Localization in random electron systems: ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ alloys and intentionally disordered $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ superlattices

The localization properties of single-particle and collective excitations were investigated in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ alloys and in intentionally disordered $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ superlattices by magnetoresistance and Raman scattering. It is shown that the Landau damping determines the localization length of the collective plasmonlike excitations in bulk ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ alloy, while the electrons are localized due to the alloy random potential. Meanwhile, the localization lengths of both the single-particle and collective excitations are limited by disorder in the intentionally disordered superlattices. In such a case, a comparison between the localization properties of the single-particle and collective excitations propagated in the same random potential is possible. The localization length of the individual electron is found to be considerably larger than the localization length of their collective excitations. This implies that the electron-electron interaction which is fundamental for the collective excitations increases localization. However, the difference between the localization of the single-particle and collective excitations decreases with the increasing disorder. Consequently, in clean electron systems the effect of the interaction on localization of elementary excitations is stronger. Additionally, a reasonable agreement has been found between the measured localization lengths for the single particle in the disordered superlattices and those numerically obtained from transfer matrix calculations.

Figure 1

Temperature dependences of the zero-field resistivities measured in the (a) insulating and (b) metallic ${\mathrm{Al}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{As}$ alloys. The full lines in panels (a) and (b) represent the calculated variable-range hopping resistivity and the resistivity due to the quantum interference effects, respectively.

Figure 2

Relative magnetoresistivities measured at $T=1.6\mathrm{K}$ in the metallic (M) and insulating (I) transport regimes in ${\mathrm{Al}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{As}$ alloys with $n=9.0\times {10}^{17}{\mathrm{cm}}^{-3}$ and $n=4.4\times {10}^{17}{\mathrm{cm}}^{-3}$, respectively.

Figure 3

Temperature dependences of the coherence lengths $L_{\phi }$ obtained in the metallic (closed circles) and insulating (open circles) ${\mathrm{Al}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{As}$ alloys with $n=9.0\times {10}^{17}{\mathrm{cm}}^{-3}$ and $n=4.4\times {10}^{17}{\mathrm{cm}}^{-3}$, respectively. The full line is the dependence calculated according to $T^{-2}$.

Figure 4

Localization lengths of the AlAs-like plasmon–LO-phonon collective excitations measured in differently doped insulating (I) and metallic (M) ${\mathrm{Al}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{As}$ alloys at $T=10\mathrm{K}$. The full line exhibits the decrease of the plasmon localization length caused by the interaction of the plasmons with the ionized impurities (Ref. 23). The dash line shows the dependence of the inverse characteristic wave number $\pi ∕k_c$ on the electron concentration. Typical Raman lines due to the AlAs-like LO phonons and the coupled mode in the insulating and metallic alloys, respectively, are shown in the corresponding insets together with the fitting data. A weak contribution caused by the forbidden LO phonons is seen in the heavily doped metallic alloy.

Figure 5

The full line in panel (a) shows the energy spectrum of the plasmons coupled to the AlAs-like LO phonons calculated in the ${\mathrm{Al}}_{0.11}{\mathrm{Ga}}_{0.89}\mathrm{As}$ alloy with the electron concentration $n=9.0\times {10}^{17}{\mathrm{cm}}^{-3}$. The dotted line represents the dispersion of the uncoupled plasmons. The dash line shows the spectrum of the single-particle electron excitations. The vertical dash-dotted line indicates the wave number of the light used for excitation. Panel (b) displays the calculated Raman intensity obtained by the fit of the experimental spectrum, as explained in the text.

Figure 6

Relative high field parallel magnetoresistance of the ${\left(\mathrm{Ga}\mathrm{As}\right)}_m{\left({\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.6}\mathrm{As}\right)}_6$ superlattice with the disorder strength ${\delta }_{\mathit{SL}}=0.82$ and the electron density $n=2.0\times {10}^{17}{\mathrm{cm}}^{-3}$ measured at $T=1.6\mathrm{K}$ with different orientations of the magnetic field (full lines) and the calculated magnetoresistances (dash lines).

Figure 7

Temperature dependences of the relative parallel (open circles) and vertical (closed circles) conductivities measured in the ${\left(\mathrm{Ga}\mathrm{As}\right)}_m{\left({\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.6}\mathrm{As}\right)}_6$ superlattices with the disorder strength ${\delta }_{\mathit{SL}}=0.4$ and the electron density $n=6.5\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 8

Temperature dependences of the phase-breaking time $\left({\tau }_{\phi \Vert }\right)$ and of the coherence length $\left(L_{\phi \Vert }\right)$ of the electrons propagated parallel to the layers in the ${\left(\mathrm{Ga}\mathrm{As}\right)}_m{\left({\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.6}\mathrm{As}\right)}_6$ superlattice with the disorder strength ${\delta }_{\mathit{SL}}=0.82$ and the electron density $n=2.0\times {10}^{17}{\mathrm{cm}}^{-3}$.

Figure 9

Localization lengths of (a) the single electrons and (b) their collective excitations measured in the ${\left(\mathrm{Ga}\mathrm{As}\right)}_m{\left({\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.6}\mathrm{As}\right)}_6$ superlattices with different disorder strengths and the fixed electron densities (a) $n=5.0\times {10}^{17}{\mathrm{cm}}^{-3}$ and (b) $n=1.7\times {10}^{18}{\mathrm{cm}}^{-3}$, respectively. Bars in panel (a) mark the interval containing the localization lengths obtained for a hundred different realizations of 50-period disordered superlattices; the inset shows the sample structure used for vertical transport measurements. The inset in panel (b) shows the localization lengths of the collective excitations obtained in the differently doped superlattices with the fixed disorder ${\delta }_{\mathit{SL}}=0.18$.