Localization and the integer-quantized Hall effect: Diffusion constant for high Landau levels and white noise potential

The diffusion constant and the diagonal conductivity for non-interacting electrons in a two-dimensional, disordered system are studied. A homogeneous magnetic field perpendicular to the electron system is assumed. For weak short-range random potentials and high fields the Landau quantum numbern can be used as expansion parameter. In the limit of high Landau levels the system shows metallic behaviour. Corrections for finiten decrease the conductivity and indicate localized states in the whole energy band. A breakdown of the expansion and stronger localization are observed only for the lowest Landau levels if the typical experimental length scale of the quantized Hall effect is used.     

Optical Hall conductivity of systems with gapped spectral nodes

We calculate the optical Hall conductivity within the Kubo formalism for systems with gapped spectral nodes, where the latter have a power-law dispersion with exponent n. The optical conductivity is proportional to n and there is a characteristic logarithmic singularity as the frequency approaches the gap energy. The optical Hall conductivity is almost unaffected by thermal fluctuations and disorder for n = 1, whereas disorder has a stronger effect on transport properties if n = 2.     

Effect of bismuth on the electrical properties of Pb0.8Sn0.2Te thin films

D.C. conductivity and Hall coefficient studies were made on bismuth doped Pb_0.8Sn_0.2Te thin films in the temperature range 77–300 K. Hall coefficient and Hall mobility are found to decrease with the increase in doping density of bismuth. Films doped with even 0.3 at.% Bi changed fromp-type ton-type due to the donor action of bismuth in these films. Analysis of mobility-temperature data revealed that the lattice and defect scattering mechanisms are predominant in these films. Defect limited mobility is calculated for all the films and it is found to decrease with increase in doping concentration of bismuth suggesting the increase in defect density.     

Physical properties of n-CdGeAs2 single crystals prepared by low-temperature crystallization

The first results obtained in studies of the temperature dependences of electrical conductivity and Hall constant of n-CdGeAs₂ single crystals prepared by low-temperature crystallization are reported. It has been established that the method developed permits growing single crystals with a free-electron concentration ⋍(1−2)×10¹⁸ cm⁻³ and a Hall mobility ⋍10000 cm²/(Vs) at T=300 K. It is shown that the temperature dependence of Hall mobility exhibits a behavior characteristic of electron scattering by lattice vibrations, whereas below 150 K a deviation from this law is observed to occur evidencing an increasing contribution of static lattice defects to scattering. The Hall mobility in the crystals prepared was found to reach ⋍36000 cm²/(Vs) at 77 K. Photosensitive heterojunctions based on n-CdGeAs₂ single crystals were prepared. The spectral response of the photosensitivity of these structures is analyzed. It is concluded that this method is promising for preparation of perfect CdGeAs₂ crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1190–1193 (July 1999)     

Hall effect in hopping conduction in an ensemble of quantum dots

The Hall effect in heterostructures with a two-dimensional array of tunneling-coupled Ge quantum dots grown by molecular-beam epitaxy on Si is investigated. The conductivity of these structures in zero magnetic field at 4.2 K varies in the range of 10^?12?10^?4 Ω^?1, which includes both the diffusive transport under weak localization conditions and hopping conduction. It is shown that the Hall effect can be discerned against the magnetoresistance-related background in both high- and low-conductivity structures. The Hall coefficient in the hopping regime exhibits a nonmonotonic dependence on the occupancy of quantum dots by holes. This behavior correlates with that of the localization length of the hole wavefunctions.     

Transport properties of electrons in energy band tails

Transport properties of electrons in energy band tails of disordered semiconductors are studied experimentally using a material system in which (i) the width and shape of the band-tail are approximately known and (ii) the Fermi energy is controllable. The material is heavily-doped, closely-compensated, crystalline n-GaAs whose compensation ratio can be made arbitrarily close to unity by the use of two techniques that are described in detail. This control of the Fermi level through compensation permits the measurement of the transport properties of electrons at various energies in the band-tail.

Using band tails having a width of ～50 meV, measurements have been made of the temperature dependence of the d.c. conductivity and Hall coefficient, the frequency dependence of the a.c. conductivity and the electric field dependence of the d.c. conductivity (the last two at low temperatures).

The evidence demonstrates the progressively greater localization of states deeper in the tails. No sign is found of a sharp mobility edge. There is a number of close similarities to the properties of amorphous semiconductors but some significant differences. The frequency dependence of the a.c. conductivity at low temperatures is essentially identical with that of amorphous semiconductors in accord with the general interpretation that conductivity at low temperatures takes place by electron hopping among localized states near the Fermi energy. The detailed temperature dependence of the d.c. conductivity at low temperatures is log σ=σ ₀ exp [?(T ₀/T)^1/2], thus disagreeing with a theoretical expectation that the exponent for low temperature hopping conduction should be 1/4. At low temperatures, the electric field dependence of the conductivity shows a variation as σ～exp (bF/T) over a considerable range extending down to field strengths close to 1 V/cm. This closely resembles recent observations on amorphous semiconductors but the range of field strengths here is lower by several orders of magnitude.     

Localization length at the conductivity minima of the quantum Hall effect

The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length as a function of magnetic field at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that with the exponent between one and , depending on the model. In particular, for the “white-noise” random potential roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.     

Renormalized vertex modification of Hall conductivity for dilute magnetic alloys

By means of the renormalized vertex procedure for the motion of Green's function developed by the authors, the vertex function of magnetic alloys, based on thes-d exchange interaction, is solved exactly and the corresponding Hall conductivity tensors are obtained. It is found that the value of the renormalized Hall conductivity is (1+h ²)^–1 times less than that before the renormalization (hereh is a reduced magnetic field). It is shown that the renormalized modification of the conductivity is very important in the cases with not too weak external magnetic field and slow relaxation time.     

The Hall effect in La0.67Ba0.33MnO3

The Hall effect in polycrystalline barium-substituted lanthanum manganite La_0.67Ba_0.33MnO₃ has been investigated in the temperature interval 298<T<355 K. It is found that the anomalous Hall coefficient in this material is two orders of magnitude greater than the normal coefficient. At T ₀=333 K the normal Hall coefficient changes sign, which indicates a change in the type of conductivity. The temperature dependence of the normal Hall coefficient, electrical conductivity, and magnetoresistance is explained on the basis of the concept of motion of the mobility edge attendant as the temperature changes. Zh. éksp. Teor. Fiz. 113, 981–987 (March 1998)     

Bulk and surface electron transport in topological insulator candidate YbB6–δ

We report the study of transport and magnetic properties of the YbB_6–δsingle crystals grown by inductive zone melting. A strong disparity in the low temperature resistivity, Seebeck and Hall coefficients is established for the samples with the different level of boron deficiency. The effective parameters of the charge transport in YbB_6–δ are shown to depend on the concentration of intrinsic defects, which is estimated to range from 0.09% to 0.6%. The pronounced variation of Hall mobility μ_H found for bulk holes is induced by the decrease of transport relaxation time from τ ≈ 7.7 fs for YbB_5.994 to τ ≈ 2.2 fs for YbB_5.96. An extra contribution to conductivity from electrons with μ_H≈ –1000 cm² V^–1 s^–1 and the very low concentration n /n_Yb≈ 10^–6 discovered below 20 K for all the single crystals under investigation is suggested to arise from the surface electron states appeared in the inversion layer due to the band bending. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Gravitational Instability of a Rotating Viscous Thermally Conducting Plasma

This paper deals with the gravitational instability of an infinite homogeneous viscous rotating plasma of finite electrical conductivity in the combined presence of effects of Hall currents, finite Larmor radius (FLR) and thermal conductivity. The ambient magnetic field is assumed to be uniform and acting along the vertical direction. Both longitudinal and transverse modes of wave propagation have been studied. It is shown that Jean's criterion determines the gravitational instability even in the presence of the effects of thermal conductivity, viscosity, finite electrical conductivity, FLR, rotation and Hall currents. Further it is found that while FLR, viscosity and rotation have a stabilizing influence, both the thermal and the electrical conductivities have a destabilizing influence on the gravitational instability of a plasma.     

Preparation and properties of co-evaporated bismuth telluride [Bi2Te3] thin films

Thin films of bismuth telluride have been prepared by the reactive evaporation method. Film properties, such as conductivity, Hall effect, and thermoelectric power were studied in the temperature range from liquid nitrogen to 350 K. The films prepared were of n-type with a carrier concentration of 1.25 x 10²⁰ at room temperature. The temperature dependence of the Hall mobility is found to be T^?1.8 indicating lattice scattering.     

Transport properties of a and c axis oriented (Y1?xCax)Ba2Cu3Oy thin films

Anisotropy and Hall effect measurements have been performed in calcium-doped, i.e., overdoped YBa₂Cu₃O_y ((Y_1−xCa_x)Ba₂Cu₃O_y) thin films witha andc axis orientations. In highly overdoped films (x=0.4), the anisotropy of the normal resistivity decreases and a drastic change in Hall conductivity in the mixed state is observed. The change in Hall conductivity in the overdoped region is consistent with recent experimental results for La_2−xSr_xCuO₄ films and seems to be common in highT _c superconductors.     

Edge states and distributions of edge currents in semi-infinite graphene

The distributions of edge currents in semi-infinite graphene under a uniform perpendicular magnetic field are investigated. We show unambiguously that the edge current is finite at the armchair edge but vanishes at the zigzag edge. It is shown that the current density oscillates with the distance away from the boundary and tends to zero deep inside the graphene. The study shows that the total current is independent of edge configurations. The interplay of the bulk and edge contributions to the total current is presented. The quantized plateaus of Hall conductivity at (4e ²/h)(n+1/2) provide a direct evidence of the connection between the edge states and topological properties of relativistic fermions in a magnetic field.     

Weak localization corrections to the anomalous Hall effect

We calculate localization corrections to the anomalous Hall conductivity in the framework of side-jump and skew scattering mechanisms. In contrast to the ordinary Hall effect, there exists a nonvanishing localization correction to the anomalous Hall resistivity. The correction to the anomalous Hall conductivity vanishes in case of side-jump mechanism, but is nonzero for the skew scattering.     

New experimental results for electron transport in weak accumulation layers of ZnO crystals

Previous Hall measurements on (0001) and (0001&#x0304;) faces of ZnO have shown a Hall mobility oscillating as a function of Hall surface electron density in the range between N_SH=10⁶ and 10¹¹ cm^?2. Here we report on new results obtained by a field effect arrangement for free surfaces in UHV. With donors from H exposure or by illumination weak accumulation layers (n_sh <10¹¹ cm^?2) are established. The field effect shows oscillations in surface conductivity as a function of gate voltage. Also the combination of a field effect with a Hall effect measurement reveals discrete values of Hall surface electron density n_sh. Various pretreatments do not change the periodicity of these oscillations. Necessary preconditions are a temperature below 130 K, a Hall surface electron density below 3 × 10¹² cm^?2 and a source-drain field of a few V/cm. A model regarding impurity levels in the space charge layer relates the results of the field effect measurements to the results of the Hall effect measurements.     

Effect of the Landau level broadening on the quantum Hall conductance

Summary In a previous paper, Kliroset al. presented a model calculation of the Hall conductivity as a function of the Landau level broadening Γ for finite temperatures. In this paper, the effect of Landau-level broadening on the structure of the Hall conductivity is investigated. The experimental data regarding the Si-MOSFET and GaAs-heterostructure experiments are reproduced including a functional dependence of Γ on the magnetic field. The influence of the effectiveg-factor is considered as well.     

Magneto-optics of monolayer and bilayer graphene

The optical conductivity of graphene and bilayer graphene in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. Correspondences between the transition frequencies and the magneto-optical features are established using the theoretical results. The main optical transitions obey the selection rule Δn = 1 with the Landau number n. The Faraday rotation and light transmission in the quantizing magnetic fields are calculated. The effects of temperatures and magnetic fields on the chemical potential are considered.     

Quantum Hall Effect on the Hyperbolic Plane

In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between K-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case. Received: 17 March 1997 / Accepted: 24 April 1997     

Hall mobility and defect structure in undoped and Cr or Ti-doped CoO at high temperature

The conductivity and the Hall effect of pure CoO and of CoO doped with titanium or chromium have been measured. The measurements were done over a wide range of oxygen pressures and the range of temperatures was 988–1280°C. The Hall effect changes sign from p to n type near the phase boundary Co/CoO and the dopants move the point of changeover to higher oxygen pressure. We found that the Hall mobility of the electrons is between 0·36–0·6 cm²/V-sec with a tendency to rise with rising temperature. The Hall mobility of the holes is 0·06 cm²/V-sec, in agreement with previous work.