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)     

Capacitance spectroscopy investigation of the spin polarization of two-dimensional electronic systems

It is shown that capacitance spectroscopy can be used to investigate the spin polarization of two-dimensional electronic systems (2DESs). We employed this method to investigate the spin polarization of 2DESs in a GaAs/AlGaAs heterojunction for filling factors of the magneticquantization levels 0.28<ν<0.9. It is proved that in the presence of states of the fractional quantum Hall effect with ν _f =1/3 and 2/3 the ground state of a 2DES with ν>2/3 is incompletely spin-polarized. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 102–107 (10 January 1997)     

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al _x Ga_1−x As heterojunction. The results are in good agreement with the existing experimental data.     

Hall effect in microscopically inhomogeneous magnetic alloys

A theory of the generalized conductivity for the normal component of the Hall effect is developed. It is shown that the normal Hall effect coefficient R ₀ of microscopically inhomogeneous magnetic alloys GdZn_xCu_1−x , which at low temperatures consist of ferro-, antiferro-, and paramagnetic phases, can be described satisfactorily on the basis of an effective-medium theory. The experimentally observed relationship between the coefficient R ₀(x) and the resistivity ρ(x) is obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 98–102 (January 1999)     

Investigation of low-temperature electrical conduction mechanisms in highly resistive GaN bulk layers extracted with Simple Parallel Conduction Extraction Method

The electrical conduction mechanisms in various highly resistive GaN layers of Al _x Ga_1−x N/AlN/GaN/AlN heterostructures are investigated in a temperature range between T=40 K and 185 K. Temperature-dependent conductivities of the bulk GaN layers are extracted from Hall measurements with implementing simple parallel conduction extraction method (SPCEM). It is observed that the resistivity (ρ) increases with decreasing carrier density in the insulating side of the metal–insulator transition for highly resistive GaN layers. Then the conduction mechanism of highly resistive GaN layers changes from an activated conduction to variable range hopping conduction (VRH). In the studied temperature range, ln (ρ) is proportional to T ^−1/4 for the insulating sample and proportional to T ^−1/2 for the more highly insulating sample, indicating that the transport mechanism is due to VRH.     

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).     

Generators of KMS Symmetric Markov Semigroups on {\mathcal{B}({\rm h})} Symmetry and Quantum Detailed Balance

We find the structure of generators of norm-continuous quantum Markov semigroups on B(h){\mathcal{B}({\rm h})} that are symmetric with respect to the scalar product tr (ρ ^1/2 x*ρ ^1/2 y) induced by a faithful normal invariant state ρ and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the so-called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal.     

Lifshits quantum phase transitions and rearrangement of the Fermi surface upon a change in the hole concentration in high-temperature superconductors

Changes in the electronic structure in the normal phase of high-T _c superconductors (HTSCs), viz., layered cuprates, are considered. The results of LDA + GTB calculations of the electron structure and the Fermi surface of La_{2 − x} Sr _x CuO₄ one-layer cuprates with allowance for strong correlations are compared with ARPES and quantum oscillations data. Two critical points x _c1 and x _c2 are discovered at which the rear-rangement of the Fermi surface takes place. In the vicinity of these points, changes in the thermodynamic properties at low temperatures are determined using the Lifshits ideology concerning 2.5-order quantum phase transitions. A singularity δ(C/T) ∝ (x − x _e )^1/2 in the electron heat capacity agrees well with the available experimental data in the vicinity of x _c1 ≈ 0.15. Sign reversal of the Hall constant upon doping is also considered qualitatively.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

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)     

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.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

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.     

Influence of grain boundaries on resistivity of manganites La1 − x K x MnO3

Results of investigation of resistivity and magnetoresistance of manganites La_{1 − x} K _x MnO₃ (x = 0.050–0.175) are presented. Behavior of resistivity ρ(T) in the paramagnetic and ferromagnetic phases has been described. To describe ρ(T) near the phase-transition temperature, notions of the percolation theory have been used. Two maxima have been found in the dependence ρ(T); their appearance has been attributed to the ceramic nature of the studied samples. The observed increase in magnetoresistance with a decrease in temperature is caused by intergranular spin-polarized tunneling of charge carriers.     

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.     

Metal-insulator transition in electron-doped Ba1−x La x MnO3 compounds

Electron-doped (Ba_1−x La _x )MnO₃ compounds were prepared for x=0−0.5. Measurements of X-ray diffraction (XRD) at room temperature and temperature variation of dc electrical resistivity down to 20 K were carried out. Samples with x=0.2–0.5 exhibit metal-insulator (M-I) transition. The maximum M-I transition temperature (T _c) of 289 K was observed for 30% of La doping (x=0.3). XRD patterns of these samples (x=0.2−0.5) were analyzed using Rietveld refinement. These samples are found to be mostly in single-phase form with orthorhombic symmetry (space group Pbnm). We have found strong correlation between Mn-O-Mn bond angles and T _c of M-I transition. The resistivity data below T _c could be fitted to the expression ρ=ρ ₁+ρ ₂ T ² and this shows that double exchange interaction plays a major role even in Mn⁴⁺-rich compound. Above T _c the resistivity data were fitted to variable range hopping and small polaron models.     

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.     

Magnetic breakdown and quantum magnetotransport with a constant pseudospin under tilted magnetic fields in an n -In x Ga1? x As/GaAs double quantum well

A procedure is proposed for precise scanning of the (B _⊥, B _‖) plane between the magnetic field projections that are perpendicular and parallel to (quasi-)two-dimensional layers when measuring their longitudinal and Hall magnetoresistances. Investigations of a n-In _x Ga_1−x As/GaAs double quantum well (x ≈ 0.2) performed using this procedure make it possible to reveal a number of the features of the magnetoresistance, which appear due to a complex energy spectrum of the double quantum well in a parallel field, and to separate them from the structures associated with the magnetic breakdown. The trajectories representing the features of the magnetoresistance in the (B _⊥, B _‖) plane are described by the semiclassical calculations of the quantization of the energy spectrum of the double quantum well under the action of the perpendicular field component. The structures appearing due to the magnetic breakdown are amplified with increasing the total magnetic field magnitude and, in the samples with low mobility, completely suppress the features caused by the motion of an electron with a constant pseudospin component. The peaks corresponding to the magnetic breakdown are split in a strong parallel field due to the spin splitting of the Landau levels. These splittings correspond to the effective Landé factor |g*| ≈ 3. Original Russian Text ? M.V. Yakunin, S.M. Podgornykh, V.N. Neverov, 2007, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 132, No. 1, pp. 241–249.