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  1. Abstract

    Re-configurable materials and meta-materials can jump between space symmetry classes during their deformations. Here, we introduce the concept of singular symmetry enhancement, which refers to an abrupt jump to a higher symmetry class accompanied by an un-avoidable reduction in the number of dispersion bands of the excitations of the material. Such phenomenon prompts closings of some of the spectral resonant gaps along singular manifolds in a parameter space. In this work, we demonstrate that these singular manifolds can carry topological charges. As a concrete example, we show that a deformation of an acoustic crystal that encircles aconfiguration of an array of cavity resonators results in an adiabatic cycle that carries a Chern number in the bulk and displays Thouless pumping at the edges. This points to a very general guiding principle for recognizing cyclic adiabatic processes with high potential for topological pumping in complex materials and meta-materials, which rests entirely on symmetry arguments.

     
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    Free, publicly-accessible full text available April 1, 2025
  2. The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological spectral gaps in spin systems based on the methods of noncommutativeK-theory. By realizing that the structure of the observable algebra of spin textures is determined by the algebraic properties of the noncommutative torus, we arrive at a unified understanding of topological electronic states which we predict to arise in various noncollinear setups. The power of our approach lies in an ability to categorize emergent topological states algebraically without referring to smooth real- or reciprocal-space quantities. This opens a way towards an educated design of topological phases in aperiodic, disordered, or nonsmooth textures of spins and charges containing topological defects.

    <supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevResearch.6.013102" target="_blank" title="Link to document DOI" data-ostiid="10555583"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10416317-revealing-topology-metals-using-experimental-protocols-inspired-theory" itemprop="url"> <span class='span-link' itemprop="name">Revealing topology in metals using experimental protocols inspired by K-theory</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1038/s41467-023-38862-2" target="_blank" title="Link to document DOI">https://doi.org/10.1038/s41467-023-38862-2  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Cheng, Wenting</span> <span class="sep">; </span><span class="author" itemprop="author">Cerjan, Alexander</span> <span class="sep">; </span><span class="author" itemprop="author">Chen, Ssu-Ying</span> <span class="sep">; </span><span class="author" itemprop="author">Prodan, Emil</span> <span class="sep">; </span><span class="author" itemprop="author">Loring, Terry A.</span> <span class="sep">; </span><span class="author" itemprop="author">Prodan, Camelia</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2023-05-27">May 2023</time> , Nature Communications) </span> </div> <div style="cursor: pointer;-webkit-line-clamp: 5;" class="abstract" itemprop="description"> <title>Abstract

    Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field ofC-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator—mathematically derived from theK-theory of the problem—as a new Hamiltonian whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behaviour across a wide array of artificial and natural materials that lack bulk band gaps.

     
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  3. Abstract

    Twisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twistedn-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

     
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  4. Free, publicly-accessible full text available January 1, 2026
  5. Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations of the internal structures of the seed resonators, the dynamical matrices of the materials generate the full self-adjoint sector of the stabilized group C*-algebra of the frieze group. As a consequence, in applications where the positions, orientations and internal structures of the seed resonators are adiabatically modified, the spectral bands of the dynamical matrices carry a complete set of topological invariants that are fully accounted by the K-theory of the mentioned algebra. By resolving the generators of the K-theory, we produce the model dynamical matrices that carry the elementary topological charges, which we implement with systems of plate resonators to showcase several applications in spectral engineering. The paper is written in an expository style.

     
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    Free, publicly-accessible full text available June 1, 2025
  6. Free, publicly-accessible full text available April 1, 2025
  7. We consider synthetic materials consisting of self-coupled identical resonators carrying classical internal degrees of freedom. The architecture of such material is specified by the positions and orientations of the resonators. Our goal is to calculate the smallest C*-algebra that covers the dynamical matrices associated to a fixed architecture and adjustable internal structures. We give the answer in terms of a groupoid C*-algebra that can be canonically associated to a uniformly discrete subset of the group of isometries of the Euclidean space. Our result implies that the isomorphism classes of these C*-algebras split these architected materials into classes containing materials that are identical from the dynamical point of view. 
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