Universal Features of Terahertz Absorption in Disordered Materials

Using an analytical theory, experimental terahertz time-domain spectroscopy data, and numerical evidence, we demonstrate that the frequency dependence of the absorption coupling coefficient between far-infrared photons and atomic vibrations in disordered materials has the universal functional form, $C(\omega )=A+B{\omega }^2$, where the material-specific constants $A$ and $B$ are related to the distributions of fluctuating charges obeying global and local charge neutrality, respectively.

Figure 1

Experimental TDS frequency dependence of the absorption coupling coefficient in the FIR range for (a) $g\mathrm{\text{−}}{\mathrm{SiO}}_2$ and (b) $g\mathrm{\text{−}}{\mathrm{As}}_2{\mathrm{S}}_3$ (solid lines). Other experimental data from Ref. 20 (○), Ref. 24 (×), Ref. 23 (+) in (a) and Ref. 22 (○) in (b) are shown for comparison. The dot-dashed lines represent the numerical data obtained from MD models. The dashed lines show the fits of the experimental data by Eq. (1) with $A=4000{\mathrm{cm}}^{-2}$, $B=0.3{\mathrm{cm}}^{-1}$ for $g\mathrm{\text{−}}{\mathrm{SiO}}_2$ and $A=1780{\mathrm{cm}}^{-2}$, $B=75{\mathrm{cm}}^{-1}$ for $g\mathrm{\text{−}}{\mathrm{As}}_2{\mathrm{S}}_3$. The insets show the VDOS used to extract $C(\omega )$. The dashed line in the insets show the Debye VDOS, with the Debye temperature being 330 K for $g\mathrm{\text{−}}{\mathrm{SiO}}_2$ and 164 K for $g\mathrm{\text{−}}{\mathrm{As}}_2{\mathrm{S}}_3$.

Figure 2

(a),(b) Incoherent and (c),(d) coherent contributions to the coupling coefficients for MD models of $g\mathrm{\text{−}}{\mathrm{SiO}}_2$ and $\alpha$-cristobalite (a),(c) and of $g\mathrm{\text{−}}{\mathrm{As}}_2{\mathrm{S}}_3$ and orpiment (b),(d) to the total coupling coefficient (dot-dashed line). Solid lines represent crystalline models and dashed lines are for glassy ones.

Figure 3

Frequency dependence of $C(\omega )$ for MD models of $\alpha$-cristobalite (a) and orpiment (b) with uncorrelated (thin solid lines), correlated (dot-dashed lines), and both types of charge disorder (dashed lines). The uncorrelated charges were drawn from normal distributions with standard deviations, ${\sigma }_{\mathrm{Si}}/q_{\mathrm{Si}}={\sigma }_{\mathrm{O}}/|q_{\mathrm{O}}|=0.04$ and ${\sigma }_{\mathrm{As}}/q_{\mathrm{As}}={\sigma }_{\mathrm{S}}/|q_{\mathrm{S}}|=0.06$, and zero means. The correlated charges were taken from a normal distribution with mean values and standard deviations of $⟨q_{2i,\mathrm{Si}}⟩=2.4$, $⟨q_{2i,\mathrm{O}}⟩=-1.2$, $⟨q_{2i,\mathrm{As}}⟩=0.56$, $⟨q_{2i,\mathrm{S}}⟩=-0.37$ and ${\sigma }_{2,\mathrm{Si}}/⟨q_{2i,\mathrm{Si}}⟩=0.6$, ${\sigma }_{2,\mathrm{As}}/⟨q_{2i,\mathrm{As}}⟩=0.6$. The random values of $q_{2i}$ have been compensated by $-q_{2i}/Z$ placed on $Z$ nearest neighbors in order to maintain local charge neutrality. The parameters of the distributions for uncorrelated charges were chosen to fit the experimental data for the plateau value [parameter $A$ in Eq. (1)], and for correlated charges to fit the frequency dependence of $C(\omega )$ in the glassy MD models (solid lines).