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)     

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)     

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.     

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.     

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.     

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)     

Temperature- and magnetic field dependence of the Hall effect in the heavy fermion system CeCu6

The temperature dependence of the Hall coefficient and the magnetic field dependence of the Hall resistivity of CeCu₆ have been determined in the temperature range 80 mK<T<10 K and in magnetic fields up to 10T. The Hall coefficientR _H shows a very strong temperature dependence with two extrema and a change of sign, and the Hall resistivity _xy has a strong field dependence with up to two changes of sign. The observed behavior can partially be explained by the field- and temperature dependence of the skew scattering contribution to the Hall coefficient.     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

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)     

Manganese energy level in <Emphasis Type="Italic">p</Emphasis>-InAs〈Mn〉 under pressure

Resistivity ρ and the Hall coefficient R _H at atmospheric pressure in the temperature range of 77–400 K and the dependences of these parameters (ρ(P) and R _H(P)) and magnetic susceptibility (χ(P)) on hydrostatic pressures of up to P ≤ 7 GPa at 300 K in p-InAs〈Mn〉 single crystals was investigated. The baric coefficients of the ionization energy of Mn impurity centers and the pressure dependence of the dielectric constant ɛ(P) were determined.     

Anomalous Hall effect in granular alloys

A theoretical study is performed of the anomalous Hall effect in granular alloys with giant magnetoresistance. The calculation is carried out within the Kubo formalism and the Green’s function method. The mechanism of asymmetric scattering of the spin-polarized current carriers is considered with allowance for a size effect associated with scattering not only by one grain, but also with more complicated processes of transport among two and three grains. It is shown that scattering of conduction electrons by the interfaces of the grains and the matrix has a substantial effect on the magnitude of the anomalous Hall effect and determines its sign. In general, correlation between the quantities ρ _H and ρ ² is absent, where ρ _H is the Hall resistivity and ρ is the total resistivity of the granular alloy. However, numerical calculation shows that for certain values of the model parameters ρ _H∼ρ ^3.8 and for these same parameter values the amplitude of the giant magnetoresistance reaches 40%, which is found to be in quantitative agreement with the experimental data for Co₂₀Ag₈₀ alloys [P. Xiong, G. Xiao, J. Q. Wang et al., Phys. Rev. Lett. 69, 3220 (1992)]. It is also shown that increasing the resistivity of the matrix leads to a significant growth in the anomalous Hall effect, and more substantial growth for alloys with small grain size, which is in good agreement with experiment [A. B. Pakhomov, X. Yan, and Y. Xu, J. Appl. Phys. 79, 6140 (1996); [X. N. Jing, N. Wang, and A. B. Pakhomov, Phys. Rev. B 53, 14032 (1996)]. Zh. éksp. Teor. Fiz. 112, 2198–2209 (December 1997)     

Magnetoresistivity and acoustoelectronic effects in a tilted magnetic field in <Emphasis Type="Italic">p</Emphasis>-Si/SiGe/Si structures with an anisotropic <Emphasis Type="Italic">g</Emphasis> factor

Magnetoresistivity ρ _xx and ρ _xy and the acoustoelectronic effects are measured in p-Si/SiGe/Si with an impurity concentration p = 1.99 × 10¹¹ cm⁻² in the temperature range 0.3–2.0 K and an tilted magnetic field up to 18 T. The dependence of the effective g factor on the angle of magnetic field tilt θ to the normal to the plane of a two-dimensional p-Si/SiGe/Si channel is determined. A first-order ferromagnet-paramagnet phase transition is observed in the magnetic fields corresponding to a filling factor ν = 2 at θ ≈ 59°–60°.     

The high-pressure-induced spin-reorientation transition in a ferromagnetic semiconductor Cd<Subscript>0.7</Subscript>Mn<Subscript>0.3</Subscript>GeAs<Subscript>2</Subscript>

The dependences of the longitudinal magnetoresistance (Δρ _zz /ρ₀)(P), transverse magnetoresistance (Δρ _xx /ρ₀)(P), and magnetic susceptibility (χ/χ₀(P)) on hydrostatic pressure P ≤ 7 GPa in the ferromagnetic semiconductor Cd_0.7Mn_0.3GeAs₂ at room temperature were investigated.     

Quantized Hall effect in disordered GaAs layers with 3D spectrum in tilted magnetic fields

The quantum Hall effect structure in the transverse magnetoresistance R _xx and the Hall resistance R _xy of heavily doped GaAs layers with a three-dimensional spectrum of the charge carriers is investigated for different field orientations. The characteristic structures (minima in R _xx and plateaus in R _xy ) shift much more slowly to higher fields and are suppressed much more rapidly in comparison with the expected angular dependence for a two-dimensional system. The results are discussed in terms of the anisotropic change of the three-dimensional conductivity tensor with magnetic field rotation. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 305–308 (25 August 1998)     

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     

Pressure-induced metamagnetic transition in the Cd<Subscript>0.7</Subscript>Mn<Subscript>0.3</Subscript>GeAs<Subscript>2</Subscript> ferromagnetic semiconductor

The magnetic susceptibility χ/χ₀ and the longitudinal Δρ _zz /ρ₀ and transverse Δρ _xx /ρ₀ magnetoresistances have been measured as functions of the hydrostatic pressure P ≤ 7 GPa at room temperature in the high-temperature ferromagnetic semiconductor Cd_0.7Mn_0.3GeAs₂ with a chalcopyrite structure and the Curie temperature T _c = 355 K. A pressure-induced metamagnetic transition from the low-magnetization state to the high-magnetization state has been observed in Cd_0.7Mn_0.3GeAs₂ near the magnetic ordering temperature. This transition is accompanied by the hysteresis of the magnetic susceptibility and magnetoresistance.     

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)     

Low-temperature resistivity of YBa2Cu3O6+x single crystals in the normal state

A scan of the superconductor-nonsuperconductor transformation in single crystals of YBa₂Cu₃O_6+x (x≈0.37) is done in two alternative ways, namely, by applying a magnetic field and by reducing the hole concentration through oxygen rearrangement. The in-plane normal-state resistivity ρ_ab obtained in the two cases is quite similar; its temperature dependence can be fitted by a logarithmic law in a temperature range of almost two decades. However, an alternative representation of the temperature dependence of σ_ab=1/ ρ _ab by a power law, typical for a 3D material near a metal-insulator transition, is also plausible. The vertical conductivity σ_c=1/ρ_c followed a power law, and neither σ_c(T), nor ρ_c(T) could be fitted by log T. It follows from the ρ_c measurements that the transformation at T=0 is split into two transitions: superconductor-normal-metal and normal-metal-insulator. In our samples, they are separated in oxygen content by Δx≈0.025. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 11, 834–839 (10 June 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Anomalous hall effect in HoB<Subscript>12</Subscript>

Within a wide temperature range of 1.8–300 K, the Hall effect in holmium dodecaboride is investigated. The measurements of the angular dependences of the Hall resistance ρ_H(φ, T, H) for HoB₁₂ performed in a high magnetic field up to 80 kOe at helium and intermediate temperatures made it possible to separate the normal and anomalous contributions to the Hall effect. Analysis of the anomalous component behavior in the paramagnetic and Néel phases suggests the appearance of the 5d-state magnetic polarization (the spin polaron effect) and makes it possible to compare the revealed features of the Hall coefficient R _H(T, H) with the H-T magnetic phase diagram of HoB₁₂.