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The compressibility Χ of dilute two-dimensional electron and hole gases in GaAs semiconductor structures has been studied in the ranges of the interaction parameter r s = 1-2.5 and r s = 10-30 for the electron and hole system, respectively. Nonmonotonic dependence of Χ -1 with an upturn at low carrier densities is observed. Despite the large difference in r s the behavior of Χ -1 in both systems can be accurately described by the theory of nonlinear screening of disorder by the carriers.

Charge density waves are thought to be common in two-dimensional electron systems in quantizing magnetic fields. Such phases are formed by the quasiparticles of the topmost occupied Landau level when it is partially filled. One class of charge density wave phases can be described as electron solids. In weak magnetic fields (at high Landau levels) solids with many particles per unit cell - bubble phases - predominate. In strong magnetic fields (at the lowest Landau level) only crystals with one particle per unit cell - Wigner crystals - can form. Experimental identification of these phases is facilitated by the fact that even a weak disorder influences their dc and ac magnetotransport in a very specific way. In the ac domain, a range of frequencies appears where the electromagnetic response is dominated by magnetophonon collective modes. The effect of disorder is to localize the collective modes and to create an inhomogeneously broadened absorption line, the pinning mode. In recent microwave experiments pinning modes have been discovered both at the lowest and at high Landau levels. We present the theory of the pinning mode for a classical two-dimensional electron crystal collectively pinned by weak impurities. We show that long-range Coulomb interaction causes a dramatic line narrowing, in qualitative agreement with the experiments., Comment: 6 pages, 3 figures. To be presented at EP2DS-15, Nara, Japan. One typo corrected

Activated dissipative conductivity σxx = σ*xxexp(−Δ/T) and the activated deviation of the Hall conductivity from the precise quantization δσxy = σxy −ie2/h= σ*xyexp(−Δ/T) are studied in a plateau range of the quantum Hall effect. The prefactors σ*xx and σ*xy are calculated for the case of a long-range random potential in the framework of a classical theory. There is a range of temperatures T1 ≪ T ≪ T2 where σ*xy = e2/h. In this range σ*xy ≈ (e2/h)(T/T2)80/21 ≪ σ*xx. At large T ≫ T2, on the other hand, σ*xy = e2/h and σ*xx = (e2h)(T2T)10/13 ≪ σ*xy. Similar results are valid for a fractional plateau near the filling factor p/q if charge e is replaced by e/q.

The Hall conductivity $\sigma_{\rm xy}$ of a two-dimensional electron system is quantized in units of $e^2/h$ when the Fermi level is located in the mobility gap between two Landau levels. We consider the deviation of $\sigma_{\rm xy}$ from a quantized value caused by the thermal activation of electrons to the extended states for the case of a long range random potential. This deviation is of the form $\sigma_{\rm xy}^*\exp(-\Delta/T)$. The prefactor $\sigma_{\rm xy}^*$ is equal to $e^2/h$ at temperatures above a characteristic temperature $T_2$. With the temperature decreasing below $T_2$, $\sigma_{\rm xy}^*$ decays according to a power law: $\sigma_{\rm xy}^* = \frac{e^2}{h}(T/T_2)^\gamma$. Similar results are valid for a fractional Hall plateau near filling factor $p/q$ if $e$ is replaced by the fractional charge $e/q$., Comment: 4 pages in PostScript (figures included)

The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length ξ as a function of magnetic field B at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that ξ∝B−α with the exponent α between one and 10 3 , depending on the model. In particular, for the “white-noise” random potential ξ roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.