Observation of collective excitations in MgZnO/ZnO two-dimensional electron systems by resonant Raman scattering

The neutral excitations in two-dimensional electron systems (2DES) confined at ${\mathrm{Mg}}_x{\mathrm{Zn}}_{1-x}\mathrm{O}/\text{ZnO}$ heterojunctions were studied by a resonant inelastic light scattering (ILS) technique. At zero magnetic field the ILS spectra of intra- and intersubband collective excitations are detected in the wavelength range close to the ZnO direct band gap. The intersubband spectrum is represented by collective modes of charge- and spin-density excitations along with single-particle excitation continuum. The energies of these excitations were characterized on the series of samples and shown to grow sublinearly with the two-dimensional electron density. The intrasubband 2D plasmon was observed at plasma frequency and its square-root momentum dispersion was ascertained. Strong electron-electron correlations are manifested in the energy structure of intersubband excitations. Depolarization and excitonic contributions to the charge- and spin-density excitation energies are extracted in the wide range of 2D-electron densities. The negative excitonic contribution dominates among the many-particle energy terms and results in an unusual hierarchy of 2DES intersubband collective excitation energies.

Figure 1

(a) The evolution of the ILS optical spectrum as the laser wavelength is tuned. The Raman line, marked by a dashed line, tracks the laser line in a parallel manner. Its intensity is enhanced in the region between 3664 and 3667 Å. PL features on the right side preserve their spectral positions irrespective of the photoexcitation conditions. The inset shows a magnified view of the spectrum for ${\lambda }_L=3646.8\text{Å}$ (outside the range of the main tableau). Both the SPE and the CDE Raman bands are present thereupon. (b) The profiles of resonant excitation for two Raman features CDE and SPE. Peak intensities of lines are plotted as a function of excitation laser wavelength. Data points to the left of a dashed vertical line are not shown on the waterfall of plot (a) due to a weak signal level. The arrow marks the position ${\lambda }_L=3646.8\text{Å}$, corresponding to the inset of panel (a).

Figure 2

Linearly polarized ILS spectra of intersubband collective excitations measured on sample 426 with $n_s=3.5\times {10}^{11}{\mathrm{cm}}^{-2}$. Two Raman features, CDE and SDE, have been tested at different configurations of linear polarizers. In plot legends $\left(\right|\left|\right)$ means that incident and detected light beams are collinearly polarized, and for $(\perp )$ spectra they are cross-polarized. The Raman feature CDE in panel (a) with a Raman shift of approximately 13 meV emerges exclusively in a collinear configuration of polarizers. According to the polarization selection rules, this is a true indication of the charge-density excitation. In contrast, the weak Raman feature at $\sim 10.9$ meV, seen in the PL background in panel (b), is observed in cross-polarized configuration only and is therefore identified as a signal from spin-density excitation. Note, that owing to different resonant conditions, spectra are taken at different absolute laser positions, indicated on the corresponding panels.

Figure 3

(a) The dispersion of the CDE and SDE measured for small values of in-plane momentum by varying the angle of the optical fibers with respect to the sample surface. The sketch in the inset illustrates momentum transfer to the 2DES in the light-scattering process. (b) The dispersion of the intrasubband 2D-plasmon excitation. The curve represents calculated values of the plasmon dispersion assuming $m^{*}=0.31m_0$ and ${\varepsilon }_{\text{ZnO}}=8.5$). The inset shows two Raman spectra of 2D plasmon recorded at different transferred momenta $k_{\left|\right|}=0.9 \times {10}^5{\mathrm{cm}}^{-1}$ and $k_{\left|\right|}=2.0 \times {10}^5{\mathrm{cm}}^{-1}$. The excitation laser wavelengths are ${\lambda }_L=3665.9\text{Å}$ and ${\lambda }_L=3663.63\text{Å}$, respectively.

Figure 4

(a) The energies of all three intersubband excitations measured on a set of MgZnO/ZnO heterostructures with varying electron density covering the range ${10}^{11}$–${10}^{12}{\mathrm{cm}}^{-2}$. Open and solid circles represent the energy of the CDE and SDE. Squares indicate the energy of the SPE mode. The inset illustrates the confinement potential and subband energy levels in MgZnO/ZnO heterostructures. (b) Magnitude of the exciton binding and depolarization energy contributions to the energy of the SDE and CDE intersubband excitation modes. The values are extracted from the data contained in Fig. 4.