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)     

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.     

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)     

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 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)     

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)     

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 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)     

Resistivity peak values at the transition between fractional quantum hall states

Experimental data available in the literature for peak values of the diagonal resistivity in the transitions between the fractional quantum Hall states (ρ _xx ^max ) are compared with the theoretical predictions. It is found that the majority of the peak values are close to the theoretical values for two-dimensional systems with moderate mobilities. The text was submitted by the author in English.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (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     

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     

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)     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

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°.     

Thermally activated dissipative conductivity in the fractional quantum Hall effect regime

Experimental investigations of thermally activated dissipative conductivity σ_xx in the fractional quantum Hall effect at filling factors v=1/3 and near zero were performed with GaAs/AlGaAs heterojunction based field-effect transistors with an electronic channel. To within our accuracy of 10%, the pre-exponential factor measured for v=1/3 is equal to 2e*2/h (e*=e/3 is the charge of the quasiparticles), the value expected for the case when the quasielectrons and quasiholes make the same contribution to the conductivity. The observed change in the temperature dependence of the conductivity when n deviates from 1/3 is associated with the change in the filling of the energy levels of the quasielectrons and quasiholes and indicates that there is no gap in the quasiparticle density of states averaged over the sample. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 67–72 (10 January 1996)     

Electronic topological transition in an <Emphasis Type="Italic">n</Emphasis>-BiSb semiconductor alloy in the quantum limit range of magnetic fields for H‖<Emphasis Type="Italic">C</Emphasis><Subscript>2</Subscript>

The galvanomagnetic properties of single-crystal samples of the Bi_0.93Sb_0.07 semiconductor alloy with the electron density n = 1.6 × 10¹⁷ cm⁻³ in magnetic fields up to 14 T at T = 1.6 K have been investigated. The resistivity ρ and Hall coefficient R have been measured as functions of the magnetic field directed along the binary axis of a crystal for a current flowing through a sample along the bisector axis; i.e., the components ρ₂₂ and R _{32, 1} have been measured. The strong anisotropy of the electron spectrum of the samples makes it possible to separately observe quantum oscillations of the magnetoresistance ρ₂₂(H) for H ‖ C ₂ in low magnetic fields for two equivalent ellipsoids with small extremal cross sections (secondary ellipsoids) and in high magnetic fields for electrons of the ellipsoid with a large extremal cross section (main ellipsoid). An increase in the energy of the electrons of secondary ellipsoids in the quantum limit magnetic fields is accompanied by the flow of electrons to the main ellipsoid; i.e., an electronic topological transition occurs from the three-valley electron spectrum to the single-valley one. After the flow stops, the Fermi energy E _F increases from 18 meV to 27.8 meV. With an increase in the quantizing magnetic field, the Fermi energy of the electrons decreases both in the region of quantum oscillations of the resistance that are attributed to the electrons of the secondary ellipsoids and in the region of oscillations associated with the electrons of the main ellipsoid. The Hall coefficient R _{32, 1} decreases in high magnetic fields; this behavior indicates the absence of the electron magnetic freezing effect.     

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.     

Influence of magnetic field on the superconducting transition in a Nd1.82Ce0.18CuO4−δ film

The temperature and magnetic-field dependences of the resistivity ρ and Hall effect R(j‖ab, B‖c) in a Nd_1.82Ce_0.18CuO_4−δ single crystal film (T _c =6 K) is investigated at temperatures 1.4≤T≤20 K and magnetic fields 0≤B≤5.5 T. At the lowest temperature T=1.4 K the resistive state (exhibiting resistivity and the Hall effect) arises in a magnetic field B=0.5 T. A transition to the normal state is completed at B _c 2≃3 T, where the Hall coefficient becomes nearly constant. The negative magnetoresistance due to the weak-localization effect in the normal state is observed for B>3 T. The nonmonotonic behavior and the inversion of the sign of R(B) in the mixed state are explained in a reasonable way by the flux-flow model with the effect of pinning taken into account. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 407–411 (25 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.