Emergent properties and the multiscale characterization challenge in condensed matter, from crystals to complex materials: a Review

Abstract

The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline solids-have provided deep insights into symmetry, order, and electronic structure, they fall short in describing the rich, multiscale organization of hierarchical and soft materials. These systems exhibit structural correlations across multiple length and time scales, often governed by nonlinear interactions that span from molecular to macroscopic domains. This review explores how the convergence of emerging experimental and computational strategies are redefining our ability to characterize and model such systems. We examine how multimodal techniques-combining scattering, imaging, and spectroscopy-can map structural order and dynamics across scales, with methods like small-angle scattering tensor tomography, dark-field imaging, and ultrafast spectroscopies providing unprecedented spatiotemporal resolution. On the computational front, machine learning approaches such as graph neural networks, neural operators, and physics-informed models offer powerful tools to connect disparate scales and uncover hidden correlations in high-dimensional data. These advancements have the potential to close the gap between structure and function in complex materials, thereby addressing one of the grand challenges of contemporary material science: understanding and engineering multiscale architectures, whose emergent properties underpin the behavior of next-generation functional materials, biological systems, and adaptive technologies.

References in corpus (61)

• A Comprehensive Survey on Graph Neural Networks
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• The spread of epidemic disease on networks
• Mantid - Data Analysis and Visualization Package for Neutron Scattering and $\mu SR$ Experiments
• Crackling Noise
• Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Symmetry Protected Topological phases of Quantum Matter
• musrfit: A free platform-independent framework for muSR data analysis
• Structure and dynamics of core-periphery networks
• Damage and fluctuations induce loops in optimal transport networks
• A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials
• A Dynamical Classification of the Cosmic Web
• The critical exponents of the superfluid transition in He4
• Scale-invariance of galaxy clustering
• Engineered Dissipation for Quantum Information Science
• Channel Formation and Intermediate Range Order in Sodium Silicate Melts and Glasses
• Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training
• Li diffusion in Li${}_x$CoO${}_2$ probed by muon-spin spectroscopy
• Split superconducting and time-reversal symmetry-breaking transitions, and magnetic order in Sr${}_2$RuO${}_4$ under uniaxial stress
• Competition-induced criticality in a model of meme popularity
• Dissipative Phase Transition in the Open Quantum Rabi Model
• Time- and Angle-Resolved Photoemission Studies of Quantum Materials
• Structure determination of disordered materials from diffraction data
• Intrinsic Paramagnetic Meissner Effect due to s-wave Odd-Frequency Superconductivity
• Three-Dimensional Fermi Surface of Overdoped La-Based Cuprates
• Interpretable deep learning for guided structure-property explorations in photovoltaics
• XNet: A convolutional neural network (CNN) implementation for medical X-Ray image segmentation suitable for small datasets
• Multi-scale structural complexity of natural patterns
• High-performance versatile setup for simultaneous Brillouin-Raman micro-spectroscopy
• Topological Deep Learning: A Review of an Emerging Paradigm
• Collective dynamics of active cytoskeletal networks
• X-ray photon correlation spectroscopy of protein dynamics at nearly diffraction limited storage rings
• Magnon spectrum of the helimagnetic insulator Cu2OSeO3
• Infrared and Terahertz Spectroscopy of Strongly Correlated Electron Systems under Extreme Conditions
• Small-angle scattering from multi-phase fractals
• Deconvolving Instrumental and Intrinsic Broadening in Excited State X-ray Spectroscopies
• Photoinduced time-resolved electrodynamics of superconducting metals and alloys
• Unfolding the complexity of quasi-particle physics in disordered materials
• Revealing and exploiting hierarchical material structure through complex atomic networks
• Magnetism and Ion Diffusion in Honeycomb Layered Oxide K${}_2$Ni${}_2$TeO${}_6$: First Time Study by Muon Spin Rotation & Neutron Scattering
• Scale free chaos in the confined Vicsek flocking model
• Structural diversity in electrohydrodynamically driven active and organized liquid states
• Diffusive Dynamics of Water inside Hydrophobic Carbon Micropores Studied by Neutron Spectroscopy and Molecular Dynamics Simulation
• Symmetry breaking and ascending in the magnetic kagome metal FeGe
• Self-assembly in soft matter with multiple length scales
• Robust superconductivity intertwined with charge density wave and disorder in Pd-intercalated ErTe${}_3$
• X-ray Linear Dichroic Tomography of Crystallographic and Topological Defects
• Scanning electron diffraction tomography of strain
• The Duel of Magnetic Interactions & Structural Instabilities: Itinerant Frustration in the Triangular Lattice Compound LiCrSe${}_2$
• Nuclear and magnetic spin structure of the antiferromagnetic triangular lattice compound LiCrTe${}_2$ investigated by ${\mu }^{+}$SR as well as neutron and X-ray diffraction
• Artificial Neural Networks for Predicting Mechanical Properties of Crystalline Polyamide12 via Molecular Dynamics Simulations
• Influence of the Magnetic Sub-Lattices in the Double Perovskite Compound LaCaNiReO${}_6$
• Neutron powder diffraction study of NaMn${}_2$O${}_4$ and Li${}_{0.92}$Mn${}_2$O${}_4$: New insights on spin-charge-orbital ordering
• Emergent magnetism with continuous control in the ultrahigh conductivity layered oxide PdCoO2
• Tuning of Charge Order by Uniaxial Stress in a Cuprate Superconductor
• Engineering a pure Dirac regime in ZrTe${}_5$
• Structural Evolution and Onset of the Density Wave Transition in the CDW Superconductor LaPt${}_2$Si${}_2$ Clarified with Synchrotron XRD
• Non-Conventional Critical Behavior and Q-dependent Electron-Phonon Coupling Induced Phonon Softening in the CDW Superconductor LaPt2Si2
• Revised Magnetic Structure and Tricritical Behavior of the CMR Compound NaCr${}_2$O${}_4$ Investigated with High Resolution Neutron Diffraction and ${\mu }^{+}$SR
• A two-state generalisation of the strong collision model

Cited by in corpus (1)

• Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems