Using a non-Hermitian SSH chain embedded in a photonic crystal fibre, we design and simulate a topological fibre laser whose boundary mode is selectively amplified and remains robust under fabrication disorder and nonlinear saturable gain.

The breaking and enforcing of symmetries is a crucial ingredient in designing topologically robust materials. In electronic and microwave systems, magnetic fields can break time-reversal symmetry to create Chern insulators. By contrast, at optical frequencies, natural materials cannot respond to magnetic fields, which presents a challenge for the scalable exploitation of topologically enhanced devices. Here we leverage the natural geometry of fibre to build a scalable photonic Chern insulator by twisting the fibre during fabrication. The twist inside optical fibre breaks an effective time-reversal symmetry and induces a pseudo-magnetic field, which we observe via photonic Landau levels. Unavoidably, this twist introduces a competing topology-destroying effect through a parabolic profile in the effective refractive index. Using simulations to guide experimental materials design, we discover the 'Goldilocks' regime where the real-space Chern invariant survives, guaranteeing topological protection against fabrication-induced disorder of any symmetry class.

A remarkable feat of active matter physics is that systems as diverse as collections of self-propelled particles, nematics mixed with molecular motors, and interacting robots can all be described by symmetry-based continuum theories. These descriptions rely on reducing complex effects of individual motors to a few key active parameters, which increase with activity. Here we observe a striking anomaly in the continuum description of nonreciprocal active solids, a ubiquitous class of active materials. Using a combination of metamaterial experiments and coarse-graining theory we find that as microscopic activity increases, macroscale active response can vanish: more is less. In this highly active regime, nonaffine and localized modes prevail and destroy the large-scale signature of microscopic activity. These modes exist in any dilute periodic structure and emerge in random lattices below a percolation transition. Our results unveil a counterintuitive facet of active matter, offering new principles for engineering materials far from equilibrium.

Active filaments are a workhorse for propulsion and actuation across biology, soft robotics and mechanical metamaterials. However, artificial active rods suffer from limited robustness and adaptivity because they rely on external control, or are tethered to a substrate. Here we bypass these constraints by demonstrating that non-reciprocal interactions lead to large-scale unidirectional dynamics in free-standing slender structures. By coupling the bending modes of a buckled beam anti-symmetrically, we transform the multistable dynamics of elastic snap-through into persistent cycles of shape change. In contrast to the critical point underpinning beam buckling, this transition to self-snapping is mediated by a critical exceptional point, at which bending modes simultaneously become unstable and degenerate. Upon environmental perturbation, our active filaments exploit self-snapping for a range of functionality including crawling, digging and walking. Our work advances critical exceptional physics as a guiding principle for programming instabilities into functional active materials.

Fibre lasers realise a large gain medium in a compactly coiled fibre. Disorder due to fabrication can negatively impact the stability of their lasing modes, especially in multi-core fibres. Recently, topological fibres (without gain) have been experimentally demonstrated to be robust against fabrication disorder, but topological fibre lasers have not yet been designed or modelled. Here, we use a combination of mode-coupling theory and finite-element simulations to design and model a topological laser based on a non-Hermitian Su-Schrieffer-Heeger (SSH) chain embedded in a photonic crystal fibre. Our design is based on a winding-number invariant in combination with a PT-symmetric SSH bulk. We show that the topological boundary mode is selectively amplified when extra gain is added at the topological interface. Even with nonlinearity added through saturable gain, the lasing supermode retains its robustness against disorder. We present a realistic design for a topologically robust fibre laser using readily available stack-and-draw methods with doped cores. This work establishes a new approach for imbuing non-Hermitian photonic systems with topological protection, with technological implications towards generating robust quantum and classical signals.

A floating Leidenfrost droplet exhibits curvature inversion of its underside, due to the balance of vapor pressure and surface tension. Using interferometric imaging, we find different behavior for a levitated hydrogel sphere. Curvature inversion is observed briefly just after deposition, but quickly gives way to a steady state with no inversion. We show the essential role of vaporization in shaping the underbelly of the hydrogel, where changes due to direct mass loss are more significant than the balance of vapor pressure and elastic forces.

Active systems composed of energy-generating microscopic constituents are a promising platform to create autonomous functional materials1-16 that can, for example, locomote through complex and unpredictable environments. Yet coaxing these energy sources into useful mechanical work has proved challenging. Here we engineer active solids based on centimetre-scale building blocks that perform adaptive locomotion. These prototypes exhibit a non-variational form of elasticity characterized by odd moduli8,12,17, whose magnitude we predict from microscopics using coarse-grained theories and which we validate experimentally. When interacting with an external environment, these active solids spontaneously undergo limit cycles of shape changes, which naturally lead to locomotion such as rolling and crawling. The robustness of the locomotion is rooted in an emergent feedback loop between the active solid and the environment, which is mediated by elastic deformations and stresses. As a result, our active solids are able to accelerate, adjust their gaits and locomote through a variety of terrains with a similar performance to more complex control strategies implemented by neural networks. Our work establishes active solids as a bridge between materials and robots and suggests decentralized strategies to control the nonlinear dynamics of biological systems8,18-22, soft materials5,6,9,11,12,23-25 and driven nanomechanical devices7,26-30.

When metals are magnetized, emulsions phase separate, or galaxies cluster, domain walls and patterns form and irremediably coarsen over time. Such coarsening is universally driven by diffusive relaxation toward equilibrium. Here, we discover an inertial counterpart - wave coarsening - in active elastic media, where vibrations emerge and spontaneously grow in wavelength, period, and amplitude, before a globally synchronized state called a time crystal forms. We observe wave coarsening in one- and two-dimensional solids and capture its dynamical scaling. We further arrest the process by breaking momentum conservation and reveal a far-from-equilibrium nonlinear analogue to chiral topological edge modes. Our work unveils the crucial role of symmetries in the formation of time crystals and opens avenues for the control of nonlinear vibrations in active materials.

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Active metamaterials are engineered structures that possess novel properties that can be changed after the point of manufacture. Their novel properties arise predominantly from their physical structure, as opposed to their chemical composition and can be changed through means such as direct energy addition into wave paths, or physically changing/morphing the structure in response to both a user or environmental input. Active metamaterials are currently of wide interest to the physics community and encompass a range of sub-domains in applied physics (e.g. photonic, microwave, acoustic, mechanical, etc.). They possess the potential to provide solutions that are more suitable to specific applications, or which allow novel properties to be produced which cannot be achieved with passive metamaterials, such as time-varying or gain enhancement effects. They have the potential to help solve some of the important current and future problems faced by the advancement of modern society, such as achieving net-zero, sustainability, healthcare and equality goals. Despite their huge potential, the added complexity of their design and operation, compared to passive metamaterials creates challenges to the advancement of the field, particularly beyond theoretical and lab-based experiments. This roadmap brings together experts in all types of active metamaterials and across a wide range of areas of applied physics. The objective is to provide an overview of the current state of the art and the associated current/future challenges, with the hope that the required advances identified create a roadmap for the future advancement and application of this field.

In floppy mechanical lattices, robust edge states and bulk Weyl modes are manifestations of underlying topological invariants. To explore the universality of these phenomena independent of microscopic detail, we formulate topological mechanics in the continuum. By augmenting standard linear elasticity with additional fields of soft modes, we define a continuum version of Maxwell counting, which balances degrees of freedom and mechanical constraints. With one additional field, these augmented elasticity theories can break spatial inversion symmetry and topological edge states. We also show that two additional fields are necessary to harbour Weyl points in two dimensions, and define continuum invariants to classify these states. In addition to constructing the general form of topological elasticity based on symmetries, we derive the coefficients based on the systematic homogenization of microscopic lattices. By solving the resulting partial differential equations, we efficiently predict coarse-grained deformations due to topological floppy modes without the need for a detailed lattice-based simulation. Our discovery formulates novel design principles and efficient computational tools for topological states of matter, and points to their experimental implementation in mechanical metamaterials.

Topological design enables robustness to be engineered into a system. However, a general challenge remains to experimentally characterize topological properties. In this work, we demonstrate a technique for directly observing a winding-number invariant using a single measurement. By propagating light with a sufficiently broad spectrum along a topological photonic crystal fiber, we calculate the winding number invariant from the output intensity pattern. We quantify the capabilities of this single-shot method, which works even for surprisingly narrow and asymmetric spectral distributions. We demonstrate our approach using topological fiber, but our method is generalizable to other platforms. Our method is experimentally straightforward: we use only a broadband input excitation and a single output to measure the topological invariant.

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. With many fundamental properties of motile active matter now reasonably well understood and under control, the ground is prepared for the study of physical aspects and mechanisms of motion in complex environments, of the behavior of systems with new physical features like chirality, of the development of novel micromachines and microbots, of the emergent collective behavior and swarming of intelligent self-propelled particles, and of particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics.

The breaking and enforcing of symmetries is a crucial ingredient in designing topologically robust materials. While magnetic fields can break time-reversal symmetry to create Chern insulators in electronic and microwave systems, at optical frequencies natural materials cannot respond to magnetic fields, which presents a challenge for the scalable exploitation of topologically enhanced devices. Here, we leverage the natural geometry of fibre to build a scalable photonic Chern insulator by twisting the fibre during fabrication. The twist inside optical fibre breaks an effective time-reversal symmetry and induces a pseudo-magnetic field, which we observe via photonic Landau levels. Unavoidably, this twist introduces a competing topology-destroying effect through a parabolic profile in the effective refractive index. Using simulations to guide experimental materials design, we discover the Goldilocks regime where the real-space Chern invariant survives, guaranteeing topological protection against fabrication-induced disorder of any symmetry class.

Active metamaterials are engineered structures that possess novel properties that can be changed after the point of manufacture. Their novel properties arise predominantly from their physical structure, as opposed to their chemical composition and can be changed through means such as direct energy addition into wave paths, or physically changing/morphing the structure in response to both a user or environmental input. Active metamaterials are currently of wide interest to the physics community and encompass a range of sub-domains in applied physics (e.g. photonic, microwave, acoustic, mechanical, etc.). They possess the potential to provide solutions that are more suitable to specific applications, or which allow novel properties to be produced which cannot be achieved with passive metamaterials, such as time-varying or gain enhancement effects. They have the potential to help solve some of the important current and future problems faced by the advancement of modern society, such as achieving net-zero, sustainability, healthcare and equality goals. Despite their huge potential, the added complexity of their design and operation, compared to passive metamaterials creates challenges to the advancement of the field, particularly beyond theoretical and lab-based experiments. This roadmap brings together experts in all types of active metamaterials and across a wide range of areas of applied physics. The objective is to provide an overview of the current state of the art and the associated current/future challenges, with the hope that the required advances identified create a roadmap for the future advancement and application of this field.

We report that equidistant 1D arrays of thin-film lithium niobate nano-waveguides generically support topological edge states. Unlike conventional coupled-waveguide topological systems, the topological properties of these arrays are dictated by the interplay between intra- and inter-modal couplings of two families of guided modes with different parities. Exploiting two modes within the same waveguide to design a topological invariant allows us to decrease the system size by a factor of two and substantially simplify the structure. We present two example geometries where topological edge states of different types (based on either quasi-TE or quasi-TM modes) can be observed within a wide range of wavelengths and array spacings.

Topological design enables physicists to engineer robustness into a system. When connected to a topological invariant, the propagation of light remains unchanged in the presence of disorder. However, a general challenge remains to directly characterise the topological properties of systems by experiment. In this work, we demonstrate a novel technique for directly observing a photonic winding number using a single measurement. By propagating light with a sufficiently broad spectrum along a topological photonic crystal fibre, we calculate the winding number invariant from the output intensity pattern. We quantify the limitations of this single-shot method, which works even for surprisingly narrow and asymmetric spectral distributions. Furthermore, we dynamically evaluate the effectiveness of our method by uncovering the loss of the bulk invariant as we twist the fibre. The characterisation method that we present is highly accessible and transferable across topological photonic platforms.

We explore methods for designing and analytically characterising supermodes in twisted topological photonic crystal fibre (topoPCF). We show that geometrical twist induces a pseudo-vector potential, leading to topological chiral edge states.

The breaking of detailed balance in fluids through Coriolis forces or odd-viscous stresses has profound effects on the dynamics of surface waves. Here we explore both weakly and strongly non-linear waves in a three-dimensional fluid with vertical odd viscosity. Our model describes the free surface of a shallow fluid composed of nearly vertical vortex filaments, which all stand perpendicular to the surface. We find that the odd viscosity in this configuration induces previously unexplored non-linear effects in shallow-water waves, arising from both stresses on the surface and stress gradients in the bulk. By assuming weak nonlinearity, we find reduced equations including Korteweg-de Vries (KdV), Ostrovsky, and Kadomtsev-Petviashvilli (KP) equations with modified coefficients. At sufficiently large odd viscosity, the dispersion changes sign, allowing for compact two-dimensional solitary waves. We show that odd viscosity and surface tension have the same effect on the free surface, but distinct signatures in the fluid flow. Our results describe the collective dynamics of many-vortex systems, which can also occur in oceanic and atmospheric geophysics.

Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modeled using Cosserat (also called micropolar) elasticity. In this paper, we explore Cosserat materials that include chiral active components and hence odd elasticity. We calculate static elastic properties and show that the static response to rotational stresses leads to strains that depend on both Cosserat and odd elasticity. We compute the dispersion relations in odd Cosserat materials in the overdamped regime and find the presence of exceptional points. These exceptional points create a sharp boundary between a Cosserat-dominated regime of complete wave attenuation and an odd-elasticity-dominated regime of propagating waves. We conclude by showing the effect of Cosserat and odd-elasticity terms on the polarization of Rayleigh surface waves.