Related papers: Metal insulator transition in modulated quantum Ha…
We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…
Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
Quantum spin Hall insulators, recently realized in HgTe/(Hg,Cd)Te quantum wells, support topologically protected, linearly dispersing edge states with spin-momentum locking. A local magnetic exchange field can open a gap for the edge…
Recent experiments in the integer quantum Hall regime seem to find direct transitions from a quantum Hall state with Hall conductance $\sigma_{xy} = n e^2/h $ with integer $n > 1$, to an insulating state in weak magnetic fields. We study…
Microscopic processes giving the energy gain and loss of a two-dimensional electron system in long-range potential fluctuations are studied theoretically at the breakdown of the quantum Hall effect in the case of even-integer filling…
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…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…
The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…
The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice system. We consider a Gaussian correlated random potential, study the behaviour of the current carrying states and trace their…
The reentrant integer quantum Hall effects (RIQHE) are due to formation of electronic crystals. We show analytically and numerically that topological textures in the charge density distribution in these crystals in the vicinity of charged…
The mixing of states with {\it opposite chirality} in quantum Hall system is shown to have delocalization effect. It is possible that extended states may form bands because of this mixing, as is shown through a numerical calculation on a…
A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
A two-layer system coupled via tunneling and with different carrier masses in each layer is investigated in the integer quantum Hall regime. Striking deviations of the one-layer Hall conductivity from the usual quantization are found, if…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…