[Paper Review] Edge states in polariton honeycomb lattices

Marijana Milićević, Tomoki Ozawa+9 more|arXiv (Cornell University)|Apr 22, 2015

Strong Light-Matter Interactions2 references3 citations

TL;DR

This paper demonstrates the experimental observation of edge states in a polariton honeycomb lattice formed by coupled semiconductor micropillars, using photoluminescence to visualize momentum-space dispersion. The system emulates graphene's π and π* bands, revealing unidirectional, quasi-flat edge modes at zig-zag and bearded boundaries, with polarization-dependent properties confirmed via polaritonic effects.

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.

Motivation & Objective

• To overcome experimental challenges in studying edge states in atomically thin materials by using a tunable photonic platform.
• To realize a synthetic honeycomb lattice of micropillars that emulates the electronic bands of graphene.
• To directly observe and characterize edge states—specifically at zig-zag and bearded edges—using real- and momentum-space imaging.
• To investigate polarization effects on edge state properties in a strongly interacting polariton system.
• To validate theoretical predictions of flat, unidirectional edge modes in artificial graphene systems.

Proposed method

• The system uses a 2D array of GaAs-based semiconductor micropillars coupled via evanescent fields to form a honeycomb lattice.
• The lowest two bands of the micropillar lattice emulate the π and π* bands of graphene, with tunable tunneling and on-site energy parameters.
• Photoluminescence spectroscopy is used to map the energy dispersion and real-space wavefunctions of eigenstates in momentum and real space.
• Edge states are probed by engineering lattice boundaries with zig-zag and bearded terminations to induce topological modes.
• Polarization-resolved measurements are performed to assess the impact of polariton character on edge state properties.
• Theoretical modeling based on tight-binding Hamiltonians is used to interpret the observed dispersion and edge mode localization.

Experimental results

Research questions

• RQ1 Can edge states be experimentally observed in a polariton-based artificial honeycomb lattice that emulates graphene's band structure?
• RQ2 What is the momentum-space dispersion of edge states at zig-zag and bearded lattice boundaries in this system?
• RQ3 How do polaritonic effects, such as spin-orbit coupling and polarization, influence the properties of these edge states?
• RQ4 Are the observed edge states unidirectional and quasi-flat, as predicted by theory for graphene-like systems?
• RQ5 To what extent do the edge modes exhibit topological protection and robustness against disorder?

Key findings

• The lowest two bands of the micropillar lattice successfully emulate the π and π* bands of graphene, confirming the effective Hamiltonian model.
• Edge states at zig-zag and bearded boundaries exhibit unidirectional, quasi-flat dispersions in momentum space, consistent with topological edge modes.
• Photoluminescence imaging reveals localized wavefunctions at the edges, with clear spatial separation from bulk states.
• Polarization measurements show distinct characteristics for edge states, indicating strong polaritonic effects such as spin-splitting and circular polarization dependence.
• The observed edge modes are robust and exhibit minimal backscattering, suggesting topological protection.
• The system demonstrates a direct, real-space visualization of edge states in a tunable, photonic platform, enabling in-situ probing of topological phenomena.