Explore the vast range of titles available.

A different type of defect, the coherency disclination, is added to disclination types. Disconnections that include disclination content are considered. A criterion is suggested to distinguish disconnections with dislocation content from those with disclination content. Electron microscopy reveals unit disconnections in a low albite grain boundary, defects important in grain boundary sliding. Disconnections of varying step heights are displayed and shown to define both deformed and recovered structures.

Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms.

Most natural and artificial materials have crystalline structures from which abundant topological phases emerge 1 – 6 . However, the bulk–edge correspondence—which has been widely used in experiments to determine the band topology from edge properties—is inadequate in discerning various topological crystalline phases 7 – 16 , leading to challenges in the experimental classification of the large family of topological crystalline materials 4 – 6 . It has been theoretically predicted that disclinations—ubiquitous crystallographic defects—can provide an effective probe of crystalline topology beyond edges 17 – 19 , but this has not yet been confirmed in experiments. Here we report an experimental demonstration of bulk–disclination correspondence, which manifests as fractional spectral charge and robust bound states at the disclinations. The fractional disclination charge originates from the symmetry-protected bulk charge patterns—a fundamental property of many topological crystalline insulators (TCIs). Furthermore, the robust bound states at disclinations emerge as a secondary, but directly observable, property of TCIs. Using reconfigurable photonic crystals as photonic TCIs with higher-order topology, we observe these hallmark features via pump–probe and near-field detection measurements. It is shown that both the fractional charge and the localized states emerge at the disclination in the TCI phase but vanish in the trivial phase. This experimental demonstration of bulk–disclination correspondence reveals a fundamental phenomenon and a paradigm for exploring topological materials. It is experimentally shown that topological states exist at crystallographic defects in the bulk and that disclination defects trap fractional charges characteristic of topological crystalline insulators.

The constitutive equation for a nonlocal stress tensor is represented as an integral with the suitable kernel function. In this paper, the nonlocality kernel is chosen as the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter. The solutions of nonlocal elasticity problems for the straight wedge and twist disclinations in an infinite medium are obtained in the framework of this new nonlocal theory of elasticity. The Laplace integral transform with respect to the nonlocality parameter is used. It is necessary to emphasize that the transition from the nonlocal to local stress tensor is described by the limiting value of the nonlocality parameter τ→0. The obtained stress fields do not contain nonphysical singularities at the disclination lines.

Spindle-shaped cells readily form nematic structures marked by topological defects. When confined, the defect distribution is independent of the domain size, activity and type of cell, lending a stability not found in non-cellular active nematics. Most spindle-shaped cells (including smooth muscles and sarcomas) organize in vivo into well-aligned ‘nematic’ domains 1 , 2 , 3 , creating intrinsic topological defects that may be used to probe the behaviour of these active nematic systems. Active non-cellular nematics have been shown to be dominated by activity, yielding complex chaotic flows 4 , 5 . However, the regime in which live spindle-shaped cells operate, and the importance of cell–substrate friction in particular, remains largely unexplored. Using in vitro experiments, we show that these active cellular nematics operate in a regime in which activity is effectively damped by friction, and that the interaction between defects is controlled by the system’s elastic nematic energy. Due to the activity of the cells, these defects behave as self-propelled particles and pairwise annihilate until all displacements freeze as cell crowding increases 6 , 7 . When confined in mesoscopic circular domains, the system evolves towards two identical +1/2 disclinations facing each other. The most likely reduced positions of these defects are independent of the size of the disk, the cells’ activity or even the cell type, but are well described by equilibrium liquid crystal theory. These cell-based systems thus operate in a regime more stable than other active nematics, which may be necessary for their biological function.

The plastic deformation of crystalline materials can be understood by considering their structural defects such as disclinations and dislocations. Although also glasses are solids, their structure resembles closely the one of a liquid and hence the concept of structural defects becomes ill-defined. As a consequence it is very challenging to rationalize on a microscopic level the mechanical properties of glasses close to the yielding point and to relate plastic events to structural properties. Here we investigate the topological characteristics of the eigenvector field of the vibrational excitations of a two-dimensional glass model, notably the geometric arrangement of the topological defects as a function of vibrational frequency. We find that if the system is subjected to a quasistatic shear, the location of the resulting plastic events correlate strongly with the topological defects that have a negative charge. Our results provide thus a direct link between the structure of glasses prior their deformation and the plastic events during deformation. It remains challenging to understand the relation between mechanical properties of glasses close to the yielding point and plastic behaviors at microscales. Wu et al. examine the plasticity using topological properties of the vibrational modes and identify a correlation between defects and plastic events.

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here, we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatiotemporal defect chaos characterizing active turbulence, even close to the defect-unbinding transition. At high activity, nonequilibrium torques combined with many-body screening cause the active disclinations to spontaneously break rotational symmetry, forming a collectively moving defect-ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like “electric fields,” driving the sorting of topological charge. This result demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.

We study a two-dimensional tight-binding model of a topological crystalline insulator (TCI) protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g.,p±orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless, the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. In addition, we show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed upon the addition of appropriate atomic orbitals, which implies “fragile” topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients. Following the analysis of the model, which serves as a prototypical example of 2D TCIs protected by rotation, we show that all TCIs protected by point group symmetries which do not have protected surface states are either atomic insulators or fragile phases. Remarkably, this implies that gapless surface states exist in free-electron systems if and only if there is a stable Wannier obstruction. We then use dimensional reduction to map the problem of classifying 2D TCIs protected by rotation to a zero-dimensional problem which is then used to obtain the complete noninteracting classification of such TCIs as well as the reduction of this classification in the presence of interactions.

Although elastic strains, particularly inhomogeneous strains, are able to tune, enhance or create novel properties of some nanoscale functional materials, potential devices dominated by inhomogeneous strains have not been achieved so far. Here we report a fabrication of inhomogeneous strains with a linear gradient as giant as 10 6 per metre, featuring an extremely lower elastic energy cost compared with a uniformly strained state. The present strain gradient, resulting from the disclinations in the BiFeO 3 nanostructures array grown on LaAlO 3 substrates via a high deposition flux, induces a polarization of several microcoulomb per square centimetre. It leads to a large built-in electric field of several megavoltage per metre, and gives rise to a large enhancement of solar absorption. Our results indicate that it is possible to build up large-scale strain-dominated nanostructures with exotic properties, which in turn could be useful in the development of novel devices for electromechanical and photoelectric applications. Inherent elastic strains are useful to tune the physical properties of functional materials but it is difficult to build. Here, Tang et al . report a fabrication of inhomogeneous strains with a linear gradient as giant as 10 6 per meter in a BiFeO 3 nanostructure array grown on a LaAlO 3 substrate.

While small single-stranded viral shells encapsidate their genome spontaneously, many large viruses, such as the herpes simplex virus or infectious bursal disease virus (IBDV), typically require a template, consisting of either scaffolding proteins or an inner core. Despite the proliferation of large viruses in nature, the mechanisms by which hundreds or thousands of proteins assemble to form structures with icosahedral order (IO) is completely unknown. Using continuum elasticity theory, we study the growth of large viral shells (capsids) and show that a nonspecific template not only selects the radius of the capsid, but also leads to the error-free assembly of protein subunits into capsids with universal IO. We prove that as a spherical cap grows, there is a deep potential well at the locations of disclinations that later in the assembly process will become the vertices of an icosahedron. Furthermore, we introduce a minimal model and simulate the assembly of a viral shell around a template under nonequilibrium conditions and find a perfect match between the results of continuum elasticity theory and the numerical simulations. Besides explaining available experimental results, we provide a number of predictions. Implications for other problems in spherical crystals are also discussed.