Figure 3. Absorption modified by topological surface states.

(a) When the topologically protected surface states are occupied up to the Dirac point, the two uppermost electrons (at energy −A/R) couple to empty states above the Dirac point (at A/R). As a result, the absorption cross-section contains an additional maximum (SToP, marked with an arrow) and a zero, which depend on the radius of the nanoparticle. The screening effect (along the line 2A=ħwR) occurs when the energy spacing of surface states is matched by the incident radiation and the surface conductivity becomes infinite screening the bulk. The SToP mode arises, because the surface electron acts as a mediator of the interaction between light and the α-phonon (grey dotted line), which otherwise does not absorb. This mode interacts with the localised surface plasmon (LSPP) and bulk β-phonon (the two horizontal modes) giving rise to the splittings. (b) In this figure the free carriers and β-phonon contributions to the bulk dielectric function were artificially removed, tht is, w_pβ=w_pf=0 (the absent modes marked by white dashed lines). This shows that the SToP mode (marked with an arrow) originates from the interaction of the α-phonon with the surface states. (c) Cross-section of the nanoparticle without the effect of surface states.