Fig. 1: Topological polaritonic metasurface integrating transition metal dichalcogenide (TMD) monolayer.

a Schematic image of topological metasurface with hexagonal boron nitride (hBN) spacer and MoSe₂ monolayer on top. Lattice constant is a₀ = 460 nm, Si layer thickness is h = 75 nm. b First-principle calculated photonic band structure for the cases of gapless (black dotted lines), topological (red lines) and trivial (blue dashed lines) metasurfaces. The spectral position of the exciton is shown by the dashed horizontal line (here, at 1.65 eV in absolute value, which corresponds to exciton in MoSe₂ at low temperature). The righthand y-axis is in relative energy units (as measured from the Dirac point) c Bulk band structures of topological polaritonic system obtained for one (pseudo-)spin from the analytical model for cases without (blue dashed lines) and with exciton-photon coupling q_d (red solid lines). In the uncoupled case, horizontal black dashed line (\({\tilde{\omega }}_{ex}=-0.1\) eV here to better illustrate the avoided crossing and the Berry curvature distribution near it) shows the spectral position of exciton. Shaded magenta curve shows distribution of the Berry curvature over the upper polariton band with the corresponding (magenta) y-axis on the right side. d Excitonic fraction (color coded) of the band structure calculated by TBM on a supercell lattice with topological and trivial domains (10 unit cells each) separated by domain walls for the case of optimal (for maximal excitonic fraction of the edge states) crossing scenario near the Γ point.