Figure 4. Topological band inversions and Floquet k.p theory in a Wannier three-orbital model of WS₂.

(a) The relevant resonances when moving from red to blue detuning. (b) Effective k.p parameterization of the band inversion at K (Eqn. 1) starting from the three-orbital Wannier tight-binding model. (c) sketches the corresponding topological classification. At low pump strengths, the sign of M/B a₀ ² is negative in the non-trivial inverted regime. The system transitions from one (red-detuned) to two (blue-detuned) chiral edge modes when . The effective k.p model parameterized in b accounts for the Floquet state adiabatically derived from the CB, as well as the Floquet state deriving from the VB dressed by one absorbed photon, for red detuning, or from the higher-energy E′ XB dressed by one emitted photon, for blue detuning. This entails the sharp transition when sweeping the pump frequency across the two-photon resonance between VB and XB (a). Within the shaded areas, all three bands come into resonance. Thick black lines indicate degeneracies in the Floquet spectrum. (d) A corresponding numerical calculation of the global Chern number of the tight-binding model mirrors the k.p analysis. Yellow (orange) denotes () as defined in c, circles indicate parameters used for Fig. 2.