The discovery of topological phases of matter is one of the most significant breakthroughs in the recent history of solid-state physics. The hallmark of these exotic phases is the emergence, at the frontier between materials described by distinct topological invariant (e.g the so-called Chern number), of localized electronic states whose properties are insensitive to smooth deformations or local imperfections. Notable examples of these protected states are the edge conductivity plateaus in the integer and fractional quantum Hall effects (QHE), and dissipation-less spin currents at the surface of 2D and 3D topological insulators.

Recently, engineering topological invariants in synthetic lattices (e.g. cold atoms, photonic systems, and mechanical arrays) has enabled a much wider and easier exploration of this topological physics. In the Polaritons group at C2N, we aim at extending even further the frontiers of this exploration by taking profit of the unique properties of cavity polaritons confined in patterned microcavity. More precisely, we are interested in time-reversal symmetry broken phases reminiscent of the QHE as well as in nonlinear phenomena (e.g. solitons, vortices, Bose-Einstein condensationâ€¦) in topological modes; both of which are widely unexplored yet extremely promising horizons.

Taking advantage of the technological facilities available in the C2N clean-room, our group has developed state of the art semiconductor lattices enabling to fully engineer polariton band structures with well-defined topological properties. For example, honeycomb lattices [1] (i.e. artificial graphene; see figure on the right) have been implemented and show robust edge states associated to their non-trivial topology, as well as a garden variety of exotic phenomena emerging from the topological properties of Dirac cones. Furthermore, taking profit of the nonlinear properties of polaritons, we recently demonstrated the realization of a topological laser [4] in a 1D lattice where the resonating mode is protected against perturbations of his environment by topology. Finally, we are interested in topological phases of quasi-crystals [5,6] which exhibit fractal band structures and allow emulating the quantum Hall effect.

[1] T. Jacqmin *et al.* Phys. Rev. Lett. **112**, 116402 (2014)

[2] M. Milicevic *et al.* 2D Mater. **2**, 034012 (2015)

[3] M. Milicevic *et al.* Phys. Rev Lett. **118**, 107403 (2017)

[4] P. St-Jean *et al.* Nat. Photon. 11, **651** (2017)

[5] D. Tanese *et al.* Phys. Rev. Lett. **112**, 146404 (2014)

[6] F. Baboux *et al.* Phys. Rev. B (R) **95**, 161114 (2017)