Figure 2.

(a) The dispersion curves (thin lines) of the RW and LR branches of Bi₂Te₃(111) film, confined at the surface for large wavevectors q, turn smoothly into those of the corresponding leaky waves (SW_0,1) for smaller q, when the corresponding penetration lengths would exceed the film thickness. The avoided crossings with the substrate RW and LR branches (broken lines) is here neglected in view of the weak substrate-film coupling. When the strong e-ph interaction in the interface space-charge region is considered, deep Kohn anomalies (thick and dotted lines) are produced, in agreement with the BLS data for the highly-doped 50 nm Bi₂Te₃(111) film. The insets explain the mechanism: anomalies occur when the penetration depth of the surface modes is comparable to the film thickness, producing a large displacement gradient in the space-charge region (grey area).The red broken curve corresponds to the fit when the oscillatory part in the LR eigenvector is neglected (see Eq. (7) and related text). (b) Phase velocity vs. wavevector times thickness. The experimental points deduced from (a) show the anomaly in the LR (red arrow) and RW (blue arrow) mode as compared with the expected fits. The corresponding LR and RW phase velocity in GaAs are marked with a straight gray line.