A study of frequency and temperature dependence of ionic conductance

An approach to study the frequency and temperature dependence of the bulk ionic conductivity, based on the log-log representation of the frequency response, is described. Experimental results obtained on -PbF₂ thin-film samples are used to illustrate this approach. The analysis of these results permits to separate the different physical mechanisms involved and to model the cells. Using CPE (Constant Phase Element) Y=Y ₀(j) ⁿ for the interfaces, but also for the bulk ionic conductance, permits to fit the experimental results. A progressive increase of the slope n of the admittance which corresponds to the bulk ionic conductivity is observed when the temperature decreases. A graphical method is described which can be used to determine the activation energy in this case of a CPE behavior of the conductance. It is based on the obtention of a unique curye which describes the frequency and temperature dependence of the reduced conductance G=Y _r T plotted versus the reduced radial frequency u=. This curve shows the whole conductance variation which starts from pure transport with n=0 at low frequencies and high temperature, and tends for high frequencies or low temperatures toward the dielectric response (n1), corresponding to ion displacements limited to only one jump. The observed CPE behavior of the conductance at constant temperature thus appears to be the result of the very slow variation rate of the slope n of the reduced conductance versus the radial frequency.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

Break junction tunnelling on Bi2Sr2CaCu2O8+δ-single crystals

Break junction tunnelling experiments on Bi₂Sr₂CaCu₂O₈₊-single crystals were performed at different temperatures. Carefully adjusted samples exhibited conductance curves showing only one large peak at positive and negative bias voltages. From these measurements a gap value =(21.2±2.8) meV, i.e. 2/k _B T _c =(5.5±0.8), was inferred. The behaviour of the conductance curves is similar to that of conventional superconductors but with a much larger broadening of the tunnelling characteristic. Therefore, several models which could explain this smearing are compared with the experimental data. However, it is found that none of them is capable of fitting the conductance curves convincingly. In some cases tunnel characteristics similar to those predicted by a charging effect model or a multigap model were obtained.This work was supported financially by the Deutsche Forschungsgemeinschaft through SFB 252.     

On the theory of layered high-temperature superconductors

Assuming that charge carriers form a Fermi liquid state, we study a model for layered high-temperature superconductors with unretarded intralayer and interlayer pairing. Guided by band structure calculations and inverse photoemission experiments, we adopt a tight binding band with nearest and next-nearest neighbors hopping within the sheets and weak interlayer hopping. The gap equations are solved numerically, without imposing a cutoff energy, characteristic to phonon mediated superconductivity. On this basis we calculate the gap parameters,T _c , the tunneling conductance, infrared absorption and the coherence length for various band fillings =1/2–x by introducing excess holes of concentrationx. Assuming the interlayer coupling strength to be smaller than the intralayer one, our main results are as follows:T _c is dominated by the intralayer properties, reaching a maximum atx0.3, where strong coupling features appear. In the presence of interlayer pairing, the gap becomes anisotropic perpendicular to the layers, and standard BCS-behavior is modified. In particular the BCS-square root singularity in the density of states and in the tunneling conductance is replaced by van Hove singularities characterizing the anisotropic gap. In particular, we investigate the anisotropy of the tunneling conductance for specular and diffuse tunneling for a junction parallel or perpendicular to the layers, infrared absorption, as well as the coherence length, parallel and perpendicular to the layers.     

Tunneling conductance in a gapped graphene-based superconducting structure: Case of massive Dirac electrons

The tunneling conductance in a NG/SG graphene junction in which the graphene was grown on a SiC substrate is simulated. The carriers in the normal graphene (NG) and the superconducting graphene (SG) are treated as massive relativistic particles. It is assumed that the Fermi energy in the NG and SG are E_FN400 meV and E_FS400 meV+U, respectively. Here U is the electrostatic potential from the superconducting gate electrode. It is seen that the Klein tunneling disappears in the case where a gap exist in the energy spectrum. As U→∞, the zero bias normalized conductance becomes persistent at a minimal value of G/G₀1.2. The normalized conductance G/G₀ is found to depend linearly on U with constant slope of , where is the size of the gap Δ opening up in the energy spectrum of the graphene grown on the SiC substrate. It is found that G/G₀2+αU for potentials in the range −270 meV<U<0 meV and G=0 for potentials U<−270 meV. As α→∞, the conductance for eV=Δ (V is the bias voltage placed across the NG/SG junction) can be approximated by a unit step function G(eV=Δ,U)/G₀2Θ(U). This last behavior indicates that a NG/SG junction made with gapped graphene could be used as a nano switch having excellent characteristics.     

Crossover from Coulomb-blockade to ohmic conduction in small tunnel junctions

We discuss the suppression of Coulomb effects in the low temperature conductanceg(T) of small tunnel junctions with increasing dissipation or bare conductanceg. The conductance is expressed in terms of the spin correlation fuction of a classical one dimensionalXY-model with ferromagnetic nearest neighbor plus inverse square interaction. It is shown that at low temperatures the conductance vanishes asymptotically likeT ² instead of exponentially. A Coulomb gap in the sense of a thermally activated contribution tog(T) is present only for bare conductances smaller thang _c 1. A simple model for the spin correlation functions is compared with experiments.     

Electronic conductance of a multi-channel point contact in a magnetic field

We present the numerical results of the electronic conductanceG of a quantum wire with a multichannel point contact structure in a perpendicular external magnetic fieldH at zero temperature, based on the rigorous quantum mechanics of a two-dimensional noninteracting electron gas. Computational results show the approximate quantization of the electronic conductance. WheH is weak,Ginteger multiples of 2e ²/h; and whenH is trong, Ginteger multiples of 2ne ²/h, wheren is the number of channels in the point contact structure of the quantum wire. Quantum leaps take place whenH±2m ^* E _F /[e(2j+1)], wherej is either zero or a positive integer small enough for the external magnetic fieldH to be strong, andm ^* is the effective mass of an electron in the device. To our knowledge, no report on this quantization of electronic conductance has been published. Oscillations are manifest in theGH curves for comparatively narrow channels because of the quantum size effect.     

H2-induced changes in electrical conductance of β-Ga2O3 thin-film systems

H₂-induced changes of electrical conductivity in polycrystalline, undoped -Ga₂O₃ thin films in the temperature range of 400–650° C are described. The sheet conductance of these films depends reversibly, according to a power law p ^1/3, on the partial pressure of hydrogen in the ambient atmosphere of the Ga₂O₃ film. A bulk vacancy mechanism is excluded by experiments and it is shown that the interaction is based on a surface effect. Changes in conductance are discussed to result from the formation of an accumulation layer due to chemisorption on the grain surfaces. Typical coverages are determined to be approximately 10^–4 ML for pH₂=0.05 bar and T=600° C. A possible explanation of the p ^1/3 power law is provided.     

Spectral Gaps of Quantum Hall Systems with Interactions

A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb–Schultz–Mattis method [Ann. Phys. (N.Y.) 16:407 (1961)]. The model is defined on an infinitely long strip with a fixed, large width, and the Hilbert space is restricted to the lowest (n _max+1) Landau levels with a large integer n _max. We prove that, for a noninteger filling of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also prove the following two theorems: (a) If a pure infinite-volume ground state has a nonzero excitation gap for a noninteger filling , then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a nonzero excitation gap, the filling factor must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions giving the quantized Hall conductance are favored exclusively.     

Enhancement of conductance fluctuations in two-dimensional mesoscopic electron systems with valley structures

Conductance fluctuations are studied in twodimensional mesoscopic electron system with a two-hold valley degeneracy (n _v =2), which corresponds to the inversion layer of Si-MOSFET formed in (1,0,0) plane. It is shown that the intervalley scattering modifies conductance fluctuations depending on the ratio, Min { _c , _T }/ _v , where _v = ( – 2)/2 and _c , _T , and are, respectively, system traversal time, thermal diffusion time, intervalley scattering time and total life time of electrons. Conductance fluctuations are no longer universal and vary from G _univ 0.862·e ²/h to {ie223-5} at low temperatures even for isotropic systems. The conductance fluctuations increase with decreasing system size, increasing electron density and increasing intervalley scattering time. The effect of intervalley scattering is essentially the same as that of intersubband scattering as previously reported. At finite temperatures where _{T c} , the intervalley scattering modifies the fluctuations through the change in the energy correlation range to results in the reduction of the conductance fluctuations. In Si-MOSFET formed in (1, 1, 1) plane, wheren _v =6, more enhanced fluctuations are expected. Experimental studies are desired on theoretically predicted points.     

Tunneling conductance of a Bi2Sr2CaCu2O8-SnO2 junction along the c-axis

fine structure was observed in the conductance curve of a tunneling junction composed of a single crystalline Bi2212 and an evaporated SnO₂ film. It is similar to those of Bi2212-GaAs mechanical junctions and there is a certain correspondence between the structure and the phonon density of states. Thus the previous conclusion that the structure is due to phonons has been complemented by this work. The energy gap 2 was 57 meV at 13 K and T _c was 78 K. 2(0)/k _B T _c is then 8.3. (T) showed the BCS-like temperature dependence.     

Transmission of information through mesoscopic scattering systems

The storage and transmission of information is well defined using the notions of entropy, mutual information and channel capacity as formalized by Shannon. These quantities are calculated for a quantum mesoscopic system in terms of scattering parameters. For a one-dimensional system, the mutual information is related to the thermal conductance. This relation allows to show that for an incident signal of power P, the channel capacity C has a universal upper bound given by C independent of quantum statistics. A general framework is proposed which makes use of a natural underlying symplectic structure, to relate the entropy of a quantum mesoscopic system to the scattering matrix.     

The effect of water vapor on the electrical properties and sensitivity of thin-film gas sensors based on tin dioxide

The results of theoretical and experimental studies into the effect of water vapor on the electrical conductance of a gas sensor and the sensor response to hydrogen action are discussed. A relation describing the dependence of electrical conductance G₀ on absolute humidity in the pure air is derived using a hypothesis of the presence of space-charge regions depleted of electrons between the SnO ₂ grains in a polycrystalline tin dioxide film. Due to dissociative chemisorption of water molecules, the energy-band bending at the SnO ₂ grain interfaces decreases and the oxygen-vacancy concentration in the grains increases, resuling in an increase in G₀. An equation for the sensor response to hydrogen action is derived (the G₁/G₀, ratio, where G₁ is the sensor conductance in a gas mixture containing molecular hydrogen). The expression describes the dependence of G₁/G₀ on the hydrogen concentration in the interval 50–6·10³ ppm, band bending at the SnO ₂ grain interface, and sensor temperature. The dependences of the sensor conductance, highest possible conductance, and energy-band bending on temperature and absolute humidity resulting from processing of the experimental data are in good agreement with the theoretical predictions. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 50–56, August, 2008.     

Derivation of an Improved Hodgkin-Huxley Model for Potassium Channel by Means of the Fokker-Planck Equation

This paper demonstrates the derivation of Hodgkin-Huxley-like equations from the Fokker-Planck equation. The primary result is that instead of the familiar equation expressing the potassium conductance as a function of the variablen which obeys a first order differential equation, the expression , whereL = 2.7, is to be used. This form is obtained by solving analytically an approximate solution to a Fokker-Planck partial difference equation. Instead of the Hodgkin-Huxley interpretation as the probability of occupying the conducting state, the parameter n(t) is now interpreted as the position of the “peak” of the population distribution function P(N, t), which changes in time described by the Fokker-Planck equation. This new approach enables close fitting of the experimental voltage clamp data for potassium conductance. In addition, the Cole-Moore shift paradox can be quantitatively explained in terms of the shift of the distribution function P(N,t) by the initial clamped transmembrane potentialV _i before the final clamped transmembrane potentialV _f is applied, thus increasing the time necessary for the establishment of equilibrium.     

Zero temperature phase diagram of a small metallic junction

We discuss the phase diagram for a metal tunnel junction with quasiparticle dissipation. We present some evidences of aT=0 phase transition induced by dissipation, by means of Monte Carlo simulation and studying the problem by means of a selfconsistent harmonic approximation. When the nominal conductance of the junctioin is large the predictions of the spin wave theory turn out to be correct and the algebraic decay of correlations implies quasi-long range order (phase with infinite susceptibility), this situation corresponds to the absence of a Coulomb blockade voltage threshold. The critical value of the nominal junction resistance is estimated to beR _t 0.6 k.     

Temperature-dependent conductance of quasi-one-dimensional electrons in a novel constricted channel with corrugated interfaces

Transport properties of a novel quasi-ballistic quantum wire field-effect transistor are studied experimentally and then discussed in relation to a theory for dirty Tomonaga–Luttinger (T–L) liquids. The sample was prepared by constricting lithographically an epitaxially grown In_0.1Ga_0.9As/GaAs quantum well channel, whose bottom interface is corrugated by a quasi-periodic array of multi-atomic steps of 20 nm in periodicity. A quasi-one-dimensional channel of about 200 nm in metallurgical width and in length was formed and its conductance parallel to the steps was measured at temperatures between 4 and 0.3 K as a function of gate voltage. Plateau-like structures substantially lower than 2e²/h were observed. The conductance at each gate voltage decreases sensitively as temperature lowers until it gets nearly constant below a critical temperature. These tendencies are found to be qualitatively consistent with the theory of Ogata and Fukuyama for dirty T–L liquids. The temperature dependence above the critical temperature is found to fit quantitatively with the formula of Ogata and Fukuyama, if the parameters are suitably chosen.     

Magnetoconductivity of thin epitaxial silver films

The magnetoconductance (MC) of thin epitaxial Ag films on Si(111) surfaces is studied as a function of film thickness (1–125 monolayers (ML)) at 20 K under ultra high vacuum (UHV) conditions. Three different regimes of magnetoconductance are observed depending on the degree of disorder in the films which is controlled by film thickness and annealing procedures. Thick films (d>3 ML) with diffuse electron transport show in the case of large elastic scattering times ₀ a classical, negative MC B ² and in the case of small ₀ a positive MC due to weak localization effects. The MC of thin films (d<2 ML) which have a conductance smaller than e ²/h, i.e. localized electron states, is negative again.     

AC electrical behaviour of a Pb2CrO5 ceramic sample with surface electrodes

ac measurements (1 Hz–10 kHz) have been carried out on a Pb₂CrO₅ ceramic sample (with surface electrodes) at room temperature as a function of voltage and intensity of visible light illuminating the sample. Cole-Cole complex impedance plots show that the electrical behaviour of Pb₂CrO₅ is strongly modified when the sample is illuminated. The bulk conductance of the sample is found to increase with increasing light intensity indicating that this dielectric material becomes semiconducting due to the photogeneration of free charge carriers in the conduction band. The dielectric constant of the sample is enhanced by illumination probably due to light-dependent space charge effects in a manner where the dielectric's relaxation time (=RC=0.7 ms) remains constant with light intensity. On the other hand, both the bulk conductance and geometrical capacitance of the sample have been found to be almost independent of the applied voltage.     

Ballistic spin-dependent transport of Rashba rings with multi-leads

Using the Landauer–Büttiker formula with the transfer matrix technique, we develop a formalism of the ballistic spin-dependent electron transport in the multi-lead Rashba rings. We give analytic formulas of the total conductance G_j, spin-σ conductance and spin polarization P_j of each outgoing lead j, and their resonant and antiresonant conditions. Analytic studying with numerical investigating Rashba rings with several symmetric and asymmetric leads, we find that G_j, and P_j oscillate with the incoming electron energy and the spin–orbit interaction (SOI) strength, and their antiresonances depend on the incoming electron energy, the SOI strength and the outgoing-lead angle with the incoming lead. For the symmetric-lead rings, G_j, and P_j have some symmetries, , and P_j = −P_N−j for symmetric leads, j and N − j, where the angles between the symmetric outgoing leads j and N − j and the incoming lead are γ_N−j = 2π − γ_j. The spin polarization of the outgoing lead with γ_j = π is exactly zero for even-N-symmetric-lead rings. These symmetries originate from the lead symmetry and time reversal invariance. For asymmetry-lead rings these symmetries vanish.     

Electron Conductance and Lifetimes in a Ballistic Electron Waveguide

Ballistic electron waveguides are open quantum systems that can be formed at very low temperatures at a GaAs/AlGaAs interface. Dissipation due to electron–phonon and electron–electron interactions in these systems is negligible. Although the electrons only interact with the walls of the waveguide, they can have a complicated spectrum including both positive energy bound states and quasibound states which appear as complex energy poles of the scattering S-matrix or energy Green's function. The quasibound states can give rise to zeros in the waveguide conductance as the energy of the electrons is varied. The width of the conduction zeros is determined by the lifetimes of the quasibound states. The complex energy spectrum associated with the quasibound states also governs the survival probability of electrons placed in the waveguide cavities.