Edge states in polariton honeycomb lattices

Abstract

The experimental study of edge states in atomically-thin layered materials remains a challenge due to the difficult control of the geometry of the sample terminations, the stability of dangling bonds and the need to measure local properties. In the case of graphene, localised edge modes have been predicted in zig-zag and bearded edges, characterised by flat dispersions connecting the Dirac points. Polaritons in semiconductor microcavities have recently emerged as an extraordinary photonic platform to emulate 1D and 2D Hamiltonians, allowing the direct visualization of the wavefunctions in both real-and momentum-space as well as of the energy dispersion of eigenstates via photoluminescence experiments. Here we report on the observation of edge states in a honeycomb lattice of coupled micropillars. The lowest two bands of this structure arise from the coupling of the lowest energy modes of the micropillars, and emulate the π and π* bands of graphene. We show the momentum space dispersion of the edge states associated to the zig-zag and bearded edges, holding unidimensional quasi-flat bands. Additionally, we evaluate polarisation effects characteristic of polaritons on the properties of these states.

Modulational instability and solitary waves in polariton topological insulators

“…The latter was used for recent demonstrations of superfluidity [22,23], generation of dark quasi-solitons and vortices [24][25][26][27], bright spatial and temporal solitons [28][29][30], and other effects. The observed polariton effects with linear and nonlinear lattice potentials include one- [31] and twodimensional [32,33] gap polariton solitons, visualization of Dirac cones [34] and flat bands [35], and visualization of non-topological edge states [21]. Recently, it has been shown theoretically that attractive nonlinear interaction between polaritons with opposite spins can compensate and exceed Zeeman energy shifts due to magnetic field and thereby lead to the inversion of the propagation direction of the edge states [36].…”

Orbital Edge States in a Photonic Honeycomb Lattice

“…The origin of the zero-energy edge states can be understood from the winding number of the bulk Hamiltonian. We support experimental data with numerical tight-binding calculations and provide analytical expressions for the energy of the dispersive edge states.To experimentally study orbital edge states in p x,y bands we employ the polaritonic honeycomb lattice reported in [18,34] and shown in Fig. 4(c).…”

“…To experimentally study orbital edge states in p x,y bands we employ the polaritonic honeycomb lattice reported in [18,34] and shown in Fig. 4(c).…”

Klein tunneling in driven-dissipative photonic graphene

“…Along with these developments, there have been several studies on the simulation of graphene physics using photonics. Honeycomb lattice structures to simulate the physics of graphene have been realized in microwave cavities [12][13][14], propagating waveguides [10,15,16], and excitonpolariton microcavities [17][18][19][20]. All of these experimental realizations have been successfully modeled using tightbinding Hamiltonians whose band structure presents the characteristic massless Dirac cones responsible for a number of transport phenomena in graphene.…”

“…Our work demonstrates that the finite linewidth associated with losses in photonic devices does not significantly affect the phenomenon of Klein tunneling, but rather offers a useful means to experimentally simulate its microscopic details. While our discussion is focused to the specific case of polaritons in laterally patterned planar microcavities [18][19][20], it straightforwardly extends to other related systems such as microwave [7,13] and superconductor resonators [57]. This work is the first step towards the study of Klein tunneling, negative refraction, and Veselago lensing in the presence of interactions, directly accessible in exciton-polariton lattices [58].…”