skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on June 5, 2026

Title: Topological Matter: A Unified Perspective on Real and Momentum Space
Topology has emerged as a field for describing and controlling order and matter, and thereby the physical properties of materials. There are several largely disparate fields focused on examining and manipulating topology. One of these arenas is in the realm of real space, manipulating systems in terms of their spatial properties, to control the corresponding structural, mechanical, and self- assembling responses. Much of the work in soft matter topology falls within this domain. A second arena is in the domain of momentum or k-space wherein topology controls the features of the electronic band structure of materials, and topologically non-trivial features result in the development of materials with truly unique properties. This work focuses squarely on the realm of condensed matter physics. Here, we review concepts of real- and k-space topology and propose areas for convergence between these two disparate fields.  more » « less
Award ID(s):
2317843
PAR ID:
10626942
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ; ; ; ;
Publisher / Repository:
ACS
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. At the intersection of the outwardly disparate fields of nanoparticle science and three-dimensional printing lies the promise of revolutionary new “nanocomposite” materials. Emergent phenomena deriving from the nanoscale constituents pave the way for a new class of transformative materials with encoded functionality amplified by new couplings between electrical, optical, transport, and mechanical properties. We provide an overview of key scientific advances that empower the development of such materials: nanoparticle synthesis and assembly, multiscale assembly and patterning, and mechanical characterization to assess stability. The focus is on recent illustrations of approaches that bridge these fields, facilitate the design of ordered nanocomposites, and offer clear pathways to device integration. We conclude by highlighting the remaining scientific challenges, including the critical need for assembly-compatible particle–fluid systems that ultimately yield mechanically robust materials. The role of domain boundaries and/or defects emerges as an important open question to address, with recent advances in fabrication setting the stage for future work in this area. 
    more » « less
  2. Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the corresponding topological bands. However, among the vast number of theoretically predicted topological states, only a small fraction has been physically realized. To close this gap, we present a strategy capable of systematically and efficiently discovering metamaterials with desired topological state. Our approach builds on topological quantum chemistry, which systematically classifies topological states by analyzing symmetry properties at selected wavevectors. Because this method condenses the topological character into mathematical information at a small set of wavevectors, it encodes a clear and computationally efficient objective for topology optimization algorithms. We demonstrate that, for certain lattice symmetries, this classification can be further reduced to intuitive morphological features of the phonon band structure. By incorporating these band morphology constraints into topology optimization algorithms and further fabricating obtained designs, we enable the automated discovery and physical realization of metamaterials with targeted topological properties. This methodology establishes a paradigm for engineering topological elastic lattices on demand, addressing the bottleneck in material realization and paving the way for a comprehensive database of topological metamaterial configurations. 
    more » « less
  3. Abstract The identity of dark matter has remained surprisingly elusive. While terrestrial experiments may be able to nail down a model, an alternative method is to identify dark matter based on astrophysical or cosmological signatures. A particularly sensitive approach is based on the unique signature of dark matter substructure in galaxy–galaxy strong lensing images. Machine-learning applications have been explored for extracting this signal. Because of the limited availability of high-quality strong lensing images, these approaches have exclusively relied on simulations. Due to the differences with the real instrumental data, machine-learning models trained on simulations are expected to lose accuracy when applied to real data. Here domain adaptation can serve as a crucial bridge between simulations and real data applications. In this work, we demonstrate the power of domain adaptation techniques applied to strong gravitational lensing data with dark matter substructure. We show with simulated data sets representative of Euclid and Hubble Space Telescope observations that domain adaptation can significantly mitigate the losses in the model performance when applied to new domains. Lastly, we find similar results utilizing domain adaptation for the problem of lens finding by adapting models trained on a simulated data set to one composed of real lensed and unlensed galaxies from the Hyper Suprime-Cam. This technique can help domain experts build and apply better machine-learning models for extracting useful information from the strong gravitational lensing data expected from the upcoming surveys. 
    more » « less
  4. Abstract Antiferromagnets hosting structural or magnetic order that breaks time reversal symmetry are of increasing interest for “beyond von Neumann” computing applications because the topology of their band structure allows for intrinsic physical properties, exploitable in integrated memory and logic function. One such group are the noncollinear antiferromagnets. Essential for domain manipulation is the existence of small net moments found routinely when the material is synthesized in thin film form and attributed to symmetry breaking caused by spin canting, either from the Dzyaloshinskii–Moriya interaction or from strain. Although the spin arrangement of these materials makes them highly sensitive to strain, there is little understanding about the influence of local strain fields caused by lattice defects on global properties, such as magnetization and anomalous Hall effect. This premise is investigated by examining noncollinear antiferromagnetic films that are either highly lattice mismatched or closely matched to their substrate. In either case, edge dislocation networks are generated and for the former case, these extend throughout the entire film thickness, creating large local strain fields. These strain fields allow for finite intrinsic magnetization in seemingly structurally relaxed films and influence the antiferromagnetic domain state and the intrinsic anomalous Hall effect. 
    more » « less
  5. Complex disordered matter is of central importance to a wide range of disciplines, from bacterial colonies and embryonic tissues in biology to foams and granular media in materials science to stellar configurations in astrophysics. Because of the vast differences in composition and scale, comparing structural features across such disparate systems remains challenging. Here, by using the statistical properties of Delaunay tessellations, we introduce a mathematical framework for measuring topological distances between general three-dimensional point clouds. The resulting system-agnostic metric reveals subtle structural differences between bacterial biofilms as well as between zebrafish brain regions, and it recovers temporal ordering of embryonic development. We apply the metric to construct a universal topological atlas encompassing bacterial biofilms, snowflake yeast, plant shoots, zebrafish brain matter, organoids, and embryonic tissues as well as foams, colloidal packings, glassy materials, and stellar configurations. Living systems localize within a bounded island-like region of the atlas, reflecting that biological growth mechanisms result in characteristic topological properties. 
    more » « less