Emergence of Type-II Dirac Points in Graphynelike Photonic Lattices

Manipulation of Weyl Points in Reciprocal and Nonreciprocal Mechanical Lattices

We introduce feedback-measurement technologies to achieve flexible control of Weyl points and conduct the first experimental demonstration of Weyl type I-II transition in mechanical systems. We demonstrate that non-Hermiticity can expand the Fermi arc surface states from connecting Weyl points to Weyl rings, and lead to a localization transition of edge states influenced by the interplay between band topology and the non-Hermitian skin effect. Our findings offer valuable insights into the design and manipulation of Weyl points in mechanical systems, providing a promising avenue for manipulating topological modes in non-Hermitian systems.

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.

Multiple Dirac points by high-order photonic bands in plasmonic-dielectric superlattices

The emergence of Dirac points (DPs) characterizes the topological phase transition and the gapless interface states in composite metal-dielectric metamaterials. In this work, we study a kind of compound plasmonic-dielectric periodic structure (PDPS) which sustains both plasmonic modes and multiple photonic modes. The structure has primitive cell consisting of four layers made from triple constituent components. Due to the generalized Su-Schrieffer-Heeger, DPs can emerge at the Brillouin zone center. More specifically, in weak plasmonic-photonic mode interaction regime, multiple DPs would emerge at the Brillouin zone center and edge due to the band folding, from the perspective of general effective medium. From the rigorous field analysis, the origin of these DPs is clearly demonstrated. These interleaved DPs behave as the intermediate transitions of the surface impedance for the PDPS and raise fully spanned topological interface states originated from 0 to 2nd-order photonic bands in the PDPS. The cases of combining our PDPS with either a plasmonic or dielectric homogenous medium are presented.

Moiré Fringe Induced Gauge Field in Photonics

We realize moiré fringe induced gauge field in a double-layer photonic honeycomb metacrystal with mismatched lattice constants. Benefitting from the generated strong effective gauge field, we report direct measurement of the band diagrams of both Landau level flat bands and intermagnetic-domain edge states. Importantly, we observe the correlation between the momentum and orbital position of the Landau modes, serving as an evidence of the noncommuteness between orthogonal components of the momentum. Without complicated time driving mechanics and careful site-by-site engineering, moiré superlattices could emerge as a powerful means to generate effective gauge fields for photonics benefiting from its simplicity and reconfigurability, which can be applied to nonlinearity enhancement and lasing applications at optical frequencies.

Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices

The exceptional properties exhibited by two-dimensional materials, such as graphene, are rooted in the underlying physics of the relativistic Dirac equation that describes the low energy excitations of such molecular systems. In this study, we explore a periodic lattice that provides access to the full solution spectrum of the extended Dirac Hamiltonian. Employing its photonic implementation of evanescently coupled waveguides, we indicate its ability to independently perturb the symmetries of the discrete model (breaking, also, the barrier towards the type-II phase) and arbitrarily define the location, anisotropy, and tilt of Dirac cones in the bulk. This unique aspect of topological control gives rise to highly versatile edge states, including an unusual class that emerges from the type-II degeneracies residing in the complex space of k. By probing these states, we investigate the topological nature of tilt and shed light on novel transport dynamics supported by Dirac configurations in two dimensions.

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

Low-energy electrons near Dirac/Weyl nodal points mimic massless relativistic fermions. However, as they are not constrained by Lorentz invariance, they can exhibit tipped-over type-II Dirac/Weyl cones that provide highly anisotropic physical properties and responses, creating unique possibilities. Recently, they have been observed in several quantum and classical systems. Yet, there is still no simple and deterministic strategy to realize them since their nodal points are accidental degeneracies, unlike symmetry-guaranteed type-I counterparts. Here, we propose a band-folding scheme for constructing type-II Dirac points, and we use a tight-binding analysis to unveil its generality and deterministic nature. Through realizations in acoustics, type-II Dirac points are experimentally visualized and investigated using near-field mappings. As a direct effect of tipped-over Dirac cones, strongly tilted kink states originating from their valley-Hall properties are also observed. This deterministic scheme could serve as a platform for further investigations of intriguing physics associated with various strongly Lorentz-violating nodal points.

Dynamic characterization of a periodic microstructured flexural system with rotational inertia

We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and the influence and interplay between the dynamic parameters on the structure of the pass and stop bands are analysed in detail. We highlight the existence of three special dynamic regimes corresponding to a low stiffness in the supports and/or low rotational inertia of the masses; to a high stiffness and/or high rotational inertia regime; and to a transition one where dispersion degeneracies are encountered. In the low-frequency regime, a rigorous asymptotic analysis shows that the structure approximates a continuous Rayleigh beam on an elastic foundation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

Experimental Realization of Type-II Weyl Points and Fermi Arcs in Phononic Crystal

Weyl points (WPs), as the doubly degenerate points in three-dimensional momentum band structures, carry quantized topological charges and give rise to a variety of extraordinary properties, such as robust surface wave and chiral anomaly. Type-II Weyl semimetals, which have conical dispersions in Fermi surfaces and a strongly tilted dispersion with respect to type I, have recently been proposed in condensed-matter systems and photonics. Although the type-II WPs have been theoretically predicted in acoustics, the experimental realization in phononic crystals has not been reported so far. Here, we experimentally realize a type-II Weyl phononic crystal. We demonstrate the topological transitions observed at the WP frequencies and the topological surface acoustic waves between the Weyl frequencies. The experiment results are in good accordance with our theoretical analyses. Due to the violation of the Lorentz symmetry, the type-II WPs only exist in low energy systems. As the analog counterpart in classical waves, the phononic crystal brings a platform for the research of type-II WPs in macroscopic systems.

Asymmetric conical diffraction in dislocated edge-centered square lattices

We investigate linear and nonlinear evolution dynamics of light beams propagating along a dislocated edge-centered square lattice. The band structure and Brillouin zones of this novel lattice are analyzed analytically and numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of the lattice are obtained. By adopting the tight-binding approximation, we give an explanation of the asymmetry of Dirac cones. By utilizing the appropriate Bloch modes, linear and nonlinear asymmetric conical diffraction are demonstrated. We find that both the focusing and defocusing nonlinearities can enhance the asymmetry of the conical diffractions.

3D Dirac Plasmons in the Type-II Dirac Semimetal PtTe_{2}

Transition-metal dichalcogenides showing type-II Dirac fermions are emerging as innovative materials for nanoelectronics. However, their excitation spectrum is mostly unexplored yet. By means of high-resolution electron energy loss spectroscopy and density functional theory, here, we identify the collective excitations of type-II Dirac fermions (3D Dirac plasmons) in PtTe_{2} single crystals. The observed plasmon energy in the long-wavelength limit is ∼0.5  eV, which makes PtTe_{2} suitable for near-infrared optoelectronic applications. We also demonstrate that interband transitions between the two Dirac bands in PtTe_{2} give rise to additional excitations at ∼1 and ∼1.4  eV. Our results are crucial to bringing to fruition type-II Dirac semimetals in optoelectronics.

Photonic Weyl phase transition in dynamically modulated brick-wall waveguide arrays

We investigate the topological phase transition between Type-I and Type-II Weyl points (WPs) in a composite three-dimensional lattice composed of a two-dimensional brick-wall waveguide array and a synthetic frequency dimension created by dynamic modulation. By imposing different modulation amplitudes and phases in the two sublattices, we can break either parity or time-reversal symmetry and realize the phase transition between Type-I and Type-II WPs. As the array is truncated to have two edges, two Fermi-arc surface states will emerge, which propagate in opposite directions for Type-I WPs while in same directions for Type-II WPs, accompanied by bidirectional and unidirectional frequency shifts for the optical modes. Particularly at the phase transition point, we find that one of two bands becomes flat with a vanished group velocity along frequency axis in the vicinity of WPs. The study paves a way towards realizing different topological phases in the same photonic structure, which offers new opportunities to control wave transportation both in spatial and frequency domains.

Type-II Dirac Photons at Metasurfaces

Topological characteristics of energy bands, such as Dirac and Weyl nodes, have attracted substantial interest in condensed matter systems as well as in classical wave systems. Among these energy bands, the type-II Dirac point is a nodal degeneracy with tilted conical dispersion, leading to a peculiar crossing dispersion in the constant-energy plane. Such nodal points have recently been found in electronic materials. The analogous topological feature in photonic systems remains a theoretical curiosity, with experimental realization expected to be challenging. Here, we experimentally realize the type-II Dirac point using a planar metasurface architecture, where the band degeneracy point is protected by the underlying mirror symmetry of the metasurface. Gapless edge modes are found and measured at the boundary between the different domains of the symmetry-broken metasurface. Our Letter shows that metasurfaces are simple and practical platforms for realizing electromagnetic type-II Dirac points, and their planar structure is a distinct advantage that facilitates applications in two-dimensional topological photonics.

Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces

Pseudorelativistic Dirac quasiparticles have emerged in a plethora of artificial graphene systems that mimic the underlying honeycomb symmetry of graphene. However, it is notoriously difficult to manipulate their properties without modifying the lattice structure. Here we theoretically investigate polaritons supported by honeycomb metasurfaces and, despite the trivial nature of the resonant elements, we unveil rich Dirac physics stemming from a non-trivial winding in the light–matter interaction. The metasurfaces simultaneously exhibit two distinct species of massless Dirac polaritons, namely type-I and type-II. By modifying only the photonic environment via an enclosing cavity, one can manipulate the location of the type-II Dirac points, leading to qualitatively different polariton phases. This enables one to alter the fundamental properties of the emergent Dirac polaritons while preserving the lattice structure—a unique scenario which has no analog in real or artificial graphene systems. Exploiting the photonic environment will thus give rise to unexplored Dirac physics at the subwavelength scale.

Manipulating the properties of artificial graphene systems without changing the lattice has proven difficult. Here, Mann et al. theoretically show that changing the photonic environment alone can modify the fundamental properties of emergent massless Dirac polaritons in honeycomb metasurfaces.