The conductivity of a two-dimensional electronic system of finite width in the presence of a strong perpendicular magnetic field and a random potential

Starting from the Kubo formula the conductivity tensor of a two-dimensional electronic system in a perpendicular magnetic field is evaluated. It is shown that at zero temperature only the states at the Fermi level contribute. The Hall conductivity of a purely periodic system of finite width is calculated and compared with earlier suggestions by Thouless et al. For a system described by a periodic and a random potential the Hall conductivity is calculated as a function of the electron density. The results emphasize the importance of disorder independent current carrying states for the Quantum Hall effect which extend along the boundaries of the system. The plateaux values of the Hall conductivity are related to the number of these states, and are independent of the existence of extended bulk states below the Fermi energy.     

Growth and characterization of single crystals of the quaternary TlGaSeS compound

The electrical conductivity and Hall effect for TlGaSeS crystals have been investigated over a wide temperature range. The crystals we used are grown by a modified Bridgman technique and possess p-type conductivity. The energy gap has been found to be 1.63 eV, whereas the ionization energy is 0.25 eV. The variations of the Hall mobility as well as the carrier concentration with temperature have been investigated. The scattering mechanisms of the carrier are checked over the whole investigated temperature range. Furthermore, the diffusion coefficient, relaxation time, and diffusion length of holes are estimated.     

Lattice electrons on a cylinder surface in the presence of rational magnetic flux and disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.     

On the topological explanation of the integer quantum hall effect

We investigate the static and dynamic Kubo Hall conductivity of a non-interacting electron system in a random potential on a torus. Considering the universal covering space of the torus the Bloch theorem is applied for rational values of the filling factor. The localisation is simulated by the assumption of bound states. The Hall conductivity at zero temperatur is shown to be topologically quantized, if the Fermi energy lies in a spectral gap or in a localisation regime. The relation to previous formulations of the topological approach to the integer quantum Hall effect (QHE) is discussed.     

Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties

The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field as well as uniform suction and injection applied perpendicular to the parallel plates. A numerical solution for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature-dependent viscosity and thermal conductivity on both velocity and temperature distributions is examined.     

On the invariance of the 2d Hall conductivity for integer fillings

A system of independent electrons interacting with an arbitrary number of fixed point scatterers on the surface of an infinitely long cylinder is considered. It is shown that (at zero temperature) the equilibrium Byers-Yang Hall current takes the same value as for free electrons if the Fermi energy lies in an energy gap.     

Charge and spin Hall conductivity in metallic graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity sigma(xy)(SH). In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to sigma(xy)(SH) values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.     

Ab initio calculation of the intrinsic spin Hall effect in semiconductors

Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge, GaAs, and AlAs is large [approximately 100(planck/e)(Omega cm)(-1)], showing the possibility of a spin Hall effect beyond the four-band Luttinger Hamiltonian. The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller, indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors. Furthermore, it is found that the spin Hall effect can be strongly manipulated by strains, and that the ac spin Hall conductivity is large in pure as well as doped semiconductors.     

Geometric invariants of the quantum Hall effect

We study the two-dimensional Hall effect with a random potential. The Hall conductivity is identified as a geometric invariant associated with an algebra of observables. Using the pairing betweenK-theory and cyclic cohomology theory, we identify this geometric invariant with a topological index, thereby giving the Hall conductivity a new interpretation.Supported in part by the National Science Foundation under Grant No. DMS-8717185     

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.     

Theory of hopping and multiple-trapping transport in disordered systems

We present a general theory to describe equilibrium as well as nonequilibrium transport properties of systems in which the carriers perform an incoherent motion that can be described by means of a set of master equations. This includes hopping as well as trapping in the localized energy region of amorphous or perturbed crystalline semiconductors. Employing the mathematical analogy between the master equations and the tight binding problem we develop approximation schemes using methods of many-particle physics to derive expressions for the averaged propagator of the carriers and the conductivity tensor. The calculated conductivity and Hall conductivity of hopping systems compare extremely well to computer simulations over the whole range of frequency, density, and temperature. We are able to derive expressions for dispersive transport in hopping as well as trapping systems that contain the results of earlier theories of Scher, Montroll and Noolandi, Schmidlin as special cases and establish criteria for the occurrence of dispersive transport in such systems. We find that in principle hopping can lead to dispersive transport if the times and densities are very low, but actual experimental data are more easily explained in terms of multiple trapping.     

Modular invariance,universality and crossover in the quantum Hall effect

An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall states, a generalisation of the law of corresponding states from rational filling factors to complex conductivity, which has a mathematical expression in terms of an action of the modular group on the upper-half complex conductivity plane. This symmetry implies universality in quantum Hall crossovers. The assumption that the β-function for the complex conductivity is a complex analytic function, together with some experimental constraints, results in an analytic expression for the crossover, as a function of the external magnetic field.     

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.     

Theory of the phonon Hall effect in paramagnetic dielectrics

Based upon Raman spin-lattice interaction, we propose a theoretical model for the phonon Hall effect in paramagnetic dielectrics, which was discovered recently in an experiment [C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phys. Rev. Lett. 95, 155901 (2005).]. The phonon Hall effect is revealed to be a phonon analogue to the anomalous Hall effect in electron systems. The thermal Hall conductivity is calculated by using the Kubo formula. Our theory reproduces the essential experimental features of the phonon Hall effect, including the sign, magnitude, and linear magnetic field dependence of the thermal Hall conductivity.     

Integer quantum Hall effect on an interface with disclinations

The Hall conductivity of an electron gas on an interface showing topological defects as disclinations in the presence of an orthogonal constant magnetic field is investigated. This kind of defect induces either positive or negative singular curvature in the medium. It is shown that the positive curvature decreases the quantum Hall plateau widths and shifts the steps in the Hall conductivity to lower magnetic fields. In contrast, the negative one leaves to the existence of two types of plateaus, one with higher widths and the other one with lower widths in comparison to the flat case. In this case, the shift in the steps of the Hall conductivity goes to higher magnetic fields. We also investigate the Hall conductivity for electrons around a cylindrically symmetric distribution of disclinations and it turns out that it is the same as that corresponding to a single effective disclination.     

Anomalous Hall effect of heavy holes in III-V semiconductor quantum wells

The anomalous Hall effect of heavy holes in semiconductor quantum wells is studied in the intrinsic transport regime, where the Berry curvature governs the Hall current properties. Based on the first--order perturbation of wave function the expression of the Hall conductivity the same as that from the semiclassical equation of motion of the Bloch particles is derived. The dependence of Hall conductivity on the system parameters is shown. The amplitude of Hall conductivity is found to be balanced by a competition between the Zeeman splitting and the spin--orbit splitting.     

Screw dislocation-induced influence of transverse modes on Hall conductivity

The Hall conductivity of an electron gas on an interface showing a topological defectcalled screw dislocation is investigated. This kind of defect induces a singular torsionon the medium which in turn induces transverse modes in the quantum Hall effect. It isshown that this topology decreases the plateaus’ widths and shifts the steps in the Hallconductivity to lower magnetic fields. The Hall conductivity is neither enhanced nordiminished by the presence of this kind of defect alone. We also consider the presence oftwo defects on a sample, a screw dislocation together with a disclination. For a specificvalue of deficit angle, there is a reduction in the Hall conductivity. For an excess ofangle, the steps shift to higher magnetic fields and the Hall conductivity is enhanced.Our work could be tested only in common semiconductors but we think it opens a road to theinvestigation on how topological defects can influence other classes of Hall effect.     

Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.     

Electronic-transport properties of unhydrogenated amorphous gallium arsenide

Summary Hall mobility, μ_H, and electrical conductivity, σ, of unhydrogenated amorphous-gallium-arsenide films, prepared by r.f. sputtering, have been measured. Conductivity as a function of temperature shows a variable-range hopping mechanism atT<260 K, while at high temperature, conductivity and Hall mobility are both thermally activated. The results are interpreted in terms of the presence of defect complexes due to an excess of Ga. The stoichiometry and the structure of the films are used to explain the behaviour and the values of μ_H. The values of the activation energy of the conductivity seem in agreement with theoretical calculations on the position of electronic states created by defect complexes in the mobility-gap of a-GaAs.     

Electrical properties of bilayer heterojunctions in a strong magnetic field

The electrical properties of bilayer heterojunctions in a strong magnetic field at low temperatures have been considered. It has been shown that both the ohmic and Hall conductivities decrease exponentially due to the formation of neutral pairs if the electric fields in the two layers are parallel. In the antiparallel fields, the Hall conductivity is still determined by the activation energy of the excited electrons and decreases exponentially, but the ohmic conductivity decreases much slower, proportional to the temperature square.