Time-periodic corner states from Floquet higher-order topology

Artificial Multi-Stimulus-Responsive E-Skin Based on an Ionic Film with a Counter-Ion Exchange Reagent

Sensing pressure and temperature are two important functions of human skin that integrate different types of tactile receptors. In this paper, a deformable artificial flexible multi-stimulus-responsive sensor is demonstrated that can distinguish mechanical pressure from temperature by measuring the impedance and the electrical phase at the same frequency without signal interference. The electrical phase, which is used for measuring the temperature, is totally independent of the pressure by controlling the surface micro-shapes and the ion content of the ionic film. By doping the counter-ion exchange reagent into the ionic liquid before pouring, the upper temperature measuring limit increases from 35 to 50 °C, which is higher than the human body temperature and the ambient temperature on Earth. The sensor shows high sensitivity to pressure (up to 0.495 kPa-1) and a wide temperature sensing range (-10 to 50 °C). A multimodal ion-electronic skin (IEM-skin) with an 8 × 8 multi-stimulus-responsive sensor array is fabricated and can successfully sense the distribution of temperature and pressure at the same time. Finally, the sensors are used for monitoring the touching motions of a robot-arm finger controlled by a remote interactive glove and successfully detect the touching states and the temperature changes of different objects.

Machine Learning Assisted Electronic/Ionic Skin Recognition of Thermal Stimuli and Mechanical Deformation for Soft Robots

Soft robots have the advantage of adaptability and flexibility in various scenarios and tasks due to their inherent flexibility and mouldability, which makes them highly promising for real-world applications. The development of electronic skin (E-skin) perception systems is crucial for the advancement of soft robots. However, achieving both exteroceptive and proprioceptive capabilities in E-skins, particularly in terms of decoupling and classifying sensing signals, remains a challenge. This study presents an E-skin with mixed electronic and ionic conductivity that can simultaneously achieve exteroceptive and proprioceptive, based on the resistance response of conductive hydrogels. It is integrated with soft robots to enable state perception, with the sensed signals further decoded using the machine learning model of decision trees and random forest algorithms. The results demonstrate that the newly developed hydrogel sensing system can accurately predict attitude changes in soft robots when subjected to varying degrees of pressing, hot pressing, bending, twisting, and stretching. These findings that multifunctional hydrogels combine with machine learning to decode signals may serve as a basis for improving the sensing capabilities of intelligent soft robots in future advancements.

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

We present a pedagogical review of the periodically driven non-Hermitian systems, particularly on the rich interplay between the non-Hermitian skin effect and the topology. We start by reviewing the non-Bloch band theory of the static non-Hermitian systems and discuss the establishment of its generalized bulk-boundary correspondence (BBC). Ultimately, we focus on the non-Bloch band theory of two typical periodically driven non-Hermitian systems: harmonically driven non-Hermitian system and periodically quenched non-Hermitian system. The non-Bloch topological invariants were defined on the generalized Brillouin zone and the real space wave functions to characterize the Floquet non-Hermtian topological phases. Then, the generalized BBC was established for the two typical periodically driven non-Hermitian systems. Additionally, we review novel phenomena in the higher-dimensional periodically driven non-Hermitian systems, including Floquet non-Hermitian higher-order topological phases and Floquet hybrid skin-topological modes. The experimental realizations and recent advances have also been surveyed. Finally, we end with a summarization and hope this pedagogical review can motivate further research on Floquet non-Hermtian topological physics.

Robust temporal adiabatic passage with perfect frequency conversion between detuned acoustic cavities

For classical waves, phase matching is vital for enabling efficient energy transfer in many scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here, we propose a temporal quasi-phase matching method and realize robust and complete acoustical energy transfer between arbitrarily detuned cavities. In a set of three cavities, A, B, and C, the time-varying coupling is established between adjacent elements. Analogy to the concept of stimulated Raman adiabatic passage, amplitudes of the two couplings are modulated as time-delayed Gaussian functions, and the couplings' signs are periodically flipped to eliminate temporal phase mismatching. As a result, robust and complete acoustic energy transfer from A to C is achieved. The non-reciprocal frequency conversion properties of our design are demonstrated. Our research takes a pivotal step towards expanding wave steering through time-dependent modulations and is promising to extend the frequency conversion based on state evolution in various linear Hermitian systems to nonlinear and non-Hermitian regimes.

Reproducible and High-Performance WOLEDs Based on Independent High-Efficiency Triplet Harvesting of Yellow Hot-Exciton ESIPT and Blue TADF Emitters

Hot exciton organic light-emitting diode (OLED) emitters can balance the high performance of a device and reduce efficiency roll-off by fast reverse intersystem crossing from high-lying triplets (hRISC). In this study, an excited-state intramolecular proton transfer (ESIPT) fluorophore of 2-(benzo[d]thiazol-2-yl)-4-(pyren-1-yl)phenol (PyHBT) with the typical characteristic properties of a hot exciton is developed. With high efficiency of utilization of the exciton (91%), its yellow OLED exhibited high external quantum efficiency (EQE) of 5.6%, current efficiency (CE) of 16.8 cd A-1 , and power efficiency (PE) of 17.3 lm W-1 . The performance of the yellow emissive "hot exciton" ESIPT fluorophores is among the highest recorded. Due to the large Stokes shift of the ESIPT emitter, non-energy-transferred high-performance white OLEDs (WOLEDs) are developed, which are reproducible and highly efficient. This is possible because of the independent harvesting of most of the triplets in both complementary-color emitters without the interference of energy transfer. The PyHBT-based WOLEDs exhibit a maximum EQE of 14.3% and CE of 41.1 cd A-1 , which facilitates the high-yield mass production of inexpensive WOLEDs.

Dynamical Detection of Topological Spectral Density

Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.

A Ti3C2Tx@PANI core-shell heterostructure assembled into a 3D porous hydrogel as a free-standing electrode for high-energy supercapacitors

Although Ti3C2Tx MXenes have attracted attention in electrochemical energy storage devices due to their excellent electronic conductivity, controllable layer structure, and huge redox active surface area, the application of Ti3C2Tx as supercapacitor (SC) electrode materials is severely limited by the ineffective chemical ion transport kinetics caused by self-restacking. In order to increase the interlayer spacing of Ti3C2Tx, the intercalation method is hailed as an effective process. Herein, polyaniline (PANI) nanorods as intercalators were synthesized by the polymerization of an aniline (ANI) monomer chemisorbed onto Ti3C2Tx wrinkled nanosheets, and the formation of a Ti3C2Tx@PANI heterostructure is conducive to the large interlayer voids. Then, the heterostructure was integrated into a three-dimensional (3D) porous cross-linked framework via a simple graphene oxide (GO)-assisted self-convergence hydrothermal strategy with low temperatures. Due to the synergistic effect among each component and 3D porous interconnected structure, the hierarchical Ti3C2Tx@PANI-reduced graphene oxide (RGO) heterostructure hydrogel possesses the advantages of excellent electrical conductivity, high specific capacitance, repressive aggregation, and large electrochemical active area. Heterostructure hydrogel electrodes (without binders) display excellent electrochemical performance with a specific capacitance as high as 301.0 F g-1 at 1 A g-1, 90.74% capacitance retention over 10 000 cycles, and a maximum energy density of 44.6 W h kg-1 at a power density of 504.7 W kg-1. Our study provides a fresh strategy for constructing a 3D Ti3C2Tx-based framework applicable to other MXenes in the design of hybrid structures for maximizing their potential applications in energy storage.

Generation of higher-order topological insulators using periodic driving

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.

Fractal photonic anomalous Floquet topological insulators to generate multiple quantum chiral edge states

Anomalous Floquet topological insulators with vanishing Chern numbers but supporting chiral edge modes are attracting more and more attention. Since the existing anomalous Floquet topological insulators usually support only one kind of chiral edge mode even at a large lattice size, they are unscalable and unapplicable for multistate topological quantum systems. Recently, fractal topological insulators with self-similarity have been explored to support more nontrivial modes. Here, we demonstrate the first experimental realization of fractal photonic anomalous Floquet topological insulators based on dual Sierpinski carpet consisting of directional couplers using the femtosecond laser direct writing. The fabricated lattices support much more kinds of chiral edge states with fewer waveguides and enable perfect hopping of quantum states with near unit transfer efficiency. Instead of zero-dimensional bound modes for quantum state transport in previous laser direct-written topological insulators, we generate multiple propagating single-photon chiral edge states in the fractal lattice and observe high-visibility quantum interferences. These suggest the successful realization of highly indistinguishable single-photon chiral edge states, which can be applied in various quantum operations. This work provides the potential for enhancing the multi-fold manipulation of quantum states, enlarging the encodable quantum information capacity in a single lattice via high-dimensional encoding and many other fractal applications.

Observation of π solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous π modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous π modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological π solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. π solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such π solitons are determined by their power.

Non-Hermitian Floquet Topological Matter-A Review

The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird's-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Observation of π/2 Modes in an Acoustic Floquet System

Topological phases of matter have remained an active area of research in the last few decades. Periodic driving is a powerful tool for enriching such exotic phases, leading to various phenomena with no static analogs. One such phenomenon is the emergence of the elusive π/2 modes, i.e., a type of topological boundary state pinned at a quarter of the driving frequency. The latter may lead to the formation of Floquet parafermions in the presence of interaction, which is known to support more computational power than Majorana particles. In this Letter, we experimentally verify the signature of π/2 modes in an acoustic waveguide array, which is designed to simulate a square-root periodically driven Su-Schrieffer-Heeger model. This is accomplished by confirming the 4T-periodicity (T being the driving period) profile of an initial-boundary excitation, which we also show theoretically to be the smoking gun evidence of π/2 modes. Our findings are expected to motivate further studies of π/2 modes in quantum systems for potential technological applications.

Generating Many Majorana Corner Modes and Multiple Phase Transitions in Floquet Second-Order Topological Superconductors

A d-dimensional, nth-order topological insulator or superconductor has localized eigenmodes at its (d−n)-dimensional boundaries (n≤d). In this work, we apply periodic driving fields to two-dimensional superconductors, and obtain a wide variety of Floquet second-order topological superconducting (SOTSC) phases with many Majorana corner modes at both zero and π quasienergies. Two distinct Floquet SOTSC phases are found to be separated by three possible kinds of transformations, i.e., a topological phase transition due to the closing/reopening of a bulk spectral gap, a topological phase transition due to the closing/reopening of an edge spectral gap, or an entirely different phase in which the bulk spectrum is gapless. Thanks to the strong interplay between driving and intrinsic energy scales of the system, all the found phases and transitions are highly controllable via tuning a single hopping parameter of the system. Our discovery not only enriches the possible forms of Floquet SOTSC phases, but also offers an efficient scheme to generate many coexisting Majorana zero and π corner modes, which may find applications in Floquet quantum computation.

Topological sound in two dimensions

Topology is the branch of mathematics studying the properties of an object that are preserved under continuous deformations. Quite remarkably, the powerful theoretical tools of topology have been applied over the past few years to study the electronic band structure of crystals. Topological band theory can explain and predict topological phase transitions in a material, and the unusual robustness of certain band structure shapes, such as Dirac cones, against small perturbations. These findings have also unveiled a new phase of matter-topological insulators-whose exotic transport properties at their boundaries are topologically protected against imperfections and disorder. The fascinating features of topological boundary states have triggered the search for their analogs in classical wave physics. Here, we focus on the peculiar features of two-dimensional topological insulators for sound and mechanical waves. Two-dimensional Dirac cones and phononic topological insulators can emerge under certain conditions in periodic acoustic metamaterials, demonstrating great potential for acoustic and mechanical systems to demonstrate, over a tabletop platform, complex fundamental phenomena driven by topological concepts. In addition, these discoveries offer a direct path toward new technologies for enhanced sound control and manipulation.

Temporal modulation brings metamaterials into new era

Temporal modulations in photonics bring many exotic optical phenomena in the time dimension while metamaterials provide powerful ways in manipulating light in the spatial domain. The authors envision the connection, Floquet Metamaterials, may deliver novel opportunities in nanophotonics.