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The magneto-quantum and quantum interference effects in a two-dimensional gas of p-type charge carriers are studied for three quantum wells made of practically pure germanium in a Si0.6Ge0.4/Si0.2Ge0.8/Si0.6Ge0.4 heterostructure. The quantum well widths were 8 nm for sample I, 19.5 nm for sample II, and 25.6 nm for sample III. The dependences of resistance on the magnetic field for all samples exhibit Shubnikov–de Haas oscillations. Their analysis made it possible to calculate the kinetic characteristics of charge carriers for the cases of one (sample I) and two occupied subbands (samples II and III). In the region of weak magnetic fields (B < 0.1 T), the effect of weak localization of holes was revealed, which determines the negative magnetoresistance and the increase in resistance with decreasing temperature. The manifestation of the charge carriers interaction effect at various temperatures and magnetic fields is discovered and analyzed. A transition from the diffusion mode of manifestation of the quantum correction to the intermediate, and then to the ballistic mode is observed. In all regions, the behavior of the quantum correction due to the charge carriers interaction effect is in good agreement with modern theoretical predictions. The temperature dependences of the hole-phonon relaxation time are calculated. In weak magnetic fields, with an increase in the temperature of the 2D system, a transition from the "partial inelasticity" mode, characterized by the dependence τ h ph − 1 ∝ T 2 , to the small-angle scattering mode, described by the relation τ h ph − 1 ∝ T 5 , takes place. In stronger magnetic fields for samples with two occupied subbands, the dependence τ h ph − 1 ∝ T 3 was observed. Possible explanations for this dependence are presented. [ABSTRACT FROM AUTHOR]

Quantum effects in p-type Si0.2Ge0.8/Ge/Si0.2Ge0.8 heterostructure with an extremely high mobility of charge carriers μH = 1367000 cm2/(V ⋅ s) have been comprehensively studied. An analysis of Shubnikov–de Haas oscillations yielded effective mass of charge carriers, which proved to be very low, m* = 0.062m0, and the value of fluctuations of hole density along the channel δp = 3.5 ⋅ 109 cm–2. The fractional Hall effect (filling numbers 8/3, 7/3, 5/3, 4/3) observed at temperatures up to 5 K has been discovered in strong magnetic fields. The studies of quantum interference effects related to weak localization and electron-electron interaction between charge carriers, which have been conducted in such a high-mobility system for the first time, enabled calculation of spin splitting Δ = 1.07 meV and the Fermi-liquid coupling constant F 0 σ = − 0.12 , which agree with results obtained earlier. [ABSTRACT FROM AUTHOR]

The charge carrier overheating effect was studied in the p-type Si0.4Ge0.6/Ge/Si0.4Ge0.6 heterostructure with two subband occupy. The temperature dependences of hole-phonon relaxation time τ h - ph sat weak magnetic fields demonstrated transition of the 2D system from regime of “partial inelasticity” characterized by dependence τ h - ph − 1 ∝ T2 to regime of small-angle scattering, described by dependence τ h - ph − 1 ∝ T5 with temperature increase. But in higher magnetic fields the dependence τ h - ph − 1 ∝ T3 manifests itself on dependences τh-ph(Th-ph). The possible explanations of such dependences are discussed. PACS: 72.15.Lh Relaxation times and mean free path; 72.20. My Galvanomagnetic and other magnetotransport effects; 72.20. −i Conductivity phenomena in semiconductors and insulators. [ABSTRACT FROM AUTHOR]

Multisubband transport of the p-type Si0.4Ge0.6/Ge/Si0.4Ge0.6 heterostructure has been investigated by means of magnetotransport measurements at low temperatures and high magnetic fields. Two frequency Shubnikov-de Haas oscillations indicate occupation of two subbands. This allows us to determine the densities and mobilities of the charge carriers on each subband. Shubnikov-de Haas oscillations reveal two 2D conduction subbands with carrier effective masses of 0.112m0 and 0.131m0. The quantum Hall ferromagnetic states which results from the crossing of two Landau levels with opposite spin and different subband was observed in SiGe systems for the first time. [ABSTRACT FROM AUTHOR]

Weak localization effects and the interactions of charge carriers are studied in two Si0.7Ge0.3/ Si0.2Ge0.8/Si0.7Ge0.3 p-type heterostructures, where one or two quantum levels are filled, respectively. A weak localization effect for two-dimensional charge carriers is found to occur in weak magnetic fields when the spin-orbital and inelastic scattering times are close, which is indicative of splitting of the spin states under the influence of a perturbing potential related to the formation of a two-dimensional potential well (Rashba mechanism). In higher magnetic fields when one quantum level is occupied, interaction effects appear that are caused by Coulomb interactions with a scatterer. When the two quantum levels are occupied, the dominant mechanism is scattering on Friedel oscillations of the charge carrier density induced by an impurity electric field. In all regions, the quantum corrections are in good agreement with modern theoretical predictions. [ABSTRACT FROM AUTHOR]

The behaviors of resistance, magnetoresistance (up to 5 T), and Hall electromotive force (EMF) with varying temperature (10-300 K) and measuring current ( [ABSTRACT FROM AUTHOR]

The use of Shubnikov-de Haas oscillations for determining effective mass is illustrated by a study of the magnetotransport properties of the two-dimensional hole gas in Si1-xGex (x = 0.13, 0.36, 0.95, 0.98) quantum wells. For some samples the data cannot be fitted to standard theoretical curves in which the scattering of charge carriers is described by the conventional Dingle factor. The reasons for the discrepancies between the experiment the theory are: (i) the effect of spin splitting on the amplitude of the peak in the SdH oscillations; (ii) extra broadening of the Landau levels attributable to an inhomogeneous distribution of the carrier concentration; (iii) the coexistence of short and long-range scattering potentials; and, (iv) population of the second energy level in the quantum well. Ways of calculating the effective hole masses m* for all these cases are presented and values of m* are found for the heterostructures studied here. [ABSTRACT FROM AUTHOR]

This is a survey of some recent results concerning Bernstein-type inequalities for entire functions of the exponential type, harmonic majorants for classes of subharmonic functions, Phragmen-Lindelöf function, the Krein description of the Cartwright classes of entire functions with the finite logarithmic integral, structure of the Martin boundary of the Denjoy domains, smoothness properties of the Green function, etc. We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. Approximation of continuous bounded functions by entire functions of exponential type on an unbounded closed proper subset of the real line or on an unbounded quasismooth (in the sense of Lavrentiev) curve in the complex plane is studied. We discuss Totik's extension of the classical Bernstein theorem on polynomial approximation of piecewise analytic functions on a closed interval. The results are achieved by the application of methods and techniques of modern geometric function theory and potential theory. [ABSTRACT FROM AUTHOR]

The distribution of zeros and poles of best rational approximants is well understood for the functions f(x) = |x|a, a > 0. If f ε C[-1, 1] is not holomorphic on [-1, 1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [-1, 1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, a-values, and poles of best real rational approximants of degree at most n to a function f ε C[-1, 1] that is realvalued, but not holomorphic on [-1, 1]. Generalizations to the lower half of the Walsh table are indicated. [ABSTRACT FROM AUTHOR]

Changes in the conductivity of p-type quantum-well heterostructures of Si0.05Ge0.95 alloy are studied at temperatures ranging from 0.352-7.1 K and magnetic fields of up to 11 T. The distinctive feature of the sample was asymmetric doping, with layers of Si0.4Ge0.6 with boron impurity concentrations of 2·1018 and 8·1018 cm-3 positioned on opposite sides of the quantum well. Shubnikov-de Haas oscillations were observed clearly against the background of a high quasiclassical positive magnetoresistance. The field dependence of the magnetoresistance is well described by a function of the form ρxx(B)/ρxx(0)∝B12/7, as predicted by a theory including the combined effect of both short- and long-range disorder. The contribution to the temperature and magnetic field dependences of the resistance owing to quantum corrections associated with weak localization and charge carrier interactions is determined. Strong spin-orbital scattering of holes on the quantum well is revealed by analyzing these corrections. A study of the variations in the amplitude of the Shubnikov-de Haas oscillations with temperature and magnetic field (including the monotonic behavior of the resistance with changing magnetic field) makes it possible to determine the effective mass of the charge carriers, m*=0.17m0 The temperature dependence of the hole-phonon relaxation time was found by studying the overheating of charge carriers by an electric field. [ABSTRACT FROM AUTHOR]

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. Approximation of continuous bounded functions by entire functions of exponential type on unbounded closed proper subsets of the real line is studied. [ABSTRACT FROM AUTHOR]

Recently Totik and Varjú [17] presented an estimate of the uniform norm of a monic polynomial with prescribed zeros on the unit circle. In this paper we improve their estimate and extend it to the case of polynomials with some zeros on an arbitrary analytic curve in the complex plane. [ABSTRACT FROM AUTHOR]

Quantum interference effects, such as weak localization and electron-electron interaction (EEI), have been investigated in magnetic fields up to 11 T for hole gases in a set of Si1− xGe x quantum wells with 0.13< x<0.95. The temperature dependence of the hole phase relaxation time has been extracted from the magneto-resistance between 35 mK and 10 K. The spin-orbit effects that can be described within the Rashba model were observed in low magnetic fields. A quadratic negative magneto-resistance was observed in strong magnetic fields, due to the EEI effect. The hole-phonon scattering time was determined from hole overheating in a strong magnetic field. [ABSTRACT FROM AUTHOR]

The Shubnikov-de Haas oscillations of the conductivity of a two-dimensional gas of holes in quantum wells consisting of pure germanium and silicon with low germanium content (13%) are analyzed to determine the effective masses and the g factor in these regions. The magnetic-field dependences of the resistivity ρxx obtained at temperatures from 33 mK to 4 K in magnetic fields up to 11 T are used for the analysis. [ABSTRACT FROM AUTHOR]

The effect of charge-carrier overheating in a two-dimensional (2D) hole gas is realized in a Si1-xGex quantum well, where x=0.13, 0.36, 0.8, or 0.95. The Shubnikov–de Haas (SdH) oscillation amplitude is used as a “thermometer” to measure the temperature of overheated holes. The temperature dependence of the hole-phonon relaxation time is found from an analysis of the change of the dependence of the amplitude of the SdH oscillations on temperature and applied electrical field. Analysis of the temperature dependence of the hole-phonon relaxation time reveals a transition of the 2D system from the regime of “partial inelasticity” to conditions of small-angle scattering. [ABSTRACT FROM AUTHOR]

The magnetic field dependence of the resistance of bismuth thin films (100–700 Å thick) at low temperatures (1.5–77 K) are analyzed in the conceptual framework of quantum corrections to the conductivity due to weak localization and electron interaction effects. It is shown that the diversity and variability of the magnetoresistance curves in a parallel field upon variations of the thickness and temperature are due to the fact that the spin-orbit interaction time τso increases with increasing field, altering the relationship between τso and the phase relaxation time τφ. This result supports the hypothesis that the strong spin-orbit interaction manifested in the surface scattering of electrons is due to the existence of a potential gradient near the metal surface, and a parallel magnetic field alters the orientation of the spins, accompanied by a decrease of the rate of spin-orbit processes. [ABSTRACT FROM AUTHOR]

We obtain a sharp upper bound on exponentials of logarithmic potentials at any point of the unit disk D, provided that the area of the subset of \overline{ D}, where such exponentials are at most 1, is known. [ABSTRACT FROM AUTHOR]

We give a new proof (and a generalization) of recent remarkable result by V. Totik concerning the smoothness properties of the equilibrium measure for compact subsets of the real line and the Green function for complement of these subsets taken with respect to the complex plane. [ABSTRACT FROM AUTHOR]

Using the example of a pressed sample consisting of chromium dioxide nanoparticles coated with insulating shells, we study the relationship between the electron transport system and magnetic subsystem in granular spin-polarized metals. It is shown that the spin-polarized tunneling transport current can affect the coercivity fields of the percolation cluster formed in the sample with decreasing temperature. [ABSTRACT FROM AUTHOR]

The weak localization and interaction effects for charge carriers in a two-dimensional hole gas in a pure germanium quantum well in a SiGe/Ge/SiGe heterostructure with a hole density of 5.68×1011 cm-2 and mobility of 4.68×104 cm2 V-1 s-1 are investigated. The resistance measurements were made at temperatures from 46 mK to 10 K and magnetic fields up to 15 T. The magnetic-field dependence of the resistivity exhibits Shubnikov-de Haas oscillations and quantum Hall effect steps. At very low magnetic fields (B<0.1 T) a weak localization effect for holes is revealed, which makes for a negative magnetoresistance and growth of the resistance with decreasing temperature (at T<2 K). The manifestation of the interaction effect is observed and analyzed over a wide range of temperatures and magnetic fields. With increasing temperature the manifestation of the interaction-induced quantum correction passes from the diffusive regime to an intermediate and then to the ballistic regime. In all regions the behavior of the interaction quantum correction is in good agreement with the modern theoretical predictions. [ABSTRACT FROM AUTHOR]

The Shubnikov–de Haas oscillations in a two-dimensional hole gas in a quantum well of pure germanium in a SiGe/Ge/SiGe heterostructure with a hole concentration pH=5.68×1011 cm2 and mobility μ=4.68×104 cm2V-1s-1 are investigated in magnetic fields up to 15 T at temperatures from 40 mK to 4 K. The observed deviation from the known relation describing the conductivity oscillations in the Shubnikov–de Haas effect are explained by additional broadening of the Landau levels due to the existence of a nonuniform distribution of the concentration of charge carriers, and, accordingly, of their energy, in the plane of the two-dimensional gas. It is assumed that the latter is due to natural atomic-step variations of the well width. The effective hole mass (m*=0.112m0) is determined from the temperature dependence of the oscillation amplitude, and its dependence on magnetic field is used to determine the quantum scattering time and the value of the carrier concentration fluctuations. [ABSTRACT FROM AUTHOR]

The magnetoresistance of bulk specimens of graphite nanoplatelets obtained by different methods is studied in magnetic fields up to 2.2 T. It has been established that magnetoresistance is negative for graphite nanoplatelets prepared by chemical treatment of source graphite with a solution of potassium permanganate in sulfuric acid. This negative magnetoresistance can be explained in terms of the model of charge carrier's weak localization in a system with imperfect structure. It has been established that the magnetoresistance is positive and independent of temperature for graphite nanoplatelets produced by sonication method. Moreover, magnetoresistance is linear relative to a magnetic field in fields above ∼0.7 T. It is shown that linear magnetoresistance can be explained in the terms of the Abrikosov's model of quantum linear magnetoresistance. [ABSTRACT FROM AUTHOR]

The magnetoresistance and electrical resistivity of nitrogen-doped multi-walled carbon nanotubes (N-MWCNTs) were studied in the temperature range of 1.6-100.3 and 1.6-286 K, respectively, using a standard four-probe technique. The possible mechanisms of the observed effects are discussed in detail. [ABSTRACT FROM AUTHOR]

The results of experimental investigations of magnetoresistance in nanocarbon material (NCM) containing carbon nanotubes in magnetic field up to 5 T and at temperature up to 0.54 K are reported. The obtained experimental magnetoresistance curves of NCM are described satisfactorily within the framework of the shrinkage effect of wave function of localized state in a magnetic field along with the spin-polarization mechanism. [ABSTRACT FROM AUTHOR]