Inter-layer Hall effect in double quantum wells subject to in-plane magnetic fields

We report on a theoretical study of the transport properties of two coupled two-dimensional electron systems subject to in-plane magnetic fields. The charge redistribution in double wells induced by the Lorenz force in crossed electric and magnetic fields has been studied. We have found that the redistribution of the charge and the related inter-layer Hall effect originate in the chirality of diamagnetic currents and give a substantial contribution to the conductivity.Comment: 7 RevTex pages, 4 figures, appendix added and misprint in Eq. (11) correcte

Longitudinal conductivity and transverse charge redistribution in coupled quantum wells subject to in-plane magnetic fields

In double quantum wells electrons experience a Lorentz force oriented perpendicular to the structure plane when an electric current is driven perpendicular to the direction of an in-plane magnetic field. Consequently, the excess charge is accumulated in one of the wells. The polarization of a bilayer electron system and the corresponding Hall voltage are shown to contribute substantially to the in-plane conductivity.Comment: 3 pages, 2 figure

Hall plateau diagram for the Hofstadter butterfly energy spectrum

We extensively study the localization and the quantum Hall effect in the Hofstadter butterfly, which emerges in a two-dimensional electron system with a weak two-dimensional periodic potential. We numerically calculate the Hall conductivity and the localization length for finite systems with the disorder in general magnetic fields, and estimate the energies of the extended levels in an infinite system. We obtain the Hall plateau diagram on the whole region of the Hofstadter butterfly, and propose a theory for the evolution of the plateau structure with increasing disorder. There we show that a subband with the Hall conductivity $n e^2/h$ has $|n|$ separated bunches of extended levels, at least for an integer $n \leq 2$. We also find that the clusters of the subbands with identical Hall conductivity, which repeatedly appear in the Hofstadter butterfly, have a similar localization property.Comment: 9 pages, 12 figure

Magnetoresistance of a two-dimensional electron gas with spatially periodic lateral modulations: Exact consequences of Boltzmann's equation

On the basis of Boltzmann's equation, and including anisotropic scattering in the collision operator, we investigate the effect of one-dimensional superlattices on two-dimensional electron systems. In addition to superlattices defined by static electric and magnetic fields, we consider mobility superlattices describing a spatially modulated density of scattering centers. We prove that magnetic and electric superlattices in $x$-direction affect only the resistivity component $\rho_{xx}$ if the mobility is homogeneous, whereas a mobility lattice in $x$-direction in the absence of electric and magnetic modulations affects only $\rho_{yy}$. Solving Boltzmann's equation numerically, we calculate the positive magnetoresistance in weak magnetic fields and the Weiss oscillations in stronger fields within a unified approach.Comment: submitted to PR

Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations

We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an entirely different system -- 3D metals applied with weak external periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic potentials interferes with Landau's quantization due to an applied magnetic field \Vec{B}, resulting generally in fractal energy gaps as a function of the tilting angle of \Vec{B}, for which the accompanying quantized Hall tensors are computed. The phenomenon arises from the fact that, while the present system has a different physical origin for the butterfly from the 3D tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure

Two-component model of a spin-polarized transport

Effect of the spin-involved interaction of electrons with impurity atoms or defects to the transport properties of a two-dimensional electron gas is described by using a simplifying two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points within a conduction channel. The used limit of the short-range interaction allows to solve the relevant scattering problem exactly. By varying the model parameters different transport regimes of two-terminal devices with ferromagnetic contacts can be described. In a quasi-ballistic regime the resulting difference between conductances for the parallel and antiparallel orientation of the contact magnetization changes its sign as a function of the length of the conduction channel if appropriate model parameters are chosen. The effect is in agreement with recent experimental observations.Comment: 4 RevTeX pages with 4 figure

Thermohydrodynamics in Quantum Hall Systems

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. A model of these flux densities due to hopping and drift processes is introduced for a random potential varying slowly compared to both the magnetic length and the phase coherence length. The flux measured in the standard transport experiment is derived and is used to define a transport component of the flux density. The equations of conservation can be written in terms of the transport component only. As an illustration, the theory is applied to the Ettingshausen effect, in which a one-dimensional spatial variation of the electron temperature is produced perpendicular to the current.Comment: 10 pages, 1 figur

Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice

The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New method of calculation of the Hall conductance in a 2D hole gas described by the Luttinger Hamiltonian and affected by lateral periodic potential is proposed, based on the investigation of four-component wavefunction singularities in k-space. The deviations from the quantization rules for Hofstadter "butterfly" for electrons are found, and the explanation of this effect is proposed. For the case of strong periodic potential the mixing of magnetic subbands is taken into account, and the exchange of the Chern numbers between magnetic subands is discussed.Comment: 12 pages, 5 figures; reported at the 15th Int. Conf. on High Magnetic Fields in Semicond. Phys. (Oxford, UK, 2002

Phase Diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions

We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a parameter space of the transfer energies and the magnetic field for the appearance of Hofstadter's butterfly spectrum in anisotropic crystals in 3D. (ii) We show that the orientation of the external magnetic field can be arbitrary to have the 3D butterfly. (iii) We show that the butterfly is beyond the semiclassical description. (iv) The required magnetic field for a representative organic metal is estimated to be modest ($\sim 40$ T) if we adopt higher Landau levels for the butterfly. (v) We give a simpler way of deriving the topological invariants that represent the quantum Hall numbers (i.e., two Hall conductivity in 3D, $\sigma_{xy}, \sigma_{zx}$, in units of $e^2/h$).Comment: 8 pages, 8 figures, eps versions of the figures will be sent on request to [email protected]

Duality and integer quantum Hall effect in isotropic 3D crystals

We show here a series of energy gaps as in Hofstadter's butterfly, which have been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for anisotropic three-dimensional (3D) periodic systems in magnetic fields \Vec{B}, also arise in the isotropic case unless \Vec{B} points in high-symmetry directions. Accompanying integer quantum Hall conductivities $(\sigma_{xy}, \sigma_{yz}, \sigma_{zx})$ can, surprisingly, take values $\propto (1,0,0), (0,1,0), (0,0,1)$ even for a fixed direction of \Vec{B} unlike in the anisotropic case. We can intuitively explain the high-magnetic field spectra and the 3D QHE in terms of quantum mechanical hopping by introducing a ``duality'', which connects the 3D system in a strong \Vec{B} with another problem in a weak magnetic field $(\propto 1/B)$.Comment: 7 pages, 6 figure