Ballistic transport under quantum Hall effect conditions

The paper addresses details of the single-particle electron spectrum ?_l(p)${?}_l(p)$ in narrow Coulomb channels (l is the transverse spectrum part discrete index and p   is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?_l(p)${?}_l(p)$ are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?_F≥?ω_c${?}_F\ge \mathit{?}{\omega }_c$, the spectrum ?_l(p)${?}_l(p)$ first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?_F${?}_F$ is the Fermi energy of the 2D electron system ?ω_c$\mathit{?}{\omega }_c$ is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?_F≤?ω_c${?}_F\le \mathit{?}{\omega }_c$. Calculated results are compared with available experimental data.     

On the quantum Hall effect

We consider a particle in a 2 dimensional plane in a periodic potential and a homogeneous magnetic field perpendicular to the plane. Kubo's expression for conductivity of the Hall current is an integer.

This result of Thouless, Kohomoto, Nightingale and den Nijs is interpreted geometrically.     

Edge states tunneling in the fractional quantum Hall effect: integrability and transport

This is a short review of nonperturbative techniques that have been used in the past 5 years to study transport out of equilibrium in low dimensional, strongly interacting systems of condensed matter physics. These techniques include massless factorized scattering, the generalization of the Landauer Büttiker approach to integrable quaisparticles, and duality. The case of tunneling between edges in the fractional quantum Hall effect is discussed in details. To cite this article: H. Saleur, C. R. Physique 3 (2002) 685–695.     

Correlation-induced resonances in transport through coupled quantum dots

We investigate the effect of local electron correlations on transport through parallel quantum dots. The linear conductance as a function of gate voltage is strongly affected by the interplay of the interaction U and quantum interference. We find a pair of novel correlation-induced resonances separated by an energy scale that depends exponentially on U. The effect is robust against a small detuning of the dot energy levels and occurs for arbitrary generic tunnel couplings. It should be observable in experiments on the basis of presently existing double-dot setups.     

Interlayer transport in bilayer quantum Hall systems

Bilayer quantum Hall systems have a broken symmetry ground state at a filling factor which can be viewed either as an excitonic superfluid or as a pseudospin ferromagnet. We present a theory of interlayer transport in quantum Hall bilayers that highlights remarkable similarities and critical differences between transport in Josephson junction and ferromagnetic metal spin-transfer devices. Our theory is able to explain the size of the large but finite low-bias interlayer conductance and the voltage width of this collective transport anomaly.     

From semiclassical transport to quantum Hall effect under low-field Landau quantization

The crossover from the semiclassical transport to the 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 positive magnetoresistance to refine the SdH theory.     

Imaging of Coulomb-driven quantum Hall edge states

The edges of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime are divided into alternating metallic and insulating strips, with their widths determined by the energy gaps of the QHE states and the electrostatic Coulomb interaction. Local probing of these submicrometer features, however, is challenging due to the buried 2DEG structures. Using a newly developed microwave impedance microscope, we demonstrate the real-space conductivity mapping of the edge and bulk states. The sizes, positions, and field dependence of the edge strips around the sample perimeter agree quantitatively with the self-consistent electrostatic picture. The evolution of microwave images as a function of magnetic fields provides rich microscopic information around the ν=2 QHE state.     

Ohm's law in the quantum Hall effect

The linearity of the Hall currents as functions of the voltage is investigated. We consider interacting electrons on a torusT ₂. They are subjected to a strong perpendicular magnetic field and a smooth but disordered substrate potential. In a moving frame of reference the Hamiltonian is time-dependent due to the constantly shifted substrate. Assuming a small energy gap separating the lowlying subspace, adiabatic expansion is used to construct a solution. Its general properties allow to calculate the Hall currents. Any power-law corrections to linearity are absent. The reliability of the result is assessed by estimates of the parameter controlling the expansion which is asymptotic.     

Spin-orbit scattering in the quantum Hall effect

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing, while the intrachannel potential is periodic (non-random); the channels represent two spin states. We consider channel mixing as function of the energy separation of the two extended states, and show that the phase diagram is different from the standard quantum Hall diagram for random intrachannel potential.     

Vortex drag in the quantum Hall effect

A new model of momentum and electric field transfer between two adjacent 2D electron systems in the quantum Hall effect is proposed. The drag effect is due to momentum transfer from the vortex system of one layer to the vortex system of another layer. The remarkable result of this approach is a periodic change of sign of the dragged electric field as a function of the difference between the layer filling factors. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 4, 276–279 (25 February 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.