Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised ...the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.
Abstract
Crystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the ...underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.
Topological refractions created by valley sonic crystals (VSCs) have attracted great attentions in the communities of physics and engineering owing to the advantage of zero reflection of sound and ...the potential for designing advanced acoustic devices. In previous works, topological refractions of valley edge states are demonstrated to be determined by the projections of the valleys K and K′, and two types of topological refractions generally exist at opposite terminals or different frequency bands. However, the realization of tunable topological refractions at the fixed frequency band and terminal still poses great challenge. To overcome this, we report the realization of tunable topological refractions by VSCs with triple valley Hall phase transitions. By simply rotating rods, we realize 3 types of topological waveguides (T1, T2 and T3) composed of two VSCs, in which the projections of the observed valley edge states can be modulated between K and K′. Additionally, based on the measured transmittance spectra, we experimentally demonstrate that these valleyedge states are almost immune to backscattering against sharp bends. More importantly, we realize tunable topological refractions at the fixed frequency band and terminal, and experimentally observe the coexistence of positive and negative refractions for T1 and T3, and negative refractions for T2. The proposed tunable topological refractions have potential applications in designing multi-functional sound antennas and advanced communication devices.
The charge asymmetry (Ach) dependence of anisotropic flow serves as an important tool to search for the chiral magnetic wave (CMW) in heavy-ion collisions. However, the background effect, such as the ...local charge conservation (LCC) entwined with collective flow, has not yet been unambiguously eliminated in the measurement. With the help of two models, the AMPT with initial quadrupole moment and the blast wave (BW) incorporating LCC, we discuss the features of the LCC-induced and the CMW-induced correlations between Ach and the flow. More importantly, we first propose to use the Event Shape Engineering (ESE) technique to distinguish the background and the signal for the CMW study. This method would be highly desirable in the experimental search for the CMW and provides more insights for understanding the charge-dependent collective motion of the quark-gluon plasma.
Exceptional point (EP) and exceptional ring (ER) are unique features for non-Hermitian systems, which have recently attracted great attentions in acoustics due to their rich physical significances ...and various potential applications. Despite the rapid development about the study of the EP and ER in one-dimensional acoustic systems, the realization of them in two-dimensional (2D) non-Hermitian structures is still facing a great challenge. To overcome this, we numerically and theoretically realize an ER in 2D reciprocal space based on a square-lattice non-Hermitian sonic crystal (SC). By introducing radiation loss caused by circular holes of each resonator in a Hermitian SC, we realize the conversion between a Dirac cone and the ER. Based on the theoretical analysis with the effective Hamiltonian, we obtain that the formation of the ER is closely related to different radiation losses of dipole and quadrupole modes in the resonators. Additionally, in the non-Hermitian SC, two eigenfunctions can be merged into a single self-orthogonal one on the ER, which does not exist in the Hermitian SC. Finally, by verifying the existence of the EP with topological characteristics in every direction of 2D reciprocal space, we further demonstrate the ER in the proposed non-Hermitian SC. Our work may provide theoretical schemes and concrete methods for designing various types of non-Hermitian acoustic devices.
Ce0.8Sm0.1Nd0.1O2-δ (SNDC) is one of the most promising electrolyte materials for intermediate-temperature solid oxide fuel cells (IT-SOFCs). However, the adverse effect on the preparation of the ...electrolyte due to the high sintering temperature of SNDC limits the application of SNDC as an electrolyte material in IT-SOFCs. In this work, x mol % (x = 0, 0.5, 1.0, 1.5, 2.0, 2.5) Fe-doped SNDC (xFe-SNDC) powders were firstly fabricated by sol-gel synthesis, and then the corresponding bulks were prepared by cold-pressing and sintering at 1200∼1400 °C. The effects of Fe-doping on the sintering capability and electrical conductivity of SNDC were investigated. The results showed that Fe-doping leads to significant improvements in both the relative density and the electrical conductivity of SNDC. Doping Fe reduced the sintering temperature of SNDC from 1400 °C to 1200 °C and the relative density of 0.5Fe-SNDC sintered at 1200 °C reached 95.85%. Moreover, 0.5Fe-SNDC possessed the maximum conductivity of 0.0674 S cm−1 at 750 °C, which was attributed to the highest density and the highest conductivity of grain plus grain boundary.
•Fe2O3-doped Ce0.8Sm0.1Nd0.1O2-δ materials were synthesized by sol-gel and calcination.•The dopant content affects the structure and ionic conductivity of sintered bulks.•Doping Fe reduced the sintering temperature of SNDC from 1400 °C to 1200 °C.•0.5mol% Fe-doped Ce0.8Sm0.1Nd0.1O2-δ bulk exhibits the maximum ionic conductivity.
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to ...fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.
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