Enhancement of electron and hole effective masses in back-gated $\mathrm{GaAs}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells

Both the electron and the optically created hole effective masses are found to be density dependent in a two-dimensional electron system of a $\mathrm{GaAs}∕{\mathrm{Al}}_{0.33}{\mathrm{Ga}}_{0.67}\mathrm{As}$ back-gated quantum well by magnetophotoluminescence spectroscopy. We show that the density-dependent electron effective mass increases with a decrease in the electron density $\left(n_s\right)$ to $n_s<1\times {10}^{11}{\mathrm{cm}}^{-2}$. It is found that the electron effective masses determined from the lowest and the second Landau levels are larger than those from the higher Landau levels. The hole effective mass is found to increase with a decrease in $n_s$ and the hole is found to localize at $n_s<3\times {10}^{10}{\mathrm{cm}}^{-2}$. We observe an upward convex curve of the photoluminescence peak energy at $2<\nu <3$ depending on the electron-hole distance divided by the magnetic length. These results clearly show the important roles of both electron-electron and electron-hole interactions in the recombination of a valence hole with a high-quality two-dimensional electron system.

Figure 1

Electron density dependence of the electron effective mass $m_{eT}^{*}$ obtained by Shubnikov–de Haas measurements. The values in the literature (Ref. 5) are also shown.

Figure 2

(Color online) Typical PL spectra at $n_s$=(a) $3.0\times {10}^{10}$ and (b) $9.4\times {10}^{10}{\mathrm{cm}}^{-2}$ at $B=0.4\mathrm{T}$. Landau-fan diagrams at $n_s$=(c) $3.0\times {10}^{10}$ and (d) $9.4\times {10}^{10}{\mathrm{cm}}^{-2}$. The best fitted lines are shown (solid lines). Data points indicating the average of the transition energies of the Zeeman split peaks are also shown (circles); they are included in the linear fitting procedure.

Figure 3

(a) Electron density dependence of the PL peak intensity in the vicinity of $\nu =1$ at $n_s$=0.86 (i), 1.2 (ii), 1.6 (iii), 2.3 (iv), 3.0 (v), 3.9 (vi), 5.1 (vii), and $6.3\times {10}^{10}{\mathrm{cm}}^{-2}$ (viii). An anomaly is observed at $\nu =1$ in the PL peak intensity. An anomaly at $\nu =4∕3$ (arrows) is also observed at (vii) and (viii). (b) Electron density dependence of the PL peak position between $\nu =2$ and 3, at $n_s=3.0$ (i), 3.9 (ii), 5.1 (iii), 6.3 (iv), 7.5 (v), and $9.4\times {10}^{10}{\mathrm{cm}}^{-2}$ (vi), showing the upward convex curve.

Figure 4

(Color online) (a) Electron density dependence of the electron effective masses $m_{e10}^{*}$ (i), $m_{e21}^{*}$ (ii), and $m_{e(1<\nu <2)}^{*}$ (iii), derived from fitting to the Landau-fan diagrams. The values in the literature (Ref. 15) are also shown (iv). (b) Electron density dependence of the hole effective mass $m_h^{*}$.