Evidence of Delocalized Excitons in Amorphous Solids

We studied the temperature dependence of the absorption coefficient of amorphous ${\mathrm{SiO}}_2$ in the range from 8 to 17.5 eV obtained by Kramers-Kronig dispersion analysis of reflectivity spectra. We demonstrate the main excitonic resonance at 10.4 eV to feature a close Lorentzian shape redshifting with increasing temperature. This provides a strong evidence of excitons being delocalized notwithstanding the structural disorder intrinsic to amorphous ${\mathrm{SiO}}_2$. Excitons turn out to be coupled to an average phonon mode of 83 meV energy.

Figure 1

(a) Reflectivity of $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ from 10 to 300 K by steps of 50 K (solid lines), and reflectivity of $c\mathrm{\text{−}}{\mathrm{SiO}}_2$ at 10 K (dashed line). (b) Enlargement of the peak at $\sim 10.3\mathrm{eV}$ in $a\mathrm{\text{−}}{\mathrm{SiO}}_2$. Labels represent temperatures (K) of the closest curve.

Figure 2

(a) Absorption coefficient of $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ from 10 to 300 K by steps of 50 K. (b) Enlargement of the peak at $\sim 10.4\mathrm{eV}$ in $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ (solid lines) and in $c\mathrm{\text{−}}{\mathrm{SiO}}_2$ (dashed line). Labels represent temperatures (K) of the closest curve.

Figure 3

Normalized absorption at 10 K (open circles) and at 300 K in $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ (filled circles), at 10 K in $c\mathrm{\text{−}}{\mathrm{SiO}}_2$ (triangles). Continuous lines were obtained via a Lorentzian fit of each spectrum. (a) Position of the peak in $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ as a function of temperature (b) Semilogarithmic plot of the same data on $a\mathrm{\text{−}}{\mathrm{SiO}}_2$ as in the main panel.