Fig. 1: Doping-induced topological transition by plasmon-phonon hybridization.
From: Surface plasmons induce topological transition in graphene/α-MoO3 heterostructures
a Graphene/α-MoO3 device schematic in a scattering-type scanning near-field optical microscope (s-SNOM). Inset shows an optical microscope image of a sample. Graphene doping is achieved via charge transfer with WOx. The s-SNOM tip acts as a dipole antenna, launching polaritons in all permitted directions with in-plane angle \(\theta\). Without doping, there is no propagation along [001] direction and the, b wavefront and, c isofrequency contour (IFC) are hyperbolic. Upon doping, propagation is allowed along the [001] direction and the, d wavefront and, e isofrequency contour of the first-order mode are closed curves. f Semi-analytical IFC undergoing topological transition upon doping. g Along the [100] direction, polaritons have out-of-plane propagation constant kz with Re kz » Im kz such that the out-of-plane electric field is oscillatory like a waveguide mode (HP3, left inset). Along the [001], Im kz » Re kz and polaritons are surface waves with decaying electric field (SP3, right inset). h Plasmon mode splitting (\({\omega }_{{pl}}\to {\omega }_{+}\& \,{\omega }_{-}\)) caused by the [100] α-MoO3 phonon as a function of q and θ. The plot reveals an exceptional point (EP). The doped IFC from f is a curve on the \({\omega }_{+}\) surface (red line). The IFC passes about the EP, indicating a transition from strong to weak coupling. White dotted lines are guides to the eye. i Scattering rates Γ+& Γ− of ω+ & ω− modes are anticorrelated (compare red and pink lines).
