arXiv subjects
Publications and source records attributed to S. S. Murzin.
Experimental data available in the literature on the diagonal resistivity of GaAs/AlGaAs heterostructures in a magnetic field at the filling factor 1/2 have been compared with the existing theoretical prediction [B. I. Halperin et al., Phys. Rev. B 47, 7312 (1993) and F. Evers et al., Phys. Rev. B 60, 8951 (1999)]. It has been found that the experimental results disagree with the prediction.
It is shown that the statements about the observation of the transitions between the insulating phase and the integer quantum Hall effect phases with the quantized Hall conductivity $σ_{xy}^{q}$ $\geq 3e^{2}/h$ made in a number of works are unjustified. In these works, the crossing points of the magnetic field dependences of the diagonal resistivity at different temperatures at $ω_{c}τ\approx 1$ have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative $dρ_{xx}/dT$ owing to the quantum corrections to the conductivity.
Experimental data available in the literature for peak values of the diagonal resistivity in the transitions between fractional quantum Hall states are compared with the theoretical predictions. It is found that the majority of the peak values are close to the theoretical values for two-dimensional systems with moderate mobilities.
In the fractional quantum Hall effect regime we measure diagonal ($ρ_{xx}$) and Hall ($ρ_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions, together with capacitance between 2DES and the gate. We observe 1/3- and 2/3-fractional quantum Hall effect at rather low magnetic fields where corresponding fractional minima in the thermodynamical density of states have already disappeared manifesting complete suppression of the quasiparticle energy gaps.
The temperature driven flow lines of the Hall and dissipative magnetoconductance data (σ_{xy},σ_{xx}) are studied in the fractional quantum Hall regime for a 2D electron system in GaAs/Al_{x}Ga_{1-x}As heterostructures. The flow lines are rather well described by a recent unified scaling theory developed for both the integer and the fractional quantum Hall effect in a totally spin-polarized 2D electron system which predicts that one (σ_{xy},σ_{xx}) point determines a complete flow line.
Reply to A. M. M. Pruisken and I. S. Burmistrov: cond-mat/0504763
With minima in the diagonal conductance G_{xx} and in the absolute value of the derivative |dG_{xy}/dB| at the Hall conductance value G_{xy}=e^{2}/h, spin-splitting is observed in the quantum Hall effect of heavily Si-doped GaAs layers with low electron mobility 2000 cm^2/Vs in spite of the fact that the spin-splitting is much smaller than the level broadening. Experimental results can be explained in the frame of the scaling theory of the quantum Hall effect, applied independently to each of the two spin subbands.
Oscillatory variations of the diagonal ($G_{xx}$) and Hall ($G_{xy}$) magnetoconductances are discussed in view of topological scaling effects giving rise to the quantum Hall effect. They occur in a field range without oscillations of the density of states due to Landau quantization, and are, therefore, totally different from the Shubnikov-de Haas oscillations. Such oscillations are experimentally observed in disordered GaAs layers in the extreme quantum limit of applied magnetic field with a good description by the unified scaling theory of the integer and fractional quantum Hall effect.
It is shown that recent and earlier experiments, which claimed to observe a disagreement with the global phase diagram (GPD) of the quantum Hall effect, do not, in fact, contradict the GPD. Two aspects should be taken into account: (i) insulating phases between quantum Hall phases are possible owing to the Shubnikov-de Haas oscillations of the "bare" diagonal resistivity $ρ_{xx}^{0}$; (ii) according to the two-parameter scaling theory, the filling factor $ν$ does not determine directly the positions of the quantum Hall phases on the magnetic field axis at $ω_{c}τ\lesssim 1$.
The temperature driven flow lines of the diagonal and Hall magnetoconductance data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers with different thicknesses. The flow lines are quantitatively well described by a recent universal scaling theory developed for the case of duality symmetry. The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator or the QHE state at low temperatures happens along a semicircle separatrix G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at (G_{xx},G_{xy})=(1,1).
We investigate the magnetoresistance of epitaxially grown, heavily doped n-type GaAs layers with thickness (40-50 nm) larger than the electronic mean free path (23 nm). The temperature dependence of the dissipative resistance R_{xx} in the quantum Hall effect regime can be well described by a hopping law (R_{xx} \propto exp{-(T_0/T)^p}) with p=0.6. We discuss this result in terms of variable range hopping in a Coulomb gap together with a dependence of the electron localization length on the energy in the gap. The value of the exponent p>0.5 shows that electron-electron interactions have to be taken into account in order to explain the occurrence of the quantum Hall effect in these samples, which have a three-dimensional single electron density of states.
In a recent preprint cond-mat/9906450 (published in PRL 84, 3141 (2000)) Bodo Huckestein showed that at real experimental conditions it is not possible to observe the quantum Hall effect (QHE) at $ω_{c}τ<1$ predicted by Khmelnitskii ($ω_{c}=eB/m$ is the cyclotron frequency and $τ$ is the scattering time). We would like to point out here that in fact the situation is not so hopeless due to the influence of the electron-electron interaction.
It is shown that the observed Quantum Hall Effect in epitaxial layers of heavily doped n-type GaAs with thickness (50-140 nm) larger the mean free path of the conduction electrons (15-30 nm) and, therefore, with a three-dimensional single-particle spectrum is induced by the electron-electron interaction. The Hall resistance R_xy of the thinnest sample reveals a wide plateau at small activation energy E_a=0.4 K found in the temperature dependence of the transverse resistance R_xx. The different minima in the transverse conductance G_xx of the different samples show a universal temperature dependence (logarithmic in a large range of rescaled temperatures T/T_0) which is reminiscent of electron-electron-interaction effects in coherent diffusive transport.