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.