Experimental evidence of a Mott transition in highly doped two-dimensional confined structures

Mott transition in a two-dimensional electron gas in a doped $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ quantum well is experimentally studied. The impurity band is observed at a doping level up to ${10}^{18}{\mathrm{cm}}^{-3}$. This value is two orders of magnitude higher than the Mott transition in bulk GaAs (about ${10}^{16}{\mathrm{cm}}^{-3}$). This high density Mott transition is explained by a quantitative model involving the donor distribution in the wells.

Figure 1

Absorption spectra of sample 1 multi-QW structure for different temperatures (Dashed: $10\mathrm{K}$; Full: $60\mathrm{K}$; Dotted: $120\mathrm{K}$; Dash-dotted: $240\mathrm{K}$). Inset: Doped QW with the different energy levels; the gray area represents the impurity bands caused by the broadening of the impurity levels $1s$ and $2p_z$.

Figure 2

Left: Absorption spectra of the modulation-doped sample 3 for different temperatures (Dashed: $10\mathrm{K}$; Full: $60\mathrm{K}$; Dotted: $120\mathrm{K}$; Dash-dotted: $240\mathrm{K}$). Right: the absorption of sample 4 whose population is optically tuned for different pump powers (2, 5, 15, and $50\mathrm{mW}$) at $T=8\mathrm{K}$, corresponding to estimated carrier densities of $7\times {10}^9$, $1.7\times {10}^{10}$, $5\times {10}^{10}$, and $1.7\times {10}^{11}{\mathrm{cm}}^{-2}$, respectively.

Figure 3

Absorption spectra of $4\times {10}^{11}{\mathrm{cm}}^{-2}$ $\delta$-doped sample 2 for different temperatures (Dashed: $10\mathrm{K}$ Full: $60\mathrm{K}$; Dotted: $120\mathrm{K}$; Dash-dotted: $240\mathrm{K}$).

Figure 4

Left: Spectra of sample 5 multi-QW structure for different temperatures (Dashed: $10\mathrm{K}$; Full: $60\mathrm{K}$; Dotted: $120\mathrm{K}$; Dash-dotted: $240\mathrm{K}$). Right: Model calculation of the absorption spectra of sample 5 for different temperatures (Dashed: $10\mathrm{K}$; Full: $60\mathrm{K}$; Dotted: $120\mathrm{K}$; Dash-dotted: $240\mathrm{K}$). Middle: (dashed curves of left and right figures). Experiment and theory at $10\mathrm{K}$ for comparison (Dash-dotted: experiment; Full: theory)