The c-axis optical sum rule and possible new collective mode in LSCO

We present the c-axis optical conductivity $\sigma_{1c}(\omega, T)$ of underdoped ($x$ = 0.12) and optimally doped ($x$ = 0.15) LSCO from 4 meV to 1.8 eV obtained by a combination of reflectivity and transmission spectra. In addition to the opening of the superconducting gap, we observe an {\it increase} of conductivity above the gap up to 270 meV with a maximal effect at about 120 meV. This may indicate a new collective mode at a surprisingly large energy scale. The Ferrell-Glover-Tinkham sum rule is violated for both doping levels. Although the relative value of the violation is much larger for the underdoped sample, the absolute increase of the low-frequency spectral weight, including that of the condensate, is higher in the optimally doped regime. Our results resemble in many respects the observations in YBCO.