Manipulating Type-I and Type-II Dirac Polaritons in Cavity-Embedded Honeycomb Metasurfaces

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Manipulating Type-I and Type-II Dirac Polaritons in Cavity-Embedded Honeycomb Metasurfaces ARTICLE DOI: 10.1038/s41467-018-03982-7 OPEN Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces Charlie-Ray Mann 1, Thomas J. Sturges 1, Guillaume Weick2, William L. Barnes 1 & Eros Mariani1 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. 1234567890():,; 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. 1 EPSRC Centre for Doctoral Training in Metamaterials (XM2), Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, UK. 2 Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France. Correspondence and requests for materials should be addressed to C.-R.M. (email: [email protected]) or to E.M. (email: [email protected]) NATURE COMMUNICATIONS | (2018) 9:2194 | DOI: 10.1038/s41467-018-03982-7 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03982-7 he groundbreaking discovery of monolayer graphene1 has photonic cavity and simply changing the cavity height, one can inspired an extensive quest to emulate massless Dirac induce multiple phase transitions including the multimerging of T fi quasiparticles in a myriad of distinct arti cial graphene type-I and type-II Dirac points and the annihilation of type-II Dirac – systems2 11, ranging from ultracold atoms in optical lattices3 to points. This striking tunability results in qualitatively different evanescently coupled photonic waveguide arrays4. Owing to their polariton phases, despite the preserved lattice structure. In parti- honeycomb symmetry, linear band-degeneracies manifest in the cular, we unveil a morphing between a linear and a parabolic quasiparticle spectrum which we call conventional Dirac points spectrum accompanied by a change in the topological Berry phase, (CDPs). These belong to the ubiquitous type-I class of two- and an environment-induced inversion of chirality, all of which dimensional (2D) Dirac points that are characterized by Dirac have no analog in graphene or artificial graphene systems studied cones with closed isofrequency contours. As a result, the corre- thus far. Therefore, this unique paradigm will give rise to unex- sponding quasiparticles are described by the rather exotic 2D plored Dirac-related phenomena at the subwavelength scale, such as massless Dirac Hamiltonian12, and thus offer fundamental insight anomalous Klein tunneling, negative refraction, and pseudomag- into pseudorelativistic phenomena such as the iconic Klein netic Landau levels, which can all be tuned via the photonic paradox13. The latter is responsible for the suppression of back- environment alone. scattering and for the antilocalization of massless Dirac quasi- particles, which are highly desirable properties for efficient Results quasiparticle propagation in novel devices. Hamiltonian formulation. While metamaterials have tradition- Since the existence of type-I CDPs is intrinsically linked to the ally been described in terms of macroscopic effective honeycomb structure, the fundamental properties of the massless properties30,33,43, the importance of crystallinity is becoming Dirac quasiparticles are notoriously robust and difficult to increasingly apparent44. Therefore, to capture the essential manipulate. However, by exploiting meticulous control over the physics related to complex non-local effects that arise from lattice structure, artificial graphene systems have enabled the strong multiple-scattering45, here we study the properties of the exploration of Dirac quasiparticles in new regimes that are dif- – cavity-embedded honeycomb metasurface by means of a ficult, if not impossible to achieve in graphene itself14 19. Among microscopic Hamiltonian formalism. This allows us to clearly others, the archetypal example which has attracted considerable identify the distinct physical origins of the type-I and type-II interest is the paradigm of strain-engineering, where it has been Dirac points. = shown that lattice anisotropy can induce the merging and anni- The full polariton Hamiltonian of this system reads Hpol 3,14–16,20–23 + + hilation of type-I CDPs , and that aperiodicity can Hmat Hph Hint, where the interaction Hamiltonian Hint generate large pseudomagnetic fields17,24. couples the matter and photonic subspaces whose free dynamics Moreover, the recent discovery of type-II Dirac/Weyl semi- – are governed by Hmat and Hph, respectively. We employ the metals25 29 sparked a burgeoning exploration into the prospects Coulomb gauge, where the instantaneous Coulomb interaction of a rarer type-II class of three-dimensional Dirac/Weyl points. between the meta-atoms is incorporated within the matter As the latter are characterized by critically tilted Dirac/Weyl Hamiltonian Hmat, and the effects of the dynamic photonic cones with open, hyperbolic isofrequency contours, the corre- environment—described by the transverse vector potential—are sponding Lorentz-violating Dirac/Weyl quasiparticles exhibit 46 – included through the principle of minimal-coupling . markedly different properties from their type-I counterparts25 29. – A schematic of a cavity-embedded honeycomb metasurface is Soon after their realization, electromagnetic analogs emerged30 depicted in Fig. 1. We model each subwavelength meta-atom by a 34, and this exploration has recently been extended to 2D systems single dynamical degree of freedom describing the electric-dipole where a distinct type-II class of 2D Dirac points were theoretically moment associated with its (non-degenerate) fundamental 35,36 ω predicted . However, since their existence is predicated on eigenmode with resonant frequency 0. These meta-atoms are strong anisotropy in judiciously engineered photonic structures, then oriented such that their dipole moments point normal to the one cannot manipulate their properties without modifying the plane of the lattice. Furthermore, we consider subwavelength lattice structure. nearest-neighbor separation a such that the light cone intersects This hunt for exotic quasiparticles has recently entered the ω – the Brillouin zone edge above 0, ensuring the existence of realm of polaritonics37 42. The true potential of polaritons lies in evanescently bound, subwavelength polaritons. The strength of their hybrid nature, where their light and matter constituents can the Coulomb dipole–dipole interaction between neighboring be manipulated independently, thereby providing additional meta-atoms is parametrized by Ω. Finally, the metasurface is tunable degrees of freedom. Among other examples, recent works embedded at the center of a planar photonic cavity of height L, have shown the tantalizing prospect of engineering novel topo- where the cavity walls are assumed to be lossless and perfectly logical polaritons by introducing a winding coupling between conducting metallic plates. Such a structure is imminently ordinary photons and excitons39,41. realizable across the electromagnetic spectrum from arrays of In this work, we exploit the hybrid nature of polaritons in a plasmonic nanoparticles to microwave helical resonators (see different setting, namely metasurfaces, and we unveil unique Fig. 1). Dirac physics by shifting the focus from the lattice structure and its deformations to the effect of manipulating the sur- Emergence of type-I Dirac points. The matter Hamiltonian rounding photonic environment. In particular, we theoretically within the nearest-neighbor approximation reads study the polaritons supported by imminently realizable, crys- XX ¼ ω~ y þ y þ Ω~ y þ : : ; talline metasurfaces consisting of a honeycomb array of reso- Hmat h 0 aqaq bqbq h fqbqaq H c ð1Þ nant, dipolar meta-atoms. Despitetheelementarynatureof q q these metasurfaces, we unveil the simultaneous existence of both type-I and type-II massless Dirac polaritons which have where, for brevity, we have not presented the non-resonant terms ω~ distinct physical origins. Crucially, the existence of the latter is (see Methods for derivation). In Eq. (1), 0 is the renormalized not a result of anisotropy but is intrinsically linked to the resonant frequency and Ω~ is the renormalized Coulombic inter- hybrid nature of the polaritons, emerging from a non-trivial action strength due to the cavity-induced image dipoles (see winding in the light–matter interaction. Furthermore, we show Methods for their dependence on the cavity height). The y y that by embedding the honeycomb metasurface inside a planar bosonic operators aq and bq create quanta of the quasistatic 2 NATURE COMMUNICATIONS | (2018)
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