Results and Discussion {#sec:cal}
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We plot the calculated conductivities as a function of photon energy in Fig. \[fig:sigma\]. In the left panel, the layered conductivity is represented by the mean conductivity $\langle \sigma^N(\omega) \rangle \equiv \sum_{j=1}^N \sigma^N_j(\omega)/N$ and the standard deviation $\sqrt{\frac{1}{N} \sum_{j=1}^N (\sigma^N_j(\omega)-\langle \sigma^N(\omega) \rangle)^2}$. As $N$ increases, the standard deviation (expressed by the error bars) is suppressed and it becomes noticeable that $\langle \sigma^N(\omega) \rangle$ has a weak peak structure at $\hbar \omega = 2\gamma_1$. In the right panel of Fig. \[fig:sigma\], the bunched conductivity $\sigma_{N}(\omega)$ has a strong peak structure at $\hbar \omega = 2\gamma_1$, even for a small value of $N$, such as 10. There are two factors relevant to the appearance of this peak structure; firstly, direct interband transitions (between the states with the same $k_{r}$) are optically allowed and secondary, the density of states is enhanced near the states at $r=1$ and $N+1$ for which the bandgap is $\sim 2\gamma_1$. In Appendix \[app:largeN\], we confirm analytically for a large $N$ that direct transitions are responsible for the peak structure while indirect transitions do not. The proof is performed for the bunched conductivity. Although the statement above on the two factors does not exactly 