Fig. 3: Quantum hidden order and effects of selection rules on the Kerr optical response.

a Schematic representation of the different contributions to the σ_xy,α,ν Kerr optical rotation resolved for the layer and valleys. For the sake of representation, the spin degree has been averaged. The bottom line represents the total layer-averaged σ_xy,ν = ∑_ασ_xy,α,ν. Blue/red areas represent states resulting in a positive/negative Kerr angle, respectively, while grey areas stand for null Kerr rotation. The left panel shows the hidden order before pumping. LCP laser pumping in the right panel photo-excites charges at K in layer α = + 1, and at -K in layer α = − 1. In both cases, it results in a net increase of σ_xy > 0 in each valley, resulting in a finite Kerr rotation. The system still obeys inversion symmetry, and each valley is equivalent. b Representative selection rules and Pauli-blocked optical transitions at ν = 1 valley in the absence of interlayer coupling. The absorption of an LCP photon tuned at the A-energy triggers particle-hole transitions (upward green arrow) only from the E_V,↑ state with ∣l_at∣ = 2 (blue bands) to E_C,↑ with l_at = 0 (grey bands). The resulting photo-excited charges n_V,↑ = n_C,↑ ≠ 0 induce Pauli blocking (crossed colored vertical double-arrows) at both the A- and C-resonance energies. c Same as (b) in the presence of a finite interlayer coupling, which leads to a mixed l_at character for the E_V,s bands, resulting in a large charge transfer from E_V,↑ to E_C,↑, but also in a finite charge transfer from E_V,↓ to E_C,↓, hence n_V,↓ = n_C,↓ ≠ 0. A Pauli-blocking is consequently active also for the particle-hole transitions responsible for the B-resonance.