Photonic crystals (PhCs) have been demonstrated as a versatile platform for the study of topological phenomena. The recent discovery of higher-order topological insulators introduces new aspects of topological PhCs that are yet to be explored. Here, we propose an all-dielectric PhC with an unconventional higher-order band topology. Besides the conventional spectral features of gapped edge states and in-gap corner states, topological band theory predicts that the corner boundary of the higher-order topological insulator hosts a 2/3 fractional charge. We demonstrate that in the PhC such a fractional charge can be verified from the local density-of-states of photons, through the concept of local spectral charge as an analog of the local electric charge due to the band filling anomaly in electronic systems. Furthermore, we show that by introducing a disclination in the proposed PhC, localized states and a 2/3 fractional spectral charge emerge around the disclination core. The emergence of the fractional spectral charges and topological boundary modes here, however, is distinct from the known cases; particularly by the 2/3 fractional spectral charges and the unique topological indices. The predicted effects can be readily observed in the state-of-the-art experiments and may lead to potential applications in integrated and quantum photonics.
Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.
Gauge fields are at the heart of the fundamental science of our universe and various materials. For instance, Laughlin's gedanken experiment of gauge flux insertion played a major role in understanding the quantum Hall effects. Gauge flux insertion into a single unit-cell, though crucial for detecting exotic quantum phases and for the ultimate control of quantum dynamics and classical waves, however, has not yet been achieved in laboratory. Here, we report on the experimental realization of gauge flux insertion into a single plaquette in a lattice system with the gauge phase ranging from 0 to 2pi which is realized through a novel approach based on three consecutive procedures: the dimension extension, creating an engineered dislocation and the dimensional reduction. Furthermore, we discover that the single-plaquette gauge flux insertion leads to a new phenomenon termed as the topological Wannier cycles, i.e., the cyclic spectral flows across multiple band gaps which are manifested as the topological boundary states (TBSs) on the plaquette. Such topological Wannier cycles emerge only if the Wannier centers are enclosed by the flux-carrying plaquette. Exploiting acoustic metamaterials and versatile pump-probe measurements, we observe the topological Wannier cycles by detecting the TBSs in various ways and confirm the single-plaquette gauge flux insertion by measuring the gauge phase accumulation on the plaquette. Our work unveils an unprecedented regime for lattice gauge systems and a fundamental topological response which could empower future studies on artificial gauge fields and topological materials.
The fiber geometry of communication fibers and medical fibers are always standards to evaluate the quality of optical fibers. The measurement of fiber geometry with gray scale method is one of the commonly used measurement methods. It is also the proposed method in the national standard GB15972.20-2008. In this method, the fiber geometry is obtained by fitting the elliptical curve and fitting the circular curve in two steps, but the center of the two curves may not be coincided. Thus, there is a defect in the measurement principle in the method. The measurement of fiber geometry with gray scale method has a high requirement for cutting effects and lighting conditions. When measurement conditions change, it often leads to the instability of the measured data and brings errors. In this paper, we use the arbitrary elliptical function (non-standard ellipse) which is more suitable for the fiber end face, and only use this function fitting method to get the fiber geometry to fundamentally eliminate the principle defect caused by the inconsistent center fitting between the circle fitting and the ellipse fitting. At the same time, the requirement of measurement condition is reduced, because the specific value of image distribution grayscale is not needed when calculating each parameter. Experiments show that this method can effectively improve the stability and consistency of measurement results.
Entanglement entropy is a fundamental concept with rising importance in different fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems' complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. Furthermore, the entanglement spectrum provides salient characterizations of topological phases and phase transitions beyond the conventional paradigms. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. From the pump-probe responses in phononic crystals, we obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law of entanglement entropy for various quasiparticle dispersions in one- and two-dimensions. Moreover, we observe the salient signatures of topological phases in the entanglement spectrum and entanglement entropy which unveil an unprecedented probe of topological phases without relying on the bulk-boundary correspondence. The progress here opens a frontier where entanglement entropy serves as an important experimental tool in the study of emergent phases and phase transitions which can be generalized to non-Hermitian and other unconventional regimes.
Objective To analyze the effect of dominant accessory atrioventricular pathways (AP) on the end vector of ventricular depolarization. Methods All patients had single AP confirmed by radiofrequency cathteter abalation (RFCA) and were free from organic heart disease (including 102 cases of dominant accessory AP and 38 cases of concealed AP). The AP was divided into posterior septal(P3) ,mediate septal (MS) ,anterior septal (AS), left posterior free wall (LP), left anterior free wall (LA), right posterior free wall (RP) and right anterior free wall (RA). Results The end 40 ms vector of QRS wave changed in 102 patients with manifested AP and in 4 patients with concealed AP (P < 0. 05). Conclusion The end 40 ms vector of QRS wave of any site manifested AP can change and the changes have the specihty of leads.
Key words:
Dominant accessory atrioventricular pathways; End vector; Radiofrequency cathteter ahalation
Metathetic degradation and functionalization of styrene-butadiene rubber (SBR) were performed with allyl hexanoate, allyl chloroacetate, 5-hexenyl acetate and trifluoroethyl methacrylate as chain transfer agents (CTAs) using Grubbs 2SUPnd/SUP generation catalyst. It has been demonstrated that the catalyst concentration, CTA concentration and reaction time were major factors influencing the molecular weights and polydispersity indices of targeted telechelic SBR oligomers. Well-defined oligomers with molecular weights ranging from 700 to 36600 g molSUP-1/SUP and polydispersity indices ranging from 1.17 to 4.79 were realized. The structures of the SBR oligomers were determined by FTIR and SUP1/SUPH NMR analyses, which indicated that the functional groups of the CTAs were successfully attached onto the end of the polymer chains. To further investigate the performance of SBR oligomers, differential scanning calorimetry (DSC) analysis was performed, which indicated that the glass transition temperature (TSUBg/SUB) of the metathesis products decreased with longer reaction time.
Metathetic degradation of polybutadiene (PB) in presence of a ruthenium catalyst is accomplished. Well‐defined functionalized telechelic PB oligomers with a wide range of designed molecular weights ( M n ) and polydispersity indexes (PDI) are achieved via the choice of chain transfer agents (CTAs), mole ratio of PB/CTA, mole ratio of PB/catalyst and the reaction time. Experiments are performed using Grubbs second generation catalyst (G2) in 1,2‐dichloromethane at 30 °C. It has been demonstrated that the degradation performance can be controllably tuned by using selected monomers. Additionally, when mono‐olefins are introduced, the M n of metathesis products would be on order of a few hundred g mol −1 with narrow PDI (less than 1.50). The compositions and structures of the final product is determined using GC/MS analysis, which indicates that the butadiene repeating unit number of the telechelic oligomers, could be as low as two or even only one.
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