Selection and jump rules in electronic Raman scattering from $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ artificial atoms

A theoretical description of electronic Raman scattering from $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ artificial atoms under the influence of an external magnetic field is presented. Raman spectra with laser excitation energy in the interval $E_{\text{gap}}-30\mathrm{meV}$ to $E_{\text{gap}}$ are computed in the polarized and depolarized geometry. The polarization ratios for the collective and single-particle excitations indicate a breakdown of the Raman polarization selection rules once the magnetic field is switched on. A Raman intensity jump rule at the band gap is predicted in our calculations. This rule can be a useful tool for identifying the physical nature (charge or spin) of the electronic excitations in quantum dots in low magnetic fields.

Figure 1

(Color online) Monopolar excitation spectrum of the dot.

Figure 2

(Color online) Polarized and depolarized Raman spectra at $B=0$ and $1\mathrm{T}$. The incident laser energy is $h{\nu }_i=E_{\text{gap}}-2.5\mathrm{meV}$.

Figure 3

(Color online) The collective Raman peaks at $B=4.5\mathrm{T}$ as $h{\nu }_i$ approaches the band gap.

Figure 4

(Color online) Squared Raman amplitudes related to the (a) CDE and (b) ${\mathrm{SDE}}_1$ in the polarized geometry vs the external magnetic field.

Figure 5

(Color online) The same as Fig. 4, but for the (a) $\mathrm{SPE}{\left(\mathrm{C}\right)}_1$ and (b) $\mathrm{SPE}{\left(\mathrm{S}\right)}_1$ peaks.