Thermally assisted hopping transport in disordered systems

The response to an external field of localized electrons coupled to phonons is investigated. The low frequency (ω<T) linear response function is shown to obey a kinetic equation. The transition probabilities (including multiphonon contributions) can be expressed in terms of the dynamical correlation functions(k, ?) of the phonons. The low temperature d.c. conductivity in three dimensions obeys a law σ(0)=σ₀ · exp(? (T ₀/T)^1/4). By a combined variational and “nearest neighbor” approximation upper limits for the exponential as well as the pre-exponential factor are obtained. In two dimensions the 1/4 in the exponent has to be replaced by 1/3. The one-dimensional case requires separate considerations which do not simply lead to an exponent 1/2. An expression for the thermopower in the hopping regime is derived and evaluated.     

量子化极限情况下MOS反型层二维电子气定域态电子电导率σxx的低频效应

本文分析了量子化极限情况下MOS反型层二维电子气(2DEG)定域态电子电导率的频率特性。主要内容:(1)用费密分布函数随频率变化导出了在2DEG两种主要导电过程的频率特性。即向迁移率边激发导电过程电导率σ_ME(ω)和可变程跳跃导电过程电导率σ_VRH(ω)。发现:σ_ME(ω)和σ_VRH(ω)是一个复数。(2)说明了σ_ME(ω)有较长时间常数τ_n,对应一个低频过程。σ_VRH(ω)有较短时间常数,对应一个高频过程。(3)理论与实验作了比较,拟合结果表明,在实验条件下,向迁移率边E_c激发时间常数τ_n 3.6×10^-6。 关键词：     

Frequency Dependence of the Dielectric Loss Angle in Disordered Semiconductors in the Terahertz Frequency Range

Frequency dependence of the real part of the conductivity σ₁(ω) in the region of the transition from almost linear (s < 1) to quadratic (s ≈ 2) can indicate a change in the conduction mechanism (the transition from the variable-range to the fixed-range hopping with increasing frequency); in this case, the sharpness of the change in the slope of the frequency characteristic is related to the dependence of the preexponential factor of the resonance integral on the intercenter distance in the pair. The frequency dependence of the imaginary part of the conductivity σ₂(ω) has no kink in the vicinity of the transition frequency ωcr, remaining almost linear. A large dielectric loss angle |cotγ| = |σ₂|/σ₁ can indicate that the imaginary part of the conductivity at ω < ω_cr is defined by the larger zero-phonon contribution in σ₂^res the region of weak variation in the loss angle γ(ω), which significantly exceeds the relaxation contribution σ₂^res.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

High field magnetoconductivity of Si inversion layers

The transverse magnetoconductivity (σ_χχ) of electron inversion layers on (100) Si is measured in magnetic fields up to 220 kG at temperatures from 4.2 to 1.6 K. The dependence of σ_χχ on T, H, and the electric field along the inversion layer suggests that immobile electrons between two Landau subbands are to a large extent localized out of the top of the lower subband. Fine structure, which may be indicative of inhomogeneities of electronic origin, is observed in σ_χχ vs electron density.     

Temperature dependence of the radiation-stimulated conductivity of CsI crystals upon picosecond excitation by electron beams

The temperature dependence of the pulse conductivity for CsI crystals upon excitation with an electron beam (0.2 MeV, 50 ps, 400 A/cm²) at a time resolution of 150 ps is investigated. Under experimental conditions, the time of bimolecular recombination of electrons and holes (V _k centers) is directly measured in the temperature range 100–300 K. This made it possible to calculate the temperature dependence of the effective recombination cross section S(T)=7.9×10^?8 T² cm². The temperature dependence of the conductivity σ(T) is interpreted within the model of the separation of genetically bound electron-hole pairs. The activation energy of this process is found to be E _G =0.07 eV.     

Theory for the nonlinear optical response at noble-metal surfaces with nonequilibrium electrons

We present a theory for the electron-temperature dependence T _el of optical second harmonic generation (SHG). Such an analysis is required to study the dynamics of metallic systems with many hot electrons not at equilibrium with the lattice. Using a tight-binding theory for the nonlinear susceptibility χ ⁽²⁾(ω,T _e1) and the Fresnel coefficients we present results for the SHG intensity I ⁽²⁾(ω,T _e1) and its dependence on T _el for Cu. Note, χ ⁽²⁾(ω,T _e1) rather than the Fresnel coefficients determines essentially this temperature dependence. Most interestingly we find frequency ranges where I ⁽²⁾(ω,T _e1) increases for small light intensities, while it decreases for large light intensities. Our theory yields also that SHG probes effects due to hot electrons more sensitively than linear optics. The results of our calculations are compared with recent experiments on Cu and Au.     

Current-conducting properties of paper consisting of multiwall carbon nanotubes

Electrical conductivity σ(T) of the paper consisting of multiwalled carbon nanotubes (MWCNTs) is studied in the temperature range 4.2-295 K, and its magnetoresistivity ρ(B) at various temperatures in magnetic fields up to 9 T is analyzed. The temperature dependence of the paper electrical conductivity σ(T) exhibits two-dimensional quantum corrections to the conductivity below 10 K. The dependences of negative magnetoresistivity ρ(B) measured at various temperatures are used to estimate the wavefunction phase breakdown length L _φ of conduction electrons and to obtain the temperature dependence L _φ = constT ^?p/2, where p ≈ 1/3. Similar dependences of electrical conductivity σ(T), magnetoresistivity ρ(B), and phase breakdown length L _φ(T) are detected for the initial MWCNTs used to prepare the paper.     

Elimination of the mott interband s-d enhancement of the electrical resistance of nickel and platinum owing to the excitation of electrons by femtosecond laser pulses

The dependence of electrical, σ, and thermal, κ, conductivities of metals on the electron temperature T _e at high (～1 eV) T _e values has been calculated. The two-temperature states for which the temperature T _e of heated electrons exceeds the temperature T _i of ions in the crystal lattice result from the excitation of electrons by femtosecond laser pulses. It is well known that the existence of empty d levels with a high density of states near the Fermi surface (as, e.g., in nickel, platinum, and iron) leads to a pronounced enhancement of the electrical resistance (Mott, 1936). This is due to an increase in the statistical factor related to the electron transitions to the empty states induced by collisions with phonons. It is found that the excitation of the electron subsystem significantly reduces the electron-phonon scattering to unoccupied d states since the chemical potential μ(T _e ) rises above the upper edge of the d band. The decrease in the scattering probability leads to the anomalous behavior of the conductivity σ_el-ph, which increases with the temperature T _e . Such a behavior turns out to be inverse with respect to the usual situation in condensed matter.     

NMR study of the spin polarization in dilute Al-Mn alloys

The spatial dependence of the spin density oscillations σ(r) around Mn impurities in Al-Mn dilute alloys has been studied by ²⁷Al four pulse NMR experiments. The concentration dependence of the magnetic broadening $\text{ΔH}{}^{\mathrm{i}}\text{1}\text{2}$ of the ²⁷Al line is found slower than linear. This result, together with the temperature dependence of the magnetic broadening as measured by CW NMR, demonstrates both the preasymptotic depression of σ(r) in Al-Mn and the long range damping of σ(r) associated with the finite mean free path at high T.     

Temperature dependence of the a.c. conductivity of Naβ-alumina

Low temperature a.c. conductivity of β-alumina is of the form σ(ω) = σ(ω) + Aωⁿ. Both σ(0) and A are found to be thermally activated. Simple relationships, dependent on the value of n, are shown to exist between (i) the relative magnitudes of σ(0) and A and (ii) their respective activation energies.     

Conductivity and anomalous Hall effect in film magnetic nanocomposites based on nonstoichiometric oxides

The transport properties of film nanocomposites (Co₄₀Fe₄₀B₂₀) _x (AlO _y )_{100 ? x} and (Co₈₄Nb₁₄Ta₂) _x (AlO _y )_{100 ? x} based on AlO _y oxide (y ~ 1), containing a ferromagnetic metal, are studied in the region of the metal–insulator transition (57 > x > 47 at %). It is found that at x > 49 at %, the conductivity of nanocomposites is well described by a logarithmic law of σ(T) = a + b ln T, which can be explained by the peculiarities of the Coulomb interaction in nanogranular systems with metallic conductivity near the metal—insulator transition. It is shown that parameter b is determined by the characteristic size of the percolation cluster cell, which in nanocomposites of both types happen to be the same (~8 nm) and correlates well with the results of electron microscopy studies. The temperature dependence of the anomalous Hall effect at the logarithmic dependence of conductivity is studied for the first time. In the immediate vicinity of the transition, a power-law scaling between the anomalous Hall resistance and longitudinal resistance ρ _H ^a ∝ ρ^0.4, is detected, which can be explained by the suppression of its own mechanism of the anomalous Hall effect under the strong scattering of charge carriers.     

Pressure effect on magnetization for (CoTm)90Zr10 (Tm = Cr,Mo) amorphous alloys

Temperature dependences of the forced volume magnetostriction dω/dH and the saturation magnetization σ_s for (CoTm)₉₀Zr₁₀ (Tm = Cr, Mo) amorphous alloys have recently been measured by the 3-terminal capacitance method and a vibrating sample magnetometer and magnetic balance at temperatures from 77 K to the Curie temperature T_c or the crystallization temperature. The pressure coefficient of σ_s0 at 0 K, d ln σ_s0/dp, is estimated from (dω/dH)₀ extrapolated to 0 K using the thermodynamical relation. The values of d ln σ_s0/dp increase in negative value with increasing Tm concentration. The relation between d ln σ_s0/dp and the pressure coefficient of T_c, d ln T_c/dp, estimated indirectly from dω/dH is discussed.     

Electron localization in 1D conductors due to the phonon scattering

Electron localization in 1D conductors due to scattering by dispersionless optical phonons at low temperatures has been studied by applying the Berezinsky diagram technique. The large localization length l_loc, much longer than the mean free path l, has been found. The low frequency optical absorption is described by the law: Re σ(ω) ～ ω² |ln³ω|.     

Percolation and the electron–electron interaction in an array of antidots

A square lattice of microcontacts with a period of 1 μm in a dense low-mobility two-dimensional electron gas is studied experimentally and numerically. At the variation of the gate voltage V _g , the conductivity of the array varies by five orders of magnitude in the temperature range T from 1.4 to 77 K in good agreement with the formula σ(V _g ) = (V _g ?V _g ^* (T))^β with β = 4. The saturation of σ(T) at low temperatures is absent because of the electron–electron interaction. A random-lattice model with a phenomenological potential in microcontacts reproduces the dependence σ(T, V _g ) and makes it possible to determine the fraction of microcontacts x(V _g , T) with conductances higher than σ. It is found that the dependence x(V _g ) is nonlinear and the critical exponent in the formula σ ∝ ? (x - 1/2) ^t in the range 1.3 < t(T, V _g ) < β.     

Static and high-frequency hole transport in <Emphasis Type="Italic">p</Emphasis>-Si/SiGe heterostructures in the extreme quantum limit

Complex high-frequency (HF), σ^AC = σ₁ ? iσ₂, and static, σ^DC, conductivities, as well as current-voltage characteristics, have been measured in p-Si/SiGe heterostructures with a low hole density (p = 8.2 × 10¹⁰ cm^?2) at temperatures T = 0.3–4.2 K in the ultraquantum limit, when the filling factor is v < 1. In order to determine the components of the HF conductivity, the acoustic contactless method in the “hybrid configuration” is used, when the surface acoustic wave propagates on the surface of the LiNbO₃ piezoelectric and the heterostructure is pressed to the surface by a spring. The conductivities σ₁ and σ₂ are determined from the damping and velocity of the surface acoustic waves that are measured simultaneously with varying the magnetic field. The revealed HF conductivity features—σ₁ ? |σ₂|, the negative sign of σ₂, the threshold behavior of the current-voltage characteristic, and the dependence I ∝ exp(-A/V ^0.3) in the subthreshold region—indicate the formation of a pinned Wigner crystal (glass) in the ultraquantum limit (T = 0.3–0.8 K, B > 14 T).     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Enhancement of band magnetism and features of the magnetically ordered state in the CeB<Subscript>6</Subscript> compound with strong electron correlations

Precision measurements of transport and magnetic parameters of high-quality CeB₆ single crystals are performed in the temperature range 1.8—300 K. It is shown that their resistivity in the temperature interval 5 K < T < T* ≈ 80 K obeys not a logarithmic law, which is typical of the Kondo mechanism of charge carrier scattering, but the law ρ ∝ T ^?1/η corresponding to the weak localization regime with a critical index 1/η = 0.39 ± 0.02. Instead of the Curie-Weiss dependences, the asymptotic form χ(T) ∝ T ^?0.8 is obtained for magnetic susceptibility of CeB₆ in a temperature range of 15–300 K. Analysis of the field dependences of magnetization, magnetoresistance, and the Hall coefficient in the paramagnetic and magnetically ordered phases of CeB₆ and comparison with the results of measurements of Seebeck coefficient, the inelastic neutron scattering coefficient, and EPR spectroscopy lead to the conclusion that the Kondo lattice model and skew scattering model cannot be used for describing the transport and thermodynamic parameters of this compound with strong electron correlations. On the basis of detailed analysis of experimental data, an alternative approach to interpreting the properties of CeB₆ is proposed using (1) the assumption concerning itinerant paramagnetism and substantial renormalization of the density of electron states upon cooling in the vicinity of the Fermi energy, which is associated with the formation of heavy fermions (spin-polaron states) in the metallic CeB₆ matrix in the vicinity of Ce sites; (2) the formation of ferromagnetic nanosize regions from spin polarons at 3.3 K < T < 7 K and a transition to a state with a spin density wave (SDW) at T _Q ≈ 3.3 K; and (3) realization of a complex magnetic phase H-T diagram of CeB₆, which is associated with an increase in the SDW amplitude and competition between the SDW and antiferromagnetism of localized magnetic moments of cerium ions.