Effect of Raman scattering by coupled phonon-plasmon modes in magnetic fields

Raman scattering by coupled phonon-plasmon modes in high magnetic fields is considered theoretically. The calculations of the dielectric function were performed in the long-wave approximation for the semiclassical and limiting quantum magnetic fields taking into account the electron damping and intrinsic lifetime of optical phonons. Raman scattering has resonances at the frequencies of coupled modes as well as at multiples of the cyclotron frequency. The dependence of the Raman cross section on the carrier concentration is analyzed.

Figure 1

Frequencies of the phonon-plasmon coupled modes as functions of the cyclotron frequency for the carrier plasma frequency ${\omega }_{pe}=1.4$ and ${\omega }_{\mathrm{LO}}=1.1$; all frequencies are in units ${\omega }_{\mathrm{TO}}$. The solid lines are obtained in solution to the cubic equation (see text), the dotted lines show the results ignoring the $k$-dispersion.

Figure 2

The same as in Fig. 1 but for ${\omega }_{pe}=0.6$.

Figure 3

Calculated Raman spectra for the carrier plasma frequency and cyclotron frequency indicated on the curves. All the frequencies are in units ${\omega }_{\mathrm{TO}}$; the phonon width $\Gamma =3\times {10}^{-2}{\omega }_{\mathrm{TO}}$, the carrier relaxation rate ${\tau }^{-1}=2\times {10}^{-2}{\omega }_{\mathrm{TO}}$, the plasma frequency of ions ${\omega }_{pi}=0.4{\omega }_{\mathrm{TO}}$, and the momentum transfer $k{v}_F=0.3{\omega }_{\mathrm{TO}}$. The cyclotron frequency is supposed to be in the semiclassical regime.

Figure 4

The same as in Fig. 3 but for the carrier plasma frequency indicated, ${\tau }^{-1}={10}^{-2}{\omega }_{\mathrm{TO}}$, and for the limiting quantum regime.