Resonant x-ray scattering studies of charge order in cuprates

Abstract

X-ray techniques have been used for more than a century to study the atomic and electronic structure in virtually any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional x-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom -- charge, orbital, spin, and lattice -- paved the way for the emergence and success of resonant x-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. Here we review the recent resonant x-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order -- a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant x-ray scattering, as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review will focus on the recent contributions of resonant scattering to the tremendous advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges, and discuss the future outlook for this technique.

A high-resolution version can be found at http://qmlab.ubc.ca/ARPES/PUBLICATIONS/Reviews/RXS_ARCMP.pdf

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• A `checkerboard' electronic crystal state in lightly hole-doped Ca_{2-x}Na_{x}CuO_{2}Cl_{2}
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• Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5
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• How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d
• Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa${}_2$Cu${}_3$O${}_{6+x}$
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
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• Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered YBa${}_2$Cu${}_3$O${}_{6+\delta }$ Superconductors Identified by Resonant Elastic X-ray Scattering
• Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• X-ray diffraction observation of charge density wave order at zero magnetic field in ortho-II YBa${}_2$Cu${}_3$O${}_{6.54}$
• Appearance of fluctuating stripes at the onset of the pseudogap in the high-Tc Superconductor Bi2Sr2CaCu2O8+x
• Charge ordering in the electron-doped superconductor Nd2-xCexCuO4
• Charge density wave fluctuations in La2-xSrxCuO4 and their competition with superconductivity
• Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}
• Competing charge, spin, and superconducting orders in underdoped YBa2Cu3Oy
• Quasiparticle mass enhancement approaching optimal doping in a high-Tc superconductor
• Disentangling the electronic and phononic glue in a high-Tc superconductor
• Broken translational and rotational symmetry via charge stripe order in underdoped YBCO
• Magnetic neutron scattering in hole doped cuprate superconductors
• Resonant Elastic Soft X-Ray Scattering
• Fermi Surface Evolution in an Electron-Doped High-Tc Superconductor Revealed by Magnetic Quantum Oscillations
• Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State
• Distinguishing Patterns of Charge Order: Stripes or Checkerboards
• High-energy spin and charge excitations in electron-doped copper oxide superconductors
• Rotated stripe order and its competition with superconductivity in La${}_{1.88}$Sr${}_{0.12}$CuO${}_4$
• Melting of Charge Stripes in Vibrationally Driven La1.875Ba0.125CuO4: Assessing the Respective Roles of Electronic and Lattice Order in Frustrated Superconductors
• From stripe to checkerboard order on the square lattice in the presence of quenched disorder
• Superconducting d-wave stripes in cuprates: Valence bond order coexisting with nodal quasiparticles
• Femtosecond x rays link melting of charge-density wave correlations and light-enhanced coherent transport in YBa2Cu3O6.6
• Resonant elastic soft x-ray scattering in oxygen-ordered YBa_2Cu_3O_{6+delta}
• Competing orders in thermally fluctuating superconductors in two dimensions
• Resonant X-Ray Scattering Measurements of a Spatial Modulation of the Cu 3d and O 2p Energies in Stripe-Ordered Cuprate Superconductors
• Bulk charge stripe order competing with superconductivity in La2-xSrxCuO4 (x=0.12)
• Giant Phonon Anomaly associated with Superconducting Fluctuations in the Pseudogap Phase of Cuprates
• Stripes and electronic quasiparticles in the pseudogap state of cuprate superconductors
• Microscopic theory of resonant soft x-ray scattering in systems with charge order

Cited by in corpus (254)

• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Detection of a Cooper-Pair Density Wave in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$
• Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors
• Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Rapid change of superconductivity and electron-phonon coupling through 19% doping in Bi2212
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Quantum textures of the many-body wavefunctions in magic-angle graphene
• Time- and Angle-Resolved Photoemission Studies of Quantum Materials
• Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+δ
• Stripe order from the perspective of the Hubbard model
• Charge density waves in infinite-layer NdNiO${}_2$ nickelates
• Clean 2D superconductivity in a bulk van der Waals superlattice
• Universality of pseudogap and emergent order in lightly doped Mott insulators
• Charge and spin order dichotomy in NdNiO${}_2$ driven by SrTiO${}_3$ capping layer
• Commensurate Stripes and Phase Coherence in Manganites Revealed with Cryogenic Scanning Transmission Electron Microscopy
• Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications
• Landscape of competing stripe and magnetic phases in cuprates
• Theory of hydrodynamic transport in fluctuating electronic charge density wave states
• Electronic Structure Trends Across the Rare-Earth Series in Superconducting Infinite Layer Nickelates
• Commensurate $4a_0$ period Charge Density Modulations throughout the $B{i}_{2}S{r}_{2}CaC{u}_2{O}_{8+x}$ Pseudogap Regime
• High-temperature charge density wave correlations in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ without spin-charge locking
• Intimate link between Charge Density Wave, Pseudogap and Superconducting Energy Scales in Cuprates
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Doping dependent charge order correlations in electron-doped cuprates
• Period 4 stripe in the extended two-dimensional Hubbard model
• Bad Metals from Fluctuating Density Waves
• Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering
• Cuprate superconductors as viewed through a striped lens
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Electric-Field Induced Superconductor-Insulator Transitions in Exfoliated Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ Flakes
• Conjoined Charge Density Waves in the Kagome Superconductor CsV3Sb5
• Spatial symmetry constraint of charge-ordered kagome superconductor CsV${}_3$Sb${}_5$
• Enhanced charge density wave coherence in a light-quenched, high-temperature superconductor
• Charge ordering in superconducting copper oxides
• Doping the holographic Mott insulator
• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Presence of $s$-wave pairing in Josephson junctions made of twisted ultrathin Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ flakes
• Charge order at high temperature in cuprate superconductors
• Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
• Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method
• Nature of the charge-density wave excitations in cuprates
• Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization
• Coexistence of Superconductivity and Antiferromagnetism in the Hubbard model for cuprates
• Multi-orbital charge density wave excitations and concomitant phonon anomalies in Bi${}_2$Sr${}_2$LaCuO${}_{6+\delta }$
• Strange metal behaviour from charge density fluctuations in cuprates
• Crossover of Charge Fluctuations across the Strange Metal Phase Diagram
• Incommensurate phonon anomaly and the nature of charge density waves in cuprates
• Unusual interplay between superconductivity and field-induced charge order in YBa2Cu3Oy
• Stabilization of three-dimensional charge order in YBa${}_2$Cu${}_3$O${}_{6+x}$ via epitaxial growth
• Remarkable Stability of Charge Density Wave Order in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$
• Generic character of charge and spin density waves in superconducting cuprates
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• Charge and spin instabilities in superconducting La${}_3$Ni${}_2$O${}_7$
• Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane
• Observation of a dispersive charge mode in hole-doped cuprates using resonant inelastic x-ray scattering at the oxygen K edge
• Locally commensurate charge-density wave with three-unit-cell periodicity in YBCO
• Determining the Electron-Phonon Coupling in Superconducting Cuprates by Resonant Inelastic X-ray Scattering: Methods and Results on Nd${}_{1+x}$Ba${}_{2-x}$Cu${}_3$O${}_{7-\delta }$
• Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity
• Exploring Quantum Materials with Resonant Inelastic X-Ray Scattering
• Multistage Electronic Nematic Transitions in Cuprate Superconductors: Functional-Renormalization-Group Analysis
• Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors
• Ab Initio Study on Superconductivity and Inhomogeneity in Hg-based Cuprate Superconductor
• Commensurate-to-incommensurate transition of charge-density-wave order and a possible quantum critical point in pressurized kagome metal CsV${}_3$Sb${}_5$
• Multiple charge density waves and superconductivity nucleation at antiphase domain walls in the nematic pnictide Ba${}_{1-x}$Sr${}_x$Ni${}_2$As${}_2$
• Evolution of charge order topology across a magnetic phase transition in cuprate superconductors
• Distinct fingerprints of charge density waves and electronic standing waves in ZrTe${}_3$
• Charge-Stripe Crystal Phase in an Insulating Cuprate
• Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model
• Incommensurate charge ordered states in the $t-t^{\prime }-J$ model
• $p$-orbital density wave with $d$ symmetry in high-$T_c$ cuprate superconductors predicted by the renormalization-group + constrained RPA theory
• Persistent low-energy phonon broadening near the charge order $q$-vector in bilayer cuprate Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Evidence for strong lattice effects as revealed from huge unconventional oxygen isotope effects on the pseudogap temperature in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Nuclear Magnetic Resonance in High Magnetic Field: Application to Condensed Matter Physics
• Universality of scanning tunneling microscopy in cuprate superconductors
• Stripe correlations in the two-dimensional Hubbard-Holstein model
• Vortex phase diagram and the normal state of cuprates with charge and spin orders
• Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions
• An electronic origin of charge order in infinite-layer nickelates
• Time-resolved ARPES on cuprates: Tracking the low-energy electrodynamics in the time domain
• Signatures of a pair density wave at high magnetic fields in cuprates with charge and spin orders
• Charge-screening role of $c$-axis atomic displacements in YBa${}_2$Cu${}_3$O${}_{6+x}$ and related superconductors
• Fermi surface reconstruction by a charge-density-wave with finite correlation length
• Time-resolved resonant elastic soft X-ray scattering at Pohang Accelerator Laboratory X-ray Free Electron Laser
• Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase
• Continuous doping of a cuprate surface: new insights from in-situ ARPES
• Doping evolution of charge and spin excitations in two-leg Hubbard ladders: comparing DMRG and RPA+FLEX results
• Phonon softening and slowing down of charge-density-wave fluctuations in BaNi${}_2$As${}_2$
• Identification of a Critical Doping for Charge Order Phenomena in Bi-2212 Cuprates via RIXS
• Superconductivity-insensitive order at $q$~1/4 in electron doped cuprates
• Antiferromagnetic order in Co-doped Fe${}_5$GeTe${}_2$ probed by resonant magnetic x-ray scattering
• Ubiquitous Charge Order Correlations in High-Temperature Superconducting Cuprates
• Holographic Maps of Quasiparticle Interference
• Second order Zeeman interaction and ferroquadrupolar order in TmVO${}_4$
• Evidence for a nematic phase in La${}_{1.75}$Sr${}_{0.25}$NiO${}_4$
• Charge Condensation and Lattice Coupling Drives Stripe Formation in Nickelates
• Control of charge-spin interconversion in van der Waals heterostructures with chiral charge density waves
• Fingerprints of spin-orbital polarons and of their disorder in the photoemission spectra of doped Mott insulators with orbital degeneracy
• Hydrodynamics of plastic deformations in electronic crystals
• Doping-dependence of the electron-phonon coupling in two families of bilayer superconducting cuprates
• Untwinned YBa${}_2$Cu${}_3$O${}_{7-\delta }$ thin films on MgO substrates: a platform to study strain effects on the local orders in cuprates
• Testing for pair-density-wave order in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$
• Interplay of finite-energy and finite-momentum superconducting pairing
• Emergent Charge Order from Correlated Electron-Phonon Physics in Cuprates
• Signatures of topotactic hydrogen in nickelate superconductors
• Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain walls
• Pseudogap-induced coexistence of Fermi arcs and Fermi pockets in cuprate superconductors
• Failed excitonic quantum phase transition in Ta${}_2$Ni(Se${}_{1-x}$S${}_x$)${}_5$
• Odd-frequency pair density wave correlations in underdoped cuprates
• Doping dependence of charge order in electron-doped cuprate superconductors
• Antiferromagnetic fluctuations and a dominant $d_{xy}$-wave pairing symmetry in nickelate-based superconductors
• Doping-dependent competition between superconductivity and polycrystalline charge density waves
• Phonon spectrum of underdoped ${\text{HgBa}}_2{\text{CuO}}_{4+\delta }$ investigated by neutron scattering
• Density Waves Cause Sub-Gap Structures but no Pseudogap in Superconducting Cuprates
• Robust charge-density wave correlations in the electron-doped single-band Hubbard model
• Stripes in the extended $t-t^{\prime }$ Hubbard model: A Variational Monte Carlo analysis
• Autocorrelation of quasiparticle spectral intensities and its connection with quasiparticle scattering interference in cuprate superconductors
• Magnetic and charge orders in the ground state of the Emery model -- accurate numerical results
• Intrinsic Cluster-Shaped Density Waves in Cellular Dynamical Mean-Field Theory
• Observation of electronic bound states in charge-ordered YBa${}_2$Cu${}_3$O${}_y$
• Angle Resolved Photo-Emission Spectroscopy signature of the Resonant Excitonic State
• Charge-Density Waves vs. Superconductivity: Some Results and Future Perspectives
• Orbital Symmetry and Orbital Excitations in High-$T_c$ Superconductors
• Incommensurate two-dimensional checkerboard charge density wave in the low dimensional superconductor Ta4Pd3Te16
• Bootstrapped Dimensional Crossover of a Spin Density Wave
• Interplay between charge order and superconductivity in cuprate superconductors
• Superconductor to Mott insulator transition in YBa${}_2$Cu${}_3$O${}_7$/LaCaMnO${}_3$ heterostructures
• Peak-structure in self-energy of cuprate superconductors
• Spin and charge density waves in the quasi-one-dimensional KMn6Bi5
• Little-Parks like oscillations in lightly doped cuprate superconductors
• Anomalous spin-charge separation in a driven Hubbard system
• Emergent charge order near the doping-induced Mott-insulating quantum phase transition in Sr${}_3$Ru${}_2$O${}_7$
• Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum
• Universal relationship between the energy scales of the pseudogap phase, the superconducting state and the charge density wave order in copper oxide superconductors
• Collective mode in the SU(2) theory of cuprates
• Phase diagrams of a 2D Ising spin-pseudospin model
• Electronic character of charge order in square planar low valence nickelates
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Interplay of spin and charge order in the electron-doped cuprates
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates
• Pseudogap in electron-doped cuprates: Strong correlation leading to band splitting
• Anomalous electron spectrum and its relation to peak structure of electron scattering rate in cuprate superconductors
• Quasi-Static Internal Magnetic Field Detected in the Pseudogap Phase of Bi${}_{2+x}$Sr${}_{2-x}$CaCu${}_2$O${}_{8+\delta }$ by $\mu$SR
• Creating better superconductors by periodic nanopatterning
• Stripe Symmetry of Short-range Charge Density Waves in Cuprate Superconductors
• Topological Doping and Superconductivity in Cuprates: An Experimental Perspective
• Intertwined states at finite temperatures in the Hubbard model
• Pseudo-spin Skyrmions in the Phase Diagram of Cuprate Superconductors
• Anomalous softening of phonon-dispersion in cuprate superconductors
• Unusual Hole-doping-dependent Electronic Instability and Electron-Phonon Coupling in Infinite-layer Nickelates
• Stabilization of three-dimensional charge order through interplanar orbital hybridization in Pr${}_x$Y${}_{1-x}$Ba${}_2$Cu${}_3$O${}_{6+\delta }$
• Signature of Orbital Driven Finite Momentum Pairing in a 3D Ising Superconductor
• Two Distinct Charge Orders in Infinite-layer PrNiO2+δ revealed by Resonant X-ray Diffraction
• Scaling Behaviour of Low-Temperature Orthorhombic Domains in Prototypical High-Temperature Superconductor La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$
• Anisotropic dressing of electrons in electron-doped cuprate superconductors
• Exploration of the Hg-based cuprate superconductors by Raman spectroscopy under hydrostatic pressure
• Structure of the Charge-Density Wave in Cuprate Superconductors: Lessons from NMR
• Low-temperature T-linear resistivity in the strange metal phase of overdoped cuprate superconductors due to umklapp scattering from a spin excitation
• Superconducting correlations induced by charge ordering in cuprate superconductors and Fermi arc formation
• Light-induced coherent interlayer transport in stripe-ordered ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$
• Resonant soft x-ray scattering from stripe-ordered La${}_{2-x}$Ba${}_x$CuO${}_4$ detected by a transition edge sensor array detector
• Momentum-resolved lattice dynamics of parent and electron-doped Sr${}_2$IrO${}_4$
• Quantum oscillations suggest hidden quantum phase transition in the cuprate superconductor Pr${}_2$CuO${}_{4\pm \delta }$
• Interplay between atomic fluctuations and charge density waves in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Magnetic phase diagram of La${}_{2-x}$Sr${}_x$CoO${}_4$ revised using muon-spin relaxation
• Frustration-Induced Superconductivity in the $t$-$t^{\prime }$ Hubbard Model
• Tendencies of enhanced electronic nematicity in the Hubbard model and a comparison with Raman scattering on high-temperature superconductors
• Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate
• The High Temperature Superconductivity in Cuprates: Physics of the Pseudogap Region
• Suppression of Hall number due to charge density wave order in high-$T_c$ cuprates
• Real-space Observation of Unidirectional Charge Density Wave and Complex Structural Modulation in the Pnictide Superconductor Ba${}_{1-x}$Sr${}_x$Ni${}_2$As${}_2$
• Intertwined Orders and Electronic Structure in Superconducting Vortex Halos
• Charge and current orders in the spin-fermion model with overlapping hot spots
• A framework for the description of charge order, pseudo and superconducting gap, critical temperature and pairing interaction in cuprate superconductors
• Influence of impurities on electronic structure in cuprate superconductors
• Quantum oscillations from a pair-density wave
• $\pi$-Phase shift across stripes in a charge density wave system
• Ubiquitous suppression of the nodal coherent spectral weight in Bi-based cuprates
• Robust Charge-Density Wave Correlations in Optimally-Doped YBa2Cu3Oy
• Fluctuating charge-density-wave correlations in the three-band Hubbard model
• Observation of the Yamaji effect in a cuprate superconductor
• Correlation between charge order and second-neighbor hopping in cuprate superconductors
• Pseudogap-induced anisotropic suppression of electronic Raman response in cuprate superconductors
• Cluster structure of superconducting phase and the nature of peaks in the doping dependences of the London penetration depth in iron pnictides
• Doping-dependent phonon anomaly and charge-order phenomena in the HgBa${}_2$CuO${}_{4+\delta }$ and HgBa${}_2$CaCu${}_2$O${}_{6+\delta }$
• Post-growth annealing effects on charge and spin excitations in Nd${}_{2-x}$Ce${}_x$CuO${}_4$
• Field-induced quantum critical point in the new itinerant antiferromagnet Ti${}_3$Cu${}_4$
• A short review of the recent progresses in the study of the cuprate superconductivity
• Enhancement of superconductivity by electronic nematicity in cuprate superconductors
• ARPES autocorrelation in electron-doped cuprate superconductors
• Localized character of charge excitations for La${}_{2-x}$Sr${}_x$NiO${}_{4+\delta }$ revealed by oxygen $K$-edge resonant inelastic X-ray scattering
• Theory for Anomalous Terahertz Emission in Striped Cuprate Superconductors
• A Broken Translational Symmetry State in an Infinite-Layer Nickelate
• Evolution of magnetic stripes under uniaxial stress in La${}_{1.885}$Ba${}_{0.115}$CuO${}_4$ studied by neutron scattering
• Polarized Raman spectroscopy study of metallic $(S{r}_{1-x}L{a}_x{)}_{3}I{r}_2{O}_7$: a consistent picture of disorder-interrupted unidirectional charge order
• Low-temperature T${}^2$ resistivity in the underdoped pseudogap phase versus T-linear resistivity in the overdoped strange-metal phase of cuprate superconductors
• Hidden pair-density-wave order in cuprate superconductors
• ${}^{139}$La and ${}^{63}$Cu NMR investigation of charge order in La${}_2$CuO${}_{4+y}$ ($T_c=42$K)
• The significance of "stripes" in the physics of the cuprates, the Hubbard model, and other highly correlated electronic systems
• Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate
• Charge Transport in Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$ Single Crystals
• Programmable, Spontaneous Superlattice Memory in a Monolayer Topological Insulator
• Stability of charge-stripe ordered La2-xSrxNiO4+delta at one third doping
• Theory of high-energy correlated multiphoton x-ray diffraction for synchrotron radiation sources
• Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions
• Doping and momentum dependence of coupling strength in cuprate superconductors
• Renormalization of electrons in bilayer cuprate superconductors
• Superconductivity model for a spin-vortex checkerboard
• Charge density wave solutions of the Hubbard model in the composite operator formalism
• Characteristic energy of the nematic-order state and its connection to enhancement of superconductivity in cuprate superconductors
• Edge-induced strongly correlated electronic states in two-dimensional Hubbard model: Enhancement of magnetic correlations and self-energy effects
• Quasiparticle scattering interference in cuprate superconductors
• Introducing new resonant soft x-ray scattering capability in SSRL
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
• Optically-induced Umklapp shift currents in striped cuprates
• Bulk charge density wave and electron-phonon coupling in superconducting copper oxychlorides
• Tilted stripes origin in ${\mathrm{La}}_{1.88}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_4$ revealed by anisotropic next-nearest neighbor hopping
• Charge density waves and pinning by lattice anisotropy in 214 cuprates
• Density Matrix Embedding Theory and Strongly Correlated Lattice Systems
• Competition between the Spin and Pseudospin Subsystems in a Model Cuprate
• Antiferromagnetic order in a layered magnetic topological insulator MnBi${}_2$Se${}_4$ probed by resonant soft x-ray scattering
• Incommensurate magnetic order: A fingerprint for electronic correlations in hole-doped cuprates
• Charge-Density-Wave State in Extremely Overdoped Cuprates Driven by Phonons
• Dynamic charge order from strong correlations in the cuprates
• Phonon-assisted phase separation in strongly correlated systems
• Evolution of electron Fermi surface with doping in cobaltates
• Charge Density Waves in the 2.5-Dimensional Quantum Heterostructure
• Unusual electronic structure in underdoped cuprate superconductors
• Exploring kinetically induced bound states in triangular lattices with ultracold atoms: spectroscopic approach
• Charge modulation in the background of depleted superconductivity inside vortices
• Intrinsic Hallmarks of Phonon-Induced Charge Order in Cuprates
• Empirical case for two pseudogaps in cuprate superconductors
• Boosting superconductivity in ultrathin YBa${}_2$Cu${}_3$O${}_{7-\delta }$ films via nanofaceted substrates
• Charge order dynamics in underdoped La${}_{1.6-\text{x}}$Nd${}_{0.4}$Sr${}_{\text{x}}$CuO${}_4$ revealed by electric pulses
• Development of spin fluctuations under the presence of $d$-wave bond order in cuprate superconductors
• Atomic-Scale Visualization of the Cuprate Pair Density Wave State
• The role of the pseudogap in cuprate superconductors revealed by the Hall effect
• Raman Response of the Charge Density Wave in Cuprate Superconductors
• Incommensurate charge-stripe correlations in the kagome superconductor CsV${}_3$Sb${}_{5-x}$Sn${}_x$
• Orbital-selective time-domain signature of nematicity dynamics in the charge-density-wave phase of La${}_{1.65}$Eu${}_{0.2}$Sr${}_{0.15}$CuO${}_4$
• Generalization of interlayer tunneling models to cuprate superconductors with charge density waves
• Unified model of the Hall effect from insulator to overdoped compounds in cuprate superconductors
• Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa${}_2$CuO${}_{4+\delta }$
• Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model
• Tuning Incommensurate Charge Order in Ba${}_{1-x}$Sr${}_x$Al${}_4$ and Ba${}_{1-y}$Eu${}_y$Al${}_4$
• Impurity-Scattering Assisted Umklapp Scattering as the Origin of Low-Temperature Resistivity in the Normal-State of Cuprate Superconductors
• Search for $Q\sim 0$ order near a forbidden Bragg position in Bi${}_{2.1}$Sr${}_{1.9}$CaCu${}_2$O${}_{8+x}$ with resonant soft x-ray scattering
• Momentum-resolved two-dimensional spectroscopy as a probe of nonlinear quantum field dynamics
• Electromagnetic response of cuprate superconductors with coexisting electronic nematicity
• Vortex-driven periodic and aperiodic magnetoresistance oscillations in cuprates
• Evidence for antiferromagnetism coexisting with charge order in the trilayer cuprate HgBa${}_2$Ca${}_2$Cu${}_3$O${}_{8+\delta }$
• Why the superfluid density tracks $T_{\mathrm{c}}$ in cuprate superconductors?
• Variational Monte Carlo study of stripes as a function of doping in the $t-t^{\prime }$ Hubbard model