Deterministic Scheme for Two-Dimensional Type-II Dirac Points and Experimental Realization in Acoustics

Band sorting based on global continuity of eigenvalues and topological properties of phononic crystals

Band sorting is critical to obtaining physical properties from eigenvalues and eigenvectors that constitute the band diagram. We propose a band sorting method based on the global continuity and smoothness of the eigenvalues on the parameter space. Several strategies based on the connection between neighbor eigenvalues and how to sweep the parameter space are introduced to recognize level crossing degeneracies and level repulsion degeneracies. Eigenvectors are then reassigned to each band according to their corresponding eigenvalues. As an example, the band diagram of a 2D phononic crystal is sorted, and the group velocity and Berry curvature are compared before and after band sorting. The Berry curvature shows unexpected eigenvector discontinuities, indicating that our method based on the eigenvalues only is more reliable than methods based on the eigenvectors. Our proposed method is general and allows for studying the transport and topological properties of periodic materials.

P T-symmetric photonic lattices with type-II Dirac cones

The type-II Dirac cone is a special feature of the band structure, whose Fermi level is represented by a pair of crossing lines. It has been demonstrated that such a structure is useful for investigating topological edge solitons and, more specifically, for mimicking the Klein tunneling. However, it is still not clear what the interplay between type-II Dirac cones and the non-Hermiticity mechanism will result in. Here, this question is addressed; in particular, we report the P T-symmetric photonic lattices with type-II Dirac cones for the first time to our knowledge. We identify a slope-exceptional ring and name it the type-II exceptional ring. We display the restoration of the P T symmetry of the lattice by reducing the separation between the sites in the unit cell. Curiously, the amplitude of the beam during propagation in the non-Hermitian lattice with P T symmetry only decays because of diffraction, whereas in the P T symmetry-broken lattice it will be amplified, even though the beam still diffracts. This work establishes the link between the non-Hermiticity mechanism and the violation of Lorentz invariance in these physical systems.

Topological phononics arising from fluid-solid interactions

Nontrivial band topologies have been discovered in classical systems and hold great potential for device applications. Unlike photons, sound has fundamentally different dynamics and symmetries in fluids and solids, represented as scalar and vector fields, respectively. So far, searches for topological phononic materials have only concerned sound in either fluids or solids alone, overlooking their intricate interactions in “mixtures”. Here, we report an approach for topological phononics employing such unique interplay, and demonstrate the realization of type-II nodal rings, elusive in phononics, in a simple three-dimensional phononic crystal. Type-II nodal rings, as line degeneracies in momentum space with exotic properties from strong tilting, are directly observed through ultrasonic near-field scanning. Strongly tilted drumhead surface states, the hallmark phenomena, are also experimentally demonstrated. This phononic approach opens a door to explore topological physics in classical systems, which is easy to implement that can be used for designing high-performance acoustic devices.

Fluid-solid interaction, long investigated, is mostly neglected in topological acoustics. Here the authors find that it can give rise to intriguing topological phenomena in simple phononic crystals due to intrinsic differences between sound in fluid and solid.

Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.