Figure 3: CADP modes and the unique conditions for their excitation in thin-films of Bi₂Se₃.

(a) Dispersion of the FBAWR modes observed in ref. 55 for the same Bi₂Se₃ films of different thicknesses (red dots) and the excited TE and TM guided CADP modes (green and blue dots, respectively) are shown. Red dashed line approximates the linear dispersion of FBAWR modes, whereas solid black line shows the dispersion of AP in the presence of fermion tunnelling between the opposite-surface Dirac SS, which was modelled using equation (4) with Δ=0.92 meV, C₁=5.1, and C₂=7.684. Patterned area represents the Landau damping regions. (b) A schematic representation of the FBAWR modes for films with d>15 nm and the extensional (symmetric) and flexural (antisymmetric) Lamb modes for films with d<15 nm. Blue arrows indicate the direction of the evanescent guided Lamb wave oscillations. (c) The normalized TSHG and negative TR traces for the 10 nm thick film are shown together with the fit curves (black solid lines). To guide the general tendency, the fit to the TSHG trace is shown without the oscillatory part. Inset shows zoom in on the same traces. The rise- and decay-time constants are shown in the corresponding colours. Black squares represent the temporal dynamics of the threefold symmetry component of the TSHGRA patterns (weight coefficient c₂ in equation (2)). (d) Schematic sketch of the electronic structure of Bi₂Se₃ films and the relaxation dynamics in Dirac SS due to their direct optical coupling to ∼1.51 eV incident photons (thicker red arrows). Thinner-red and multicolour arrows present the recombination and LO-phonon-assisted relaxation processes, respectively. Black dashed arrows indicate 2DEG-to-Dirac1SS scattering which balances the corresponding electron densities and completely eliminates the depletion electric field , thus leading to the dominant contribution of purely surface sixfold rotational symmetry component originating from the topmost Se atomic layer of the film.