Phonon confinement in one-dimensional hybrid periodic/quasiregular structures

We have studied the vibrational frequencies and atom displacements of one-dimensional hybrid systems formed by combinations of periodic and quasiregular (Fibonacci) blocks. The materials are described by nearest-neighbor force constants and the corresponding masses. It is found that the hybrid system exhibits a frequency spectrum with important differences as regards those corresponding to their periodic and quasiregular constituents. In this way we find a separate confinement of the atom displacements in the different parts of the hybrid structure for given frequency ranges.

Figure 1

Frequency eigenvalues versus its ordering number for (a) the periodic slab discussed in the text; (b) a 13th Fibonacci generation; (c) the hybrid structure discussed in the text (full lines indicate the frequencies whose displacements will be studied in the following figures).

Figure 2

Normalized atom displacement $u\left(n\right)$ of the hybrid structure versus the atom order number $n$ for the eigenvalue $\omega =6.242\times {10}^9\mathrm{Hz}$.

Figure 3

As in Fig. 2 for the eigenvalues: (a) $\omega =1.625\times {10}^{13}\mathrm{Hz}$; (b) $\omega =2.274\times {10}^{13}\mathrm{Hz}$; (c) $\omega =5.038\times {10}^{13}\mathrm{Hz}$.

Figure 4

As in Fig. 2 for the eigenvalue $\omega =1.544\times {10}^{13}\mathrm{Hz}$.