Charge-Fluctuation Contribution to the Raman Response in Superconducting Cuprates

We calculate the Raman response contribution due to soft collective modes, finding a strong dependence on the photon polarizations and on the characteristic wave vectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and $({\mathrm{Y}}_{1.97}{\mathrm{Ca}}_{0.3}){\mathrm{Ba}}_2{\mathrm{CuO}}_{6.05}$, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks can naturally arise from charge collective excitations at finite wavelength.

Figure 1

Direct (a) and crossed (b) diagrams for the fluctuation contributions to Raman spectra. The dots represent Raman vertices. Solid lines represent fermionic QP propagators and dashed lines represent CM propagators. (c) and (d): Hot spots joined by the critical wave vector ${\mathbf{q}}_c=(0,-q_c)$ represented by arrows. Equivalent hot spots have arrows of the same type (solid or dashed). The $+$ $(-)$ signs mark the regions where the $B_{1g}$ and $B_{2g}$ vertices are positive (negative).

Figure 2

(a) Comparison between the anomalous contribution in the experimental and calculated Raman spectra on ${\mathrm{La}}_{1.90}{\mathrm{Sr}}_{0.10}{\mathrm{CuO}}_4$. The intensity is chosen to reproduce the data with ${\Lambda }_{B_{1g}}^2=1.7$, the high-frequency cutoff is ${\omega }_0=250{\mathrm{cm}}^{-1}$. The mass used to fit the curves at different temperatures is reported in the inset, where the linear extrapolation to estimate $T^{*}$ is indicated by the dashed line. (b) Same as (a) for ${\mathrm{La}}_{1.98}{\mathrm{Sr}}_{0.02}{\mathrm{CuO}}_4$ with ${\Lambda }_{B_{2g}}^2=0.85$.

Figure 3

Comparison between the anomalous contribution in the experimental and calculated Raman spectra on $({\mathrm{Y}}_{1.97}{\mathrm{Ca}}_{0.3}){\mathrm{Ba}}_2{\mathrm{CuO}}_{6.05}$ with diffusive propagators [Eq. (1)] (solid lines). The intensity is chosen to fit the data with ${\Lambda }_{B_{2g}}^2=0.41$, the high-frequency cutoff is ${\omega }_0=100{\mathrm{cm}}^{-1}$, The dashed lines are obtained with factorized propagators [Eq. (6)] with overall intensity $B(T)=28,27,19,12$ ($\mathrm{cps}/\mathrm{mW}$) for $T=11$, 55.2, 86.2, and 127.3 K. The mass used to fit the curves with diffusive propagators is reported with open squares in the inset, where the linear extrapolation to estimate $T^{*}$ is indicated by the dashed line. $\Gamma (T)$ (open circles) and ${\omega }_{\mathrm{CM}}$ (diamonds) used with the factorized propagator are also reported in the inset.