## 3 Typical Examples of THz Conductivity in Nanomaterials
ZnO and SnO\({}_{2}\), for example, show both metallic and semiconducting natures [17,29]. Open symbols in Figures 5 and 6 show the complex conductivity in nanostructured ZnO [17] and SnO\({}_{2}\)[29] films, respectively. Fitting of the SSFTC model to the experimental data shown by solid lines produces reasonable physical parameters and these are listed in Table 1. The both nanostructured oxides discussed here have enough free carriers and hence the optical pumping technique is not employed. Note that the EMT or hopping transport model has been applied to interpret the THz conductivity in Sb-doped SnO\({}_{2}\)[29]. However, as already stated, the EMT or hopping transport mechanism does not work properly, when nanoparticles are closely packed. The measured \(\sigma_{\text{dc}}\) value (0.5-10 S\(\cdot\)cm\({}^{-1}\)) [29] is closed to the effective conductivity deduced from the SSFTC model (see Table 1). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Quantity** & **Si** & **Ge\({}_{2}\)Sb\({}_{2}\)Te\({}_{5}\)** & **ZnO** & **SnO\({}_{2}\)** & **Au** & **Cryst-ZnO** \\ \hline \(f\) & 0.83 & 0.996 & 0.94 & 0.97 & 0.999 & 1 \\ \(m^{\star}\) & 0.3 & 0.3 & 0.3 & 0.3 & 1 & 0.24 \\ \(n\) (cm\({}^{-3}\)) & \(5.3\times 10^{18}\) & \(1.5\times 10^{20}  
Let us examine the THz conductivity in nanostructured gold films. Open circles and triangles in Figure 7 show one of examples of the real and imaginary parts of conductivity in nanogold films [30]. Solid lines are predicted conductivity in the SSFTC model. As the imaginary part of conductivity shows the positive signature (curve (b) in Figure 1), it seems to be the Drude-type behavior. Fitting to the experimental data shows, however, that grain boundaries dominate the transport and hence the SSFTC model is working well in gold films as well. In fact, the dc conductivity of nanogold films [4] is very much smaller than that of conventional gold. Figure 5: Complex conductivity in nanostructured ZnO films. Open circles and triangles, respectively, are the experimental data extracted from [17]. Solid lines are conductivity predicted from the SSFTC model. Figure 6: Complex conductivity in nanostructured Sb-doped SnO\({}_{2}\) ((\(\beta\)C\({}_{500}\)P-5%). Open circles and triangles are the experimental data extracted from [29]. Solid lines are predicted conductivity from the SSFTC model. Figure 7: Complex conductivity in nanostructured Au films. Open circles and triangles are the experimental data extracted from [30]. Solid lines are the conductivity predicted by the SSFTC model. Next, we will show what is observed in a single crystalline material. An example is shown for ZnO epitaxial films in Figure 8. Open circles and triangles show the real and imaginary parts of conductivity [31]. Solid lines show the predictions from the Drude law and physical parameters are listed in Table 1.  
A good fit of the Drude law to the experimental results in epitaxial GaN has been also reported [32]. As already stated, the Drude-Smith model [21], in principle, should be applied to single crystalline materials since the disorder effect is not important in the DS model; it is simply a generalization of the Drude formula. No such non-Drude behavior, which fits to the DS model, is reported. It was stated that the SSFTC mechanism produces the Lorentz-type resonance, as shown in Table 1.0 In the Lorentz resonance, however, conductivity at a low frequency should be zero. Therefore, the SSFTC model produces a similar trend to the Lorentz resonance. As shown in Figure 9, when we change physical parameters, e.g., a decrease of \(f\) in Equation (4), in which the tunneling contribution becomes large, the resonant conductivity predicted by the SSFTC model (solid lines) becomes very close to that using the Lorentz resonance (dashed lines), described as [1; 3]:  
Table 1.1  
here, \(N\) is the number of Lorentz oscillator, \(\tau_{L}\) the damping time, and \(\omega_{p}\) the plasma frequency.