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The antiferromagnetic (AF) model is generalized for the quasielectron system composed of identical ionic-covalent dimers. The density-fluctuation and covalent-correlation operators are constructed based on the extended AF density matrices, and the quasielectron system is decomposed into 4-level subsystems for the electron ionization and affinity. By considering the nearest-neighbor hopping near the covalent limit, we can see the importance of the bonding coefficients to the effective mass of the excited carrier in the crystal of the zincblende structure., Comment: 26 pages, 4 figures

Magneto-transport measurements are performed on two-dimensional GaAs electron systems to probe the quantum Hall (QH) effect at low magnetic fields. Oscillations following the Shubnikov-de Haas (SdH) formula are observed in the transition from the insulator to QH liquid when the observed almost temperature-independent Hall slope indicates insignificant interaction correction. Our study shows that the existence of SdH oscillations in such a transition can be understood based on the non-interacting model., Comment: 17 pages

We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas (2DEG) containing self-assembled InAs dots and compare the results with recent theoretical predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase transitions are presented, the former collapsing to the latter with decreasing gate voltage and/or decreasing spin-splitting. The experimental results support a recent theory, based on modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting., Comment: 22 pages

We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator-quantum Hall transition with increasing the perpendicular magnetic field. However, such a transition does not correspond to the onset of strong localization. The temperature dependences of the Hall resistivity and Hall conductivity reveal the importance of the electron-electron interaction effects to the observed transition in our study., Comment: 9 pages, 4 figures

The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the mobility gap shows the importance of quantum localization effects. Moreover, the Lifshitz-Kosevich formula can survive as the oscillating amplitude becomes large enough for the deviation to the Dingle factor. The crossover from the semiclassical transport to the description of quantum diffusion is discussed. From our study, the difference between the mobility and cyclotron gaps indicates that some electron states away from the Landau-band tails can be responsible for the semiclassical behaviors under low-field Landau quantization., Comment: 14 pages, 6 figures

The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and involve assumptions about disorder, localized states, extended states, edge states, Fermi levels pinned by Landau levels, etc. These standard narratives give plausible reasons for the existence of the plateaus, but provide little in the way of even a qualitative understanding of the shape and width of the Hall plateaus, much less a first principles calculation. The injection model presented in this paper changes that situation. Rather than focusing on the middle of the Hall device, we follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients. We find the entire resistivity curve including the Hall plateaus is calculable as a function of magnetic field, temperature, and current. The new higher current experiments reported here show remarkable half integer features for the first time; these are faithfully reproduced by the injection theory. The Hall plateaus and half integer inflections are shown to result from the local density of states appropriate to the magnetic field and the strong electric field gradient at the injection corner., Comment: 12 pages, 4 figures

Magneto-transport measurements are performed on the two-dimensional electron system (2DES) in an AlGaAs/GaAs heterostructure. By increasing the magnetic field perpendicular to the 2DES, magnetoresistivity oscillations due to Landau quantisation can be identified just near the direct insulator-quantum Hall (I-QH) transition. However, different mobilities are obtained from the oscillations and transition point. Our study shows that the direct I-QH transition does not always correspond to the onset of strong localisation., Comment: 11 pages, 7 figures

By applying a magnetic field perpendicular to GaAs/AlGaAs two-dimensional electron systems, we study the low-field Landau quantization when the thermal damping is reduced with decreasing the temperature. Magneto-oscillations following Shubnikov-de Haas (SdH) formula are observed even when their amplitudes are so large that the deviation to such a formula is expected. Our experimental results show the importance of the positive magneto-resistance to the extension of SdH formula under the damping induced by the disorder., Comment: 9 pages, 3 figures

Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows the features of the $\Gamma$(2) modular symmetry, which includes distorted flowlines and shiftted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quantization. [B. P. Dolan, Phys. Rev. B 62, 10278.] Universal scaling is found under the reduction of the modular symmetry. It is also shown that the Hall conductivity could still be governed by the scaling law when the semicircle law and the scaling on the longitudinal conductivity are invalid. *corresponding author:yhchang@phys.ntu.edu.tw, Comment: The revised manuscript has been published in J. Phys.: Condens. Matter

The crossover from the semiclassical transport to quantum Hall effect is studied by examining a two-dimensional electron system in an AlGaAs/GaAs heterostructure. By probing the magneto-oscillations, it is shown that the semiclassical Shubnikov-de Haas (SdH) formulation can be valid even when the minima of the longitudinal resistivity approach zero. The extension of the applicable range of the SdH theory could be due to the damping effects resulting from disorder and temperature. Moreover, we observed plateau-plateau transition like behavior with such an extension. From our study, it is important to include the positive magnetoresistance to refine the SdH theory., Comment: 11 pages, 5 figures

A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B ${\bf 70}$ 125324] It is proven in this paper that both the positivity and Pauli's exclusion principle are preserved under this equation when there exists an upper bound for the transition rate. Such an equation can be generalized to model BCS-type quasiparticles, and is reduced to a Markoff master equation of Lindblad form in the low-density limit with respect to particles or holes., Comment: 25 pages. It is discussed in the revised manuscript how to prove the trace invariance. Some details are incorporated in the appendixes

We have performed low-temperature transport measurements on a GaAs two-dimensional electron system at low magnetic fields. Multiple temperature-independent points and accompanying oscillations are observed in the longitudinal resistivity between the low-field insulator and the quantum Hall (QH) liquid. Our results support the existence of an intermediate regime, where the amplitudes of magneto-oscillations can be well described by conventional Shubnikov-de Haas theory, between the low-field insulator and QH liquid., Comment: Magneto-oscillations governed by Shubnikov-de Haas theory are observed between the low-field insulator and quantum Hall liquid

Magnetic-field-induced phase transitions in the integer quantum Hall effect are studied under the formation of paired Landau bands arising from Zeeman spin splitting. By investigating features of modular symmetry, we showed that modifications to the particle-hole transformation should be considered under the coupling between the paired Landau bands. Our study indicates that such a transformation should be modified either when the Zeeman gap is much smaller than the cyclotron gap, or when these two gaps are comparable., Comment: 8 pages, 4 figures

We have obtained a set of coupled differential equations from the continuous limit of the transfer matrix method. Decoupling such a set of equations yields an extension to the Wentzel-Kramers-Brillouin (WKB) approximation for the Schr\"{o}dinger equation with the position-dependent effective mass (PDEM). In the classically allowed region, the decoupling is to ignore the reflection resulting from the variations of both the potential and effective mass. By considering an infinite-well example with the PDEM, it is shown that the extended WKB approximation can provide not only an estimation to eigenenergies, but also an analytic form to approximate wavefunctions., Comment: 10 pages, 3 figures, and 1 table. The revised manuscript has been accepted by Chinese Journal of Physics

We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor $\nu=4$ on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the $\nu=4$ quantum Hall state directly from the low-field insulator, the two-dimensional system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall conductor transition., Comment: Our experimental results are inconsistent with Huckestein's argument [PRL 84, 3141 (2000)]

By extending the mean-field Hamiltonian to include nonhermitian operators, the master equations for fermions and bosons can be derived. The derived equations reduce to the Markoff master equation in the low-density limit and to the quasiclassical master equation for homogeneuos systems., Comment: 17 pages

Plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions are observed in the two-dimensional electron system in an AlGaAs/GaAs heterostructure. At high fields, the critical conductivities are not of the expected universal values and the temperature-dependence of the width of the P-P transition does not follow the universal scaling. However, the semicircle law still holds, and universal scaling behavior was found in the P-P transition after mapping it to the I-QH transition by the Landau-level addition transformation. We pointed out that in order to get a correct critical exponent, it is essential that the scaling analysis must be performed near the critical point. And with proper analysis, we found that the P-P transition and the insulator quantum Hall conductor transitions are of the same universal class., Comment: 11 pages, 3 figures

A quantum master equation of the Lindblad form is obtained in this paper by considering the spontaneous wave-packet reduction. Different classical equations can be derived after exactly mapping such a quantum master equation to a continuous time random walk (CTRW). Although this CTRW is a quasiclassical walk, the effects due to the quantum interference can still be important in such a walk. Macroscopically, we shall consider the uncertainty of the potential and determine the effective transition probability by a family of Schr\"{o}dinger equations (or operators)., Comment: Relevant topics such as quantum trajectories and a localization model are discussed in the revised manuscript

We have performed low-temperature transport experiments on a Si/SiGe hole system. The measured transverse and longitudinal condductivities $\sigma_{xx}$ and $\sigma_{xy}$ allow us to study the magnetic-field-induced transitions in the system. In particular, we present the first study of the temperature-driven flow lines in the "anomalous Hall insulator" regime near a Landau level filling factor $\nu=1.5$. The "anomalous" temperature-driven flow lines could be due to the unusual energy level scheme in a Si/SiGe hole system. Moreover, for $3<\nu<5$, there is a temperature-independent point in $\rho_{xx} (B)$, $\rho_{xy} (B)$, $\sigma_{xx}$, and $\sigma_{xy}$ which corresponds to a boundary of the quantum phase transition., Comment: We correct the errors about the formats for figures in the PDF file

It is shown in this paper that the quantum master equation can be mapped to a modified continuous time random walk (CTRW) if the relaxation term is composed of transitions over a set of states. When the Hamiltonian is time-independent and transitions are between its eigenlevels, such a modified CTRW reduces to the Markovian walk equivalent to the Pauli master equation. On the other hand, the memory in such a modified CTRW is composed of a temporal factor and the probability determined by the Liouville flow when the relaxation term is reduced as a special dephasing term., Comment: Replaced with improvements