Robust separation of topological in-plane and out-of-plane waves in a phononic crystal

Valley degree of freedom, associated with the valley topological phase, has propelled the advancement of the elastic waveguide by offering immunity to backscattering against bending and weak perturbations. Despite many attempts to manipulate the wave path and working frequency of the waveguide, internal characteristic of an elastic wave such as rich polarization has not yet been utilized with valley topological phases. Here, we introduce the rich polarization into the valley degree of freedom, to achieve topologically protected in-plane and out-of-plane mode separation of an elastic wave. Accidental degeneracy proves its real worth of decoupling the in-plane and out-of-plane polarized valley Hall phases. We further demonstrate independent and simultaneous control of in-plane and out-of-plane waves, with intact topological protection. The presenting procedure for designing the topologically protected wave separation based on accidental degeneracy will widen the valley topological physics in view of both generation mechanism and application areas.

Acoustic Tunneling Study for Hexachiral Phononic Crystals Based on Dirac-Cone Dispersion Properties

Acoustic tunneling is an essential property for phononic crystals in a Dirac-cone state. By analyzing the linear dispersion relations for the accidental degeneracy of Bloch eigenstates, the influence of geometric parameters on opening the Dirac-cone state and the directional band gaps’ widths are investigated. For two-dimensional hexachiral phononic crystals, for example, the four-fold accidental degenerate Dirac point emerges at the center of the irreducible Brillouin zone (IBZ). The Dirac cone properties and the band structure inversion problem are discussed. Finally, to verify acoustic transmission properties near the double-Dirac-cone frequency region, the numerical calculation of the finite-width phononic crystal structure is carried out, and the acoustic transmission tunneling effect is proved. The results enrich and expand the manipulating method in the topological insulator problem for hexachiral phononic crystals.

Simultaneous Dirac-like Cones at Two Energy States in Tunable Phononic Crystals: An Analytical and Numerical Study

Simultaneous occurrence of Dirac-like cones at the center of the Brillouin zone (Г) at two different energy states is termed Dual-Dirac-like cones (DDC) in this article. The occurrence of DDC is a rare phenomenon. Thus, the generation of multiple Dirac-like cones at the center of the Brillouin zone is usually non-manipulative and poses a challenge to achieve through traditional accidental degeneracy. However, if predictively created, DDC will have multiple engineering applications with acoustics and vibration. Thus, the possibilities of creating DDC have been identified herein using a simple square periodic array of tunable square phononic crystals (PnCs) in air media. It was found that antisymmetric deaf bands may play critical roles in tracking the DDC. Hence, pivoting on the deaf bands at two different energy states, an optimized tuning parameter was found to achieve Dirac-like cones at two distinct frequency states, simultaneously. Orthogonal wave transport identified as key Dirac phenomena was achieved at two frequencies, herein. It was identified that beyond the Dirac-like cone, the Dirac phenomena remain dominant when a doubly degenerated state created by a top band with positive curvature and a near-flat deaf band are lifted from a bottom band with negative curvature. Utilizing a mechanism of rotating the PnCs near a fixed deaf band, frequencies are tracked to form the DDC, and orthogonal wave transport is demonstrated. Exploiting the dispersion behavior, unique acoustic phenomena, such as ballistic wave transmission, pseudo diffusion and acoustic cloaking are also demonstrated at the Dirac frequencies using numerical simulation. The proposed tunable acoustic PnCs will have important applications in acoustic and ultrasonic imaging, waveguiding and even acoustic computing.

Accidental Degeneracy of an Elliptic Differential Operator: A Clarification in Terms of Ladder Operators

We consider the linear, second-order elliptic, Schrödinger-type differential operator L:=−12∇2+r22. Because of its rotational invariance, that is it does not change under SO(3) transformations, the eigenvalue problem −12∇2+r22f(x,y,z)=λf(x,y,z) can be studied more conveniently in spherical polar coordinates. It is already known that the eigenfunctions of the problem depend on three parameters. The so-called accidental degeneracy of L occurs when the eigenvalues of the problem depend on one of such parameters only. We exploited ladder operators to reformulate accidental degeneracy, so as to provide a new way to describe degeneracy in elliptic PDE problems.

Chiral triclinic metamaterial crystals supporting isotropic acoustical activity and isotropic chiral phonons

Recent work predicted the existence of isotropic chiral phonon dispersion relations of the lowest bands connected to isotropic acoustical activity in cubic crystalline approximants of three-dimensional (3D) chiral icosahedral metamaterial quasi-crystals. While these architectures are fairly broadband and presumably robust against fabrication tolerances due to orientation averaging, they are extremely complex, very hard to manufacture experimentally, and they show effects which are about an order of magnitude smaller compared with those of ordinary highly anisotropic chiral cubic metamaterial crystals. Here, we propose and analyse a chiral triclinic metamaterial crystal exhibiting broadband isotropic acoustical activity. These 3D truss lattices are much less complex and exhibit substantially larger effects than the 3D quasi-crystals at the price of being somewhat more susceptible to fabrication tolerances. This susceptibility originates from the fact that we have tailored the lowest two transverse phonon bands to exhibit an ‘accidental’ degeneracy in momentum space.

Proof of the elusive high-temperature incommensurate phase in CuO by spherical neutron polarimetry

CuO is the only known binary multiferroic compound, and due to its high transition temperature into the multiferroic state, it has been extensively studied. In comparison to other prototype multiferroics, the nature and even the existence of the high-temperature incommensurate paraelectric phase (AF3) were strongly debated—both experimentally and theoretically—since it is stable for only a few tenths of a kelvin just below the Néel temperature. Until now, there is no proof by neutron diffraction techniques owing to its very small ordered Cu magnetic moment. Here, we demonstrate the potential of spherical neutron polarimetry, first, in detecting magnetic structure changes, which are not or weakly manifest in the peak intensity and, second, in deducing the spin arrangement of the so far hypothetic AF3 phase. Our findings suggest two coexisting spin density waves emerging from an accidental degeneracy of the respective states implying a delicate energy balance in the spin Hamiltonian.

Propagation and Scattering of Lamb Waves at Conical Points in Plates

Lamb waves exhibit conical dispersion at zero wave number when an accidental degeneracy occurs between thickness mode longitudinal and shear resonances of the same symmetry. Here we investigate the propagation of Lamb waves generated at the conical point frequency and the interaction of these waves with defects and interfaces. The group velocity and mode shapes of Lamb waves at the conical point are found, and it is shown that as the wavenumber gets close to zero, considerable group velocity is seen only for material properties supporting a degeneracy or near-degeneracy. The unusual wave propagation and mode conversion of Lamb waves generated at the conical point are elucidated through numerical simulations. Experimental measurements of near conical point Lamb wave interaction with holes in a plate demonstrate that these waves flow around defects while maintaining a constant phase of oscillation across that plate surface.

Pseudospin-1 Physics of Photonic Crystals

We review some recent progress in the exploration of pseudospin-1 physics using dielectric photonic crystals (PCs). We show some physical implications of the PCs exhibiting an accidental degeneracy induced conical dispersion at the Γ point, such as the realization of zero refractive index medium and the zero Berry phase of a loop around the nodal point. The photonic states of such PCs near the Dirac-like point can be described by an effective spin-orbit Hamiltonian of pseudospin-1. The wave propagation in the positive, negative, and zero index media can be unified within a framework of pseudospin-1 description. A scale change in PCs results in a rigid band shift of the Dirac-like cone, allowing for the manipulation of waves in pseudospin-1 systems in much the same way as applying a gate voltage in pseudospin-1/2 graphene. The transport of waves in pseudospin-1 systems exhibits many interesting phenomena, including super Klein tunneling, robust supercollimation, and unconventional Anderson localization. The transport properties of pseudospin-1 systems are distinct from their counterparts in pseudospin-1/2 systems, which will also be presented for comparison.