Spectroscopy of excited yellow exciton states inCu2O by forbidden resonant Raman scattering

The Raman-scattering spectrum of ${\mathrm{Cu}}_2$O at $4^{\mathrm{o}}$K was measured with a tunable cw dye laser as the exciting source. The dye laser was tuned to several hundred frequencies in the range 17 135-17 600 ${\mathrm{cm}}^{-1\mathrm{}}$ which spans the range of the excited states of the yellow exciton series. At each laser frequency, the cross section for normally forbidden Raman scattering from the strongest odd-parity phonons ${\Gamma }_{12}^{-}$ (109 ${\mathrm{cm}}^{-1\mathrm{}}$) and ${\Gamma }_{15}^{-\left(1\right)\mathrm{}}$ (LO, 154.5 ${\mathrm{cm}}^{-1\mathrm{}}$) was determined. The ${\Gamma }_{12}^{-}$ cross section increases dramatically when either the laser or the scattered light is resonant with excited $S$ or $D_1$ yellow exciton states. The location and polarization of these peaks in the cross section is entirely consistent with the quadrupole-dipole Raman-scattering mechanism which has previously been observed when the laser is resonant with the lowest $1S$ yellow exciton state. The dependence of the ${\Gamma }_{12}^{-}$ cross section on incident laser frequency thus provides a new spectroscopic technique for locating dipole-forbidden but quadrupole-permitted excitonic states without the application of symmetry-breaking perturbations such as electric fields. Interpretation of the resonance enhancement of the ${\Gamma }_{15}^{-\left(1\right)\mathrm{}}$ phonon feature is considerably more complicated. Extremely large enhancement of the LO (but not the TO) component was observed when the laser was tuned close to states previously identified as $3D_2$ and $4D_2$. We ascribe these resonances to an intraband double resonance mediated by the Fröhlich exciton-lattice interaction. We consider two potential microscopic models for those resonances: (i) optical quadrupole, dipole Fröhlich, optical dipole; (ii) optical dipole, quadrupole Fröhlich, optical dipole. The predicted behavior of these two models is compared with polarization measurements, and with the dependence of the Raman intensity on scattering angle, electric field, and laser frequency. It is found that neither model is consistent with all of the data.