Measuring topological invariants in polaritonic graphene

Abstract

Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g. graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D sub-spaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton-polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene sucht that Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems, and opens the door to the exploration of more complex topological effects, for example involving disorder and interactions.

Suppl. Mat. added; improved data/error analysis

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Cited by in corpus (14)

• Topological Anderson insulators induced by random binary disorders
• Chiral quantum optics in the bulk of photonic quantum Hall systems
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Polaritonic Quantum Matter
• Wavefront dislocations reveal the topology of quasi-1D photonic insulators
• Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions
• In-situ tunable, room-temperature polariton condensation in individual states of a 1D topological lattice
• The Coming Decades of Quantum Simulation
• Manifestation of the Berry connection in chiral lattice systems
• Designing nontrivial one-dimensional Floquet topological phases using a spin-1/2 double-kicked rotor
• Single-shot measurement of photonic topological invariant
• Topological phase transition in an all-optical exciton-polariton lattice
• Microcavity polaritons for topological photonics
• Topological Photonics on a Small Scale