Temperature Dependent of the Optical Spectral Weight in Correlated Metal Nd$_{1-x}$TiO$_{3 }$(x=0.095)

We investigated the infrared reflectance of Nd$_{1-x}$TiO$_{3}$, which is a hole-doped transition-metal-oxide system. In the metallic sample with $x$=0.095 (hole concentration=3$x$=0.285), the partial optical spectral weight, $\omega (\Omega ,T)=\int_0^\Omega {\sigma _1 (\omega ,T)d\omega } $, turns out to be a linear function of $T^{2 }$at different cutoff frequencies. Recent optical studies of LSCO [1] and BSCCO [2] also found that the optical spectral weight varies quadratically with temperature, i.e. $\omega (\Omega ,T)\simeq \omega _0 -B(\Omega )T^2$, in both superconductors and nonsuperconducting metals. The coefficient $B(\Omega )$ was considered as a ``thermal response'' of the carriers. In our study, for Nd$_{1-x}$TiO$_{3 }(x$=0.095), $B(\Omega )$ exhibits distinct features which we compare to both cuprates and conventional metals. [1] M. Ortolani \textit{et al}., Phys. Rev. Lett. \textbf{94}, 067002 (2005). [2] H. J. A. Molegraaf \textit{et al}., Science \textbf{295}, 2239 (2002).