Quantum Hall effect in the bulk semiconductors bismuth and antimony tellurides: Proof of the existence of a current-carrier reservoir

The quantization of the Hall resistivity ρ_xy in the form of plateaus in the dependence of ρ_xy on the magnetic field B is observed in the semiconductors Bi₂Te₃ and Sb₂Te₃; the minima of the transverse magnetoresistivity ρ_xx correspond to the start of the plateaus. The quantization of ρ_xy is due to the presence of a current-carrier reservoir. An impurity band with a high density of states or a different band with a much higher current-carrier effective mass serves as the reservoir. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 11, 754–758 (10 December 1999)     

Thermal conductivity and thermal Hall effect in Bi- and Y-based high-T c superconductors

Measurements of the thermal conductivity (k_xx) and the thermal Hall effect (k_xy) in high magnetic fields in Y- and Bi-based high-T _c superconductors are presented. We describe the experimental technique and test measurements on a simple metal (niobium). In the high-T _c superconductors k_xx and k_xy increase below T _c and show a maximum in their temperature dependence. k_xx has contributions from phonons and quasiparticle (QP) excitations, whereas k_xy is purely electronic. The strong increase of k_xy below T _c gives direct evidence for a strong enhancement of the QP contribution to the heat current and thus for a strong increase of the QP mean free path. Using k_xy and the magnetic field dependence of k_xx we separate the electronic thermal conductivity ( k _xx ^el ) of the CuO ₂ -planes from the phononic thermal conductivity ( k _xx ^ph ). In YBa₂Cu₃O _{7 - δ} k _xx ^el shows a pronounced maximum in the superconducting state. This maximum is much weaker in Bi₂Sr₂CaCu₂O _{8 + δ} , due to stronger impurity scattering. The maximum of k _xx ^el is strongly suppressed by a magnetic field, which we attribute to the scattering of QPs on vortices. An additional magnetic field independent contribution to the maximum of k_xx occurs in YBa₂Cu₃O _{7 - δ} , reminiscent of the contribution of the CuO-chains, as determined from the anisotropy in untwined single crystals. Our data analysis reveals that below T _c as in the normal state a transport (τ) and a Hall ( ) relaxation time must be distinguished: The inelastic (i.e. temperature dependent) contribution to τ is strongly enhanced in the superconducting state, whereas displays the same temperature dependence as above T _c . We determine also the electronic thermal conductivity in the normal state from k_xy and the electrical Hall angle. It shows an unusual linear increase with temperature. Received 23 August 2000     

Weak-field Hall resistance and effective carrier density measurements across the metal-insulator transition in Si-MOS structures

The weak-field Hall voltage in Si-MOS structures with different mobility is studied on both sides of the metal-insulator transition. In the vicinity of the critical density on the metallic side of the transition, the Hall voltage is found to deviate by 6–20 % from its classical value. The deviation does not correlate with the strong temperature dependence of the diagonal resistivity ρ _xx (T). In particular, the smallest deviation in R _xy is found in the highest-mobility sample, which exhibits the largest variation in the diagonal resistivity ρ _xx with temperature. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 48–52 (10 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Quantum corrections to the conductance of n-GaAs films in a strong magnetic field

The conductance of doped n-GaAs films is studied experimentally as a function of magnetic field and temperature in strong magnetic fields right up to the quantum limit (ħω_c = E _F). The Hall conductance G _xy is virtually independent of temperature T until the transverse conductance G _xx is quite large compared with e ²/h. In strong fields, when G _xx becomes comparable to e ²/h, G _xy starts to depend on T. The difference between the conductances G _xx at the two temperatures 4.2 and 0.35 K depends only weakly on the magnetic field H over a wide range of magnetic fields, while the conductances G _xx themselves vary strongly. The results can be explained by quantum corrections to the conductance as a result of the electron-electron interaction in the diffusion channel. The possibility of quantization of the Hall conductance as a result of the electron-electron interaction is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 201–206 (10 February 1998)     

Hopping conductivity and activated transport in InxGa1-xAs quantum wells

We present measurements of the diagonal R_xx and off-diagonal R_xy magnetoresistance under quantum Hall conditions on several high electron mobility transistors (HEMT) based on In_xGa_1-xAs quantum wells. From the magnetoresistance tensor we obtain the longitudinal conductivity σ _xx . We study the transport mechanisms near the σ _xx minima at temperatures ranging between 2 K and 35 K; activated transport is the dominant mechanism for temperatures above 7 K while variable range hopping conductivity is significant for lower temperatures. We show that electron-electron correlations should be taken into account to explain the conductivity vs temperature behaviour below 5 K. Finally, we study the behaviour of the localization length as a function of Landau level filling and obtain a critical exponent γ = 3.45±0.15. Received 6 June 2001 and Received in final form 16 October 2001     

Bistability of quantum magnetotransport in a multilayer Ge/p-Ge1−x Six heterostructure with wide potential wells

Two metastable states of a multilayer Ge/p-Ge_1−x Si_x heterosystem with wide (∼ 35 nm) potential wells (Ge) are observed in strong magnetic fields B at low temperatures. In the first state, the Hall resistivity exhibits an inflection near the value ρ_xy=h/e ² scaled to one Ge layer. The longitudinal magnetoresistivity ρ_xx(B) possesses a minimum in the range of fields where this inflection occurs. The temperature evolution of the inflection in ρ_xy(B), the minimum of ρ _xx(B), and the value of ρ_xy at the inflection indicates a weakly expressed state of the quantum Hall effect with a uniform current distribution over the layers. In the second metastable state, an unusually wide plateau near h/2e ² with a very weak field dependence is observed in ρ_xy(B). Estimates show that in these samples the Fermi level lies below but close to the top of the inflection in the bottom of the well. For this reason, the second state can be explained by separation of a hole gas in the Ge layers into two sublayers, and the saturation of ρ_xy(B) near h/2e ² can be explained by the formation of a quantum Hall insulator state. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 290–297 (25 August 1999)     

Magnetoresistance and Hall effect in La0.8Sr0.2MnO3

A comparative study of the longitudinal ρ _xx and transverse ρ _xy resistivities and magnetic susceptibility χ _ac of La_0.8Sr_0.2MnO₃ single crystals and ceramic samples has been conducted in a wide range of temperatures T=1.7–370 K and magnetic fields, H=0–13.6 T. It turned out that the relation ρ _xy ∼ρ _xx , which is expected to hold in the case of carrier scattering by magnetic fluctuations, applies to the single crystals. In polycrystals, an additional H-dependent contribution to the resistivity tentatively attributed to plane (near grain boundaries) and bulk “defects” of the magnetic sublattice has been detected. The scattering of carriers by these defects does not make a notable contribution to the anomalous Hall effect and magnetic susceptibility χ _ac. As a result, the curve of ρ _xy versus ρ _xx seems to be steeper than a linear dependence. Under the assumption that the materials under investigation are metals with constant carrier concentrations, the conductivity σ=1/ρ _xx due to the critical magnetic scattering calculated in the molecular field approximation reproduces the main features of experimental data, namely, the drop in the amplitude and shift of the resistivity peak near the Curie point with increasing magnetic field H and also a relatively slow change in the derivative dσ/dH with increasing temperature in the region T⩽T _C . The large hole concentration of about two per unit cell derived from Hall measurements indicates that carriers of opposite signs can coexist in these materials. Zh. éksp. Teor. Fiz. 116, 671–683 (August 1999)     

Anomalous Hall effect in granular Fe/SiO2 films in the tunneling-conduction regime

It is established that the Hall effect in Fe/SiO₂ nanocomposite films in the activational tunneling conduction range is anomalous, i.e., the Hall resistivity ρ_h is proportional to the magnetization and is due to the spin-orbit interaction. The parametric coupling of the Hall and longitudinal (ρ_xx) resistances ρ_h ∝ ρ _xx ^m (with temperature as the parameter) is characterized by a much lower value of the exponent m than in a uniform ferromagnetic metal. This circumstance is attributed to the characteristic features of the Hall effect mechanism in the hopping regime — in our case, the interference of the amplitudes of tunneling transitions in a set of three granules. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 87–92 (25 July 1999)     

Fractional quantum Hall effect at a suppressed energy gap

In the fractional quantum Hall effect regime, the diagonal (ρ_xx) and Hall (ρ_xy) magnetoresistivity tensor components of the two-dimensional electron system (2DES) in gated GaAs/Al_xGa_1−x As heterojunctions are measured together with the capacitance between 2DES and the gate. The 1/3-and 2/3-fractional quantum Hall effects are observed at rather low magnetic fields where the corresponding fractional minima in the thermodynamic density of the states have already disappeared, thus, implying the suppression of the quasiparticle energy gaps. The text was submitted by the authors in English.     

New type of conductivity?

Experiments yielded rapid rise in the Hall gr_xy and magnetoresistance ρ_xx, ρ_zz in Hg_0.76Cd_0.24Te to almost linear dependence in strong magnetic fields. This paper relates it to the states, which are extended at the Hall edge for ρ_xy and between the Hall edges for ρ_xx, ρ_zz, while bulk states are localized. Theory agrees with experiments, and suggests that thin enough samples may have zero magnetoresistance in strong enough magnetic fields.     

高温超导体霍尔电阻和霍尔角在涡旋玻璃相变附近的普适标度律及统一霍尔电阻方程

发现了一个钉扎效应影响霍尔电阻ρ_xy和霍尔角θ_H的普适标度律. 同时,根据纵向电阻ρ_xx的扩展幂律形式和对霍尔电导σ_xy的微观分析,给出了一个对有一次或多次霍尔反号的高温超导体都适用的霍尔电阻方程. 关键词： 高温超导体 涡旋玻璃相变 普适标度律 霍尔电阻方程     

Bilayer counterflow transport at filling factor 1 in the strong interacting regime

We review magneto-transport properties of interacting GaAs bilayer hole systems, with very small inter-layer tunneling, in a geometry where equal currents are passed in opposite directions in the two, independently contacted layers (counterflow). In the quantum Hall state at total bilayer filling ν=1 both the longitudinal and Hall counterflow resistances tend to vanish in the limit of zero temperature, suggesting the existence of a superfluid transport mode in the counterflow geometry. As the density of the two layers is reduced, making the bilayer more interacting, the counterflow Hall resistivity (ρ_xy) decreases at a given temperature while the counterflow longitudinal resistivity (ρ_xx), which is much larger than ρ_xy, hardly depends on density. Our data suggest that the counterflow dissipation present at any finite temperature is a result of mobile vortices in the superfluid created by the ubiquitous disorder in this system.     

The mystery of the alkali metals; the induced anomalous Hall effect in thin Cs films

Sandwiches made from Fe and Cs films are investigated as a function of the magnetic field and the Cs thickness. Conduction electrons which cross from the Fe to the Cs are marked by a drift velocity component perpendicular to the electric field. The anomalous Hall effect in the Fe provides this “non-diagonal” kick to the electrons that cross from the Fe into the Cs. The ballistic propagation of the conduction electrons can be monitored as a function of the Cs film thickness. The free propagation into the Cs is measured in terms of the non-diagonal conductance L_xy which we denote as the “induced anomalous Hall conductance”L _xy ⁰. For a normal (non-magnetic) metal in contact with Fe, L_xy increases with the thickness of the normal metal until the film thickness exceeds (half) the mean free path of the conduction electrons. For Cs on top of Fe the induced anomalous Hall conductance increases up to a Cs coverage of about 100 A, then, in contrast to other non-magnetic metals, L _xy ⁰ decreases for larger Cs coverage and approaches zero. This behavior cannot be explained with the free electron model. The strange behavior of the induced AHC in Cs films adds an even more challenging mystery to the already poorly understood properties of thin Cs films. These results defy explanation in the free electron model. Received 29 April 1999 and Received in final form 10 July 1999     

Zero differential resistance in a double quantum well at high filling factors

The differential resistance r _xx in a GaAs double quantum well with two occupied size-quantization subbands have been studied at temperatures T = 1.6–4.2 K in magnetic fields B < 0.5 T. It has been found that differential resistance r _xx vanishes at the maxima of magneto-intersubband oscillations with an increase in the direct current I _dc. It has been shown that the discovered r _xx ≈ 0 state appears under the condition 2R _c E _H/ħω_c < 1/2, where R _c is the cyclotron radius of electrons at the Fermi level, E _H is the Hall electric field induced by the current I _dc, and ω_c is the cyclotron frequency.     

On the distribution of a current in hall medium with metallical inclusions

Hall (σ_xx=0, σ_xy=const, where σ_ik is the conductivity tensor) medium with metallic inclusions is considered. The current (fields) distribution in such medium is established. It is shown that the electric field vanishes in the inclusion of a metallic phase and consequently the electric current streamlines miss these inclusions. The effective characteristics of the medium are calculated.     

Magneto-intersubband zener tunneling in a wide GaAs quantum well at high filling factors

The dependence of the differential resistance r _xx on the dc current density J _dc in a wide GaAs quantum well with two occupied size quantization subbands has been investigated at the temperature T = 4.2 K in the magnetic fields B < 1 T. A peak, whose position is given by the relation 2R _c eE _H = ħω_c/2, where R _c is the cyclotron radius, E _H is the Hall electric field, and ω_c is the cyclotron frequency, has been observed in the r _xx (J _dc) curves at high filling factors. The experimental results are attributed to Zener tunneling of electrons between the Landau levels of different subbands.     

On the phase boundaries of the integer quantum Hall effect. Part II

It has been shown that the observation of the transitions between the dielectric phase and the integer-quantum-Hall-effect phases with the quantized Hall conductivity σ _xy ^q ≥ 3e ²/h announced in a number of works is unjustified. In these works, the crossing points of the magnetic-field dependence of the diagonal resistivity ρ _xx at different temperatures T and ω_cτ = 1 have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative dρ _xx /dT owing to the quantum corrections to the conductivity. Here, ω_c = eB/m is the cyclotron frequency, τ is the transport relaxation time, and m is the effective electron mass.     

Topological insulators based on the semi-metallic HgCdTe

The review of peculiarity of growth and experimental results of the magneto-transport measurements (longitudinal magneto-resistance R_xx and the Hall resistance R_xy) over a wide interval of temperatures for several samples of Hg_1?xCd_xTe (x ≈ 0.13–0.15) grown by MBE is presented in this paper. An amazing temperature stability of the SdH-oscillation period and amplitude is observed in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behaviour of the Hall resistance was shown in the same temperature interval. These peculiarities of the R_xx and R_xy for strained thin layers are interpreted using quantum Hall conductivity (QHC) on topologically protected surface states (TPSS). In the case of not strained layers it is assumed that the QHC on the TPSS contributes also to the conductance of the bulk samples. The experimental results on magneto-transport (QHC and SdH) obtained for the strained 100 nm thickness Hg_1?xCd_xTe layer are interpreted on the basis of the 8 × 8 kp model and an advantage of the Hg_1?xCd_xTe as topological insulators is shown. This article is an expanded version of the scientific reports presented at the International Conference on Semiconductor Nanostructures for Optoelectronics and Biosensors 2016 ICSeNOB2016, May 22–25, 2016, Rzeszow, Poland.     

The fractional quantum hall effect under hydrostatic pressure

We report on experiments performed on a high quality, high carrier concentration heterostructure at a range of hydrostatic pressures. At a pressure of 1 bar a clear _xx minimum and Hall plateau were observed associated with a fractional state while no such structure was observed for the fractional state. At increasing pressure however structure in the resistivity components _xx and _xy for the state became increasingly pronounced. As the disorder in the sample and the measured activation energy for the state remained relatively unchanged with increasing pressure we speculate that the enhancement of the state with increasing pressure is due to an increase in the energy gap for this state.     

Optical and magnetooptical properties of granular alloys with giant magnetoresistance in the IR region of the spectrum

The features of the optical and magnetooptical properties of granular alloys with giant magnetoresistance in the IR region are examined in reference to the magnetorefractive effect and the equatorial Kerr effect. Calculations are performed within the semiclassical approximation with consideration of spin-dependent scattering in the bulk of the granules and on their surfaces (interfaces). The expressions obtained for σ _xx(ω) and σ _xy(ω) are found to be sensitive to scattering on the surfaces and in the bulk of the granules, as well as to granule size, the type of impurities trapped on the interfaces, the frequency of the incident light, and the external magnetic field. For granular thin films exhibiting giant magnetoresistance, the theory predicts significant relative changes in the optical reflection and transmission coefficients when the sample is magnetized to saturation (0.02% and 20%, respectively, for giant magnetoresistance of the order of 20%), as well as Kerr and Faraday effects that are nonlinear with respect to magnetization. Zh. éksp. Teor. Fiz. 116, 1762–1769 (November 1999)