Fig. 2: Change of the topology due to reservoir-induced blueshift.

a Schematic of the potential landscape of the ribbon polariton lattice arranged in a honeycomb lattice. b Ribbon band structure and corresponding local Chern number \({C}_{\left({{\boldsymbol{x}}}_{{0}},E\right)}^{{\rm{L}}}\) for \({{\boldsymbol{x}}}_{{0}}\) in the system’s center. In the band structure, the black lines correspond to bulk modes, and the green (red) lines denote the chiral edge mode dispersion localized at the bottom (top) side of the lattice, as shown by the color-coded arrows in (b). The gray shaded area indicates the energy range of interest. c Local density of states (LDOS) of the red line at E = 0.35 meV, \({k}_{x}=-0.6\left[\pi /a\right]\). d–f Same as (a)–(c) but with a blue overlay depicting the blueshift of the whole ribbon structure. g–i Same as (a)–(c) but with the blueshift applied only to half of the ribbon lattice. The red (and green) lines in the band structure correspond to the topological edge modes localized at the interface between the blueshifted and non-blueshifted areas (and at the bottom edge of the lattice). In (h), the local Chern number obtained from both the pumped (dashed magenta line) and unpumped (solid blue line) regions are shown. i LDOS of the red line at E = 0.35 meV, \({k}_{x}=-0.7\left[\pi /a\right]\). Simulations use a reservoir-induced blueshift of \({E}_{{\rm{blueshift}}}=0.55\,{\rm{meV}}\) and spectral localizer calculations use κ = 0.015 meV µm⁻¹ and a finite 2D system of size 26.1 µm × 23.7 µm