## 3 Results and Discussion  
In the d-InAs/u-GaAs/Hexane nanostructure, there were four coupled phonon-plasmon branches (see Figure 1b) due to the hybridization of one interface plasmon branch (at the GaAs/InAs interface) and three interface phonon branches (InAs-like and GaAs-like at the InAs/GaAs interface and GaAs-like at the GaAs/Hexane interface). At around \(N_{e}\) \(\sim\) 3 \(\times\) 10\({}^{18}\) cm\({}^{-3}\), the interface phonon-plasmon coupling was enhanced through the interaction with the single interface plasmon branch. In this nanostructure, it was the core that carried the doping, and only one interface between the core and the shell carried interface plasmons. In the u-GaAs/d-InAs/Hexane nanostructure, three interface phonon branches (InAs-like and GaAs-like at the InAs/GaAs interface and InAs-like at the InAs/Hexane interface) hybridized with two interface plasmon branches at the GaAs/InAs and InAs/Hexane interfaces. This led to five coupled phonon-plasmon branches. As seen from Figure 1c, the interface phonon-plasmon hybridization in the u-GaAs/d-InAs/Hexane nanostructure was enhanced around \(N_{e}\) \(\sim\) 2 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) (due to the higher plasmon branch) and around \(N_{e}\) \(\sim\) 7 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) (due to the lower plasmon branch). Two interface plasmon branches were present because interface plasmons were excited at both interfaces (inner and outer) of the doped shell. Similar results have been obtained for quantum numbers \(l\) > 1. The hybridized modes determined the absorption spectra of semiconductor nanoshells in the THz regime. Therefore, peaks in the absorption spectra can be used to identify hybrid phonon-plasmon modes. The peaks in the absorption spectrum can be identified with phonon-plasmon frequencies on the basis of Mie theory [26], extended to the case of concentric shells [55; 56]. To apply this theory to the present case of semiconductor nanoshells, we used the following relative dielectric permittivities:  
\[\varepsilon_{InAs(GaAs)}(\omega,N_{e})=\varepsilon_{undoped}^{InAs(GaAs)}( \omega)-\varepsilon_{\infty,InAs(GaAs)}\omega_{Pl,bulk}^{2}(N_{e})/\omega^{2}, \tag{6}\]  
where \(\varepsilon_{undoped}^{InAs(GaAs)}(\omega)\) is the relative dielectric function in undoped InAs (GaAs) tabulated from experiments [43]. For the calculation of the absorption spectrum, we used a complex dielectric function \(\varepsilon_{undoped}^{InAs(GaAs)}(\omega)\), rather than the real function \(\varepsilon_{InAs(GaAs)}(\omega)\) given by Equation (3). Figures 2 and 3 show the resulting absorption cross section as a function of the energy of the light impinging on the d-InAs/u-GaAs/Hexane and u-InAs/d-GaAs/Hexane core/shell nanostructures, respectively, for different doping levels of InAs. These nanostructures absorbed light in the energy range from 20 to 40 meV. The finite width of the absorption lines is due to the imaginary part of \(\varepsilon_{undoped}^{InAs(GaAs)}(\omega)\). In the present paper, we focus on the light absorption by the core/shell nanostructures, and do not show the scattering cross section. In nanostructures with an undoped InAs core, the positions of the absorption peaks (indicated in Figure 2a as 1 and 2) correspond exactly to the energies of the nanoshell interface phonons at \(\hbar\omega_{s,1}=28.5\) meV, \(\hbar\omega_{s,2}=33.8\) meV, and \(\hbar\omega_{s,3}=35.4\) meV. The width of peak 2 is slightly larger than the difference between energies of the two highest interface phonons \(\hbar\omega_{s,3}-\hbar\omega_{s,2}\). Therefore, peak 2 was interpreted as the result of overlapping absorption peaks of the two highest interface phonon branches. An increase of the electron concentration to \(N_{e}\) = 10\({}^{18}\) cm\({}^{-3}\) (see Figure 2b) raised the spectral weight of the peaks by a factor of \(\sim\)1.5 and weakly blue-shifts them (by approximately 1 meV).