Correlation between $T_{\mathrm{c}}$ and the Pseudogap Observed in the Optical Spectra of High $T_{\mathrm{c}}$ Superconducting Cuprates

We studied the temperature dependences of the optical spectra for optimally and underdoped Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+z}$ single crystals. Similarly to the other cuprates’ cases, a gap-like conductivity suppression was observed with reducing the temperature from above $T_{\mathrm{c}}$, creating a peak in the conductivity spectrum. The conductivity peak energy was insensitive to the doping level, namely $T_{\mathrm{c}}$, which suggests that this gap is not a superconducting gap but is related to the pseudogap. Comparing the data of various mono-, double-, and triple-layer cuprates, we found a clear correlation between the optimal $T_{\mathrm{c}}$ of each material and the pseudogap-related conductivity peak energy.