Temperature Dependence of the Optical Spectral Weight in the Cuprates: Role of Electron Correlations

We compare calculations based on the dynamical mean-field theory of the Hubbard model with the infrared spectral weight $W(\Omega ,T)$ of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and other cuprates. Without using fitting parameters we show that most of the anomalies found in $W(\Omega ,T)$ with respect to normal metals, including the existence of two different energy scales for the doping and the $T$ dependence of $W(\Omega ,T)$, can be ascribed to strong correlation effects.

Figure 1

$W(\Omega ,T)$ as a function of $T^2$ for the Hubbard model, for $\Omega =0.1D$ (left panel) and $\Omega =1.5D$ (right panel), normalized to its zero-temperature extrapolation. Symbols are the results of the DMFT calculations; lines are best fits to them.

Figure 2

$T=0$ spectral weight for $\Omega =1.5D$ as a function of doping, for both the Hubbard model (dots) and for the observations in LSCO (circles). The latter data are obtained by integrating the ${\sigma }_1(\omega )$ of LSCO in Ref. 23.

Figure 3

The relative variation of the spectral weight between the lowest $T$ and 300 K, as a function of doping for various cuprates (full symbols) is compared with present DMFT calculations (squares) and with the predictions of noninteracting models [tight-binding model (solid line), flat band (dashed line)]. The dotted line is a guide to the eye. The simple inclusion of correlation effects allows one to reproduce the observed absolute values with no need for fitting parameters. Data for LSCO are obtained from Refs. 8, 23, and for BSCCO from Ref. 5 (${\mathrm{BSCCO}}_1$) and from Ref. 2 (${\mathrm{BSCCO}}_2$).