnetic exchange coupling via orbital-selective behavior to the cluster Mott limit with quasimolecular orbitals that are delocalized over the two dimer sites. Using resonant inelastic x-ray scattering, we show that Ba<sub>3</sub>CeRu<sub>2</sub>O<sub>9</sub> with four holes per dimer resides in the intricate crossover regime between the localized Mott case and the quasimolecular limit. The spin-orbit entangled singlet ground state predominantly shows a Mott-like charge distribution with two holes per Ru site, but at the same time a dominant fraction of the holes occupies bonding orbitals. Furthermore, spin and orbital occupation contradict an exchange-based Mott scenario but agree with a cluster Mott approach. A quasimolecular trial wave function describes more than 70 % of the ground state. In this crossover regime, small changes of, e.g., the crystal field may strongly affect the character of electronic states. In Ba<sub>3</sub>CeRu<sub>2</sub>O<sub>9</sub>, both the crystal field and hopping lower the <italic>a</italic><sub>1<italic>g</italic></sub> orbitals. For spin-orbit coupling <italic>ζ</italic> = 0, Hund’s coupling favors an <italic>S</italic> = 0 ground state for small hopping but <italic>S</italic> = 1 for realistic larger hopping. Finite <italic>ζ</italic>, even though small, finally yields a non-magnetic <italic>J</italic> = 0 state.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"330 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topological quantum materials: kagome, chiral, and square-net frameworks","authors":"Avdhesh K. Sharma, Snehashish Chatterjee, Premakumar Yanda, Claudia Felser, Chandra Shekhar","doi":"10.1038/s41535-026-00902-7","DOIUrl":"https://doi.org/10.1038/s41535-026-00902-7","url":null,"abstract":"Topological quantum materials have emerged as a frontier in condensed matter physics, with electronic states governed by symmetry and lattice geometry. Among the various lattices, kagome, chiral, and square-net lattices represent distinct structural motifs where topology is intrinsically encoded. These systems exhibit diverse quantum phenomena. This review highlights the roles of lattice geometry, symmetry, spin–orbit coupling, single crystal synthesis strategies, current challenges and future directions of such topological materials.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"56 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148355686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thermal quench dynamics of visons in gapless Kitaev spin liquid","authors":"Yang Yang, Gia-Wei Chern","doi":"10.1038/s41535-026-00908-1","DOIUrl":"https://doi.org/10.1038/s41535-026-00908-1","url":null,"abstract":"Understanding the nonequilibrium relaxation dynamics of quantum spin liquids is an important and relatively unexplored frontier, where fractionalized quasiparticles and emergent gauge fields can give rise to dynamical behaviors far beyond those of conventional magnets. Here we study the relaxation dynamics of the Kitaev honeycomb model following a thermal quench, focusing on visons—gapped {{mathbb{Z}}}_{2}{{mathbb{Z}}}_{2} flux excitations of the emergent gauge field in the Kitaev spin liquid. The long-time evolution is governed by the diffusion and pair annihilation of visons, with both the activation barrier for vison motion and the effective vison-vison interactions mediated by fractionalized Majorana fermions. The resulting open-system quantum dynamics, induced by coupling to a thermal bath, can be efficiently simulated using an effective kinetic Monte Carlo approach. We uncover a rich set of temperature-dependent dynamical regimes. With decreasing temperature, the relaxation crosses over from diffusion-limited annihilation to terminal-velocity–limited kinetics, and ultimately to pronounced dynamical arrest and freezing. We show that this freezing behavior is closely tied to the formation of long-lived, metastable sqrt{3}times sqrt{3}sqrt{3}times sqrt{3} vison crystals, which strongly suppress further annihilation. Remarkably, even in the absence of true long-range crystalline order, the system exhibits a hidden coarsening dynamics of vison superclusters associated with an emergent {{mathbb{Z}}}_{3}{{mathbb{Z}}}_{3} symmetry.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"75 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
X. Shi, A. T. Bollinger, L. Aggarwal, X. He, X. Xu, A. Mitra, R. Caruso, T. Cvijetić, D. Subotić, I. Božović
{"title":"Atomic-layer-by-layer molecular beam epitaxy of Ruddlesden-Popper nickelates","authors":"X. Shi, A. T. Bollinger, L. Aggarwal, X. He, X. Xu, A. Mitra, R. Caruso, T. Cvijetić, D. Subotić, I. Božović","doi":"10.1038/s41535-026-00906-3","DOIUrl":"https://doi.org/10.1038/s41535-026-00906-3","url":null,"abstract":"The seminal discovery of high-temperature superconductivity in cuprates spurred extensive exploration of nickelates, given their structural and property similarities. It took three decades for superconductivity to be discovered in the strongly reduced nickelate Nd0.8Sr0.2NiO2, with a critical temperature Tc ≈ 8 K. In 2023, a tenfold higher Tc was detected in La3Ni2O7 under extreme pressure. In 2025, epitaxially strained thin La3Ni2O7 films were reported to superconduct at the ambient pressure, igniting worldwide exploration of various nickelates. One important research direction is to employ advanced synthesis techniques to improve the film phase purity, uniformity and crystallinity. Another is exploring other nickelate compounds. Here, we report the atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) synthesis of a series of strongly oxidized Ruddlesden-Popper nickelates Lan+1NinO3n+1, with n = 1, 2, …,7, and study of their transport properties. Unexpectedly, the dependence of resistivity on n is exponential. We successfully reproduce the data using a parallel-conductance model, with metallic-like transport in one channel and thermally activated hopping in the other. With increased n, the metallic fraction grows, while the localized one shrinks and the activation energy diminishes. We suggest that the local bond-bending lattice distortions, which lessen as n increases, play a major role.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"104 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear magneto-birefringence as a probe of altermagnetism","authors":"V. Sunko, J. Orenstein","doi":"10.1038/s41535-026-00901-8","DOIUrl":"https://doi.org/10.1038/s41535-026-00901-8","url":null,"abstract":"","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"12 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extrinsic anomalous Hall effect in altermagnets","authors":"Alexander Osin, Alex Levchenko, Maxim Khodas","doi":"10.1038/s41535-026-00895-3","DOIUrl":"https://doi.org/10.1038/s41535-026-00895-3","url":null,"abstract":"We find the extrinsic anomalous Hall conductivity (AHC) to be comparable to the intrinsic one in roughly half of the altermagnetic spin Laue groups in the limit of large exchange splitting. In materials with a finite Dzyaloshinskii-Moriya type interaction, the extrinsic contribution is essential even in the clean limit. In other altermagnets it is mostly negligible. This peculiar behavior is linked to the nonanalytic dependence of the intrinsic AHC on spin-orbit coupling. Both originate from the lifting of the spin degeneracy along the nodal planes as the weak spin-orbit coupling breaks the nonrelativistic spin symmetry.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"13 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Kitaev-derived spin liquid in the frustrated quantum magnet Na2Co2TeO6","authors":"Han Li, Xu-Guang Zhou, Gang Su, Wei Li","doi":"10.1038/s41535-026-00903-6","DOIUrl":"https://doi.org/10.1038/s41535-026-00903-6","url":null,"abstract":"The pursuit of the quantum spin liquid (QSL) predicted by the Kitaev honeycomb model remains a central yet challenging goal in quantum magnetism. Realistic candidate materials inevitably host non-Kitaev interactions that often lead to antiferromagnetic (AFM) order at low temperature. While magnetic fields can suppress such AFM order and may stabilize a QSL phase, conclusive evidence for a field-induced Kitaev QSL has remained elusive despite a decade of research. Here, we establish an effective K-J-Γ-({Gamma }^{{prime} }) model with a dominant AFM Kitaev interaction for Na2Co2TeO6, which quantitatively explains its key experimental measurements. Using high-precision tensor-network calculations, we reveal a QSL phase under intermediate [111] magnetic fields, which is possibly gapless, and find it can be adiabatically connected to the intensively studied intermediate-field QSL in the pure AFM Kitaev model. This correspondence confirms that the Kitaev model as the origin of the intermediate-field QSL in cobalt-based magnet Na2Co2TeO6, thus offering a concrete platform for exploring Kitaev-derived QSL in realistic materials.","PeriodicalId":19283,"journal":{"name":"npj Quantum Materials","volume":"8 1","pages":""},"PeriodicalIF":5.7,"publicationDate":"2026-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148287207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}