Interband electron Raman scattering in a quantum wire in a transverse magnetic field

Electron Raman scattering (ERS) is investigated in a parabolic semiconductor quantum wire in a transverse magnetic field neglected by phonon-assisted transitions. The ERS cross section is calculated as a function of a frequency shift and magnetic field. The process involves an interband electronic transition and an intraband transition between quantized subbands. We analyze the differential cross section for different scattering configurations. We study selection rules for the processes. Some singularities in the Raman spectra are found and interpreted. The scattering spectrum shows density-of-states peaks and interband matrix elements maxima and a strong resonance when the scattered frequency equals the “hybrid” frequency or confinement frequency depending on the light polarization. Numerical results are presented for a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum wire.

Figure 1

The Raman spectra of the parabolic quantum wire in the $X$ scattering configuration for $H=0$. The diameter $d$ of the quantum wire is $2000\mathrm{\AA }$. The incident radiation frequency $\hslash {\nu }_0=1.68\mathrm{eV}$. The positions of the singularities are defined by Eqs. (A22, A23). Resonant electron-hole transitions are indicated by $N_{1h},N_{1e},N_{2h},N_{2e}$.

Figure 2

Same that in Fig. 1 for $H=8\mathrm{T}$.

Figure 3

Same that in Fig. 1 for $H=16\mathrm{T}$.

Figure 4

The Raman spectra for the $Z$ scattering configuration for the magnetic fields $H=8\mathrm{T}$. Other parameters coincide with those of Figs. 1, 2, 3.

Figure 5

The Raman spectra for the $Z$ scattering configuration for the magnetic fields $H=16\mathrm{T}$. Other parameters coincide with those of Figs. 1, 2, 3.