Square Root Dependence Research Articles

Resistance and tunneling spectra of aligned multiwalled carbon nanotube arrays

The resistance and tunneling spectra of samples formed by depositing silver electrodes at the two ends of aligned, template-grown, carbon nanotube arrays were measured in the temperature range 0.67–440 K. Two types of samples were fabricated, one with small oxide tunnel junctions separating the carbon nanotubes from the metal electrodes, the other with a significant Al2O3 tunnel barrier. The measurements indicate the presence of three regimes for dI/dV(V). For T>220 K, dI/dV(V) and the zero-bias conductivity show a broad minimum and an activation temperature dependence suggesting semiconductor behavior. In the temperature range 10<T<140 K, the zero-bias conductivity shows a square-root temperature dependence. For T<2 K, a very steep rise in the zero-bias tunneling resistance is observed with a strong simultaneous suppression of the tunneling conductivity near the Fermi energy. Coulomb blockade is suggested as a plausible explanation of the observed behavior.

Sputtered thin films of CuBr as electrochemical microsensors for NH 3 gas: structure, sensitivity and aging effects

Sputtered films of CuBr with inter-digitated copper electrodes are used as electrochemical detectors for NH 3 gas. The current–voltage characteristics are ohmic and depend on the NH 3 partial pressure, P, with a fast response. The quantitative relation between the resistivity change Δ ρ and P is described by a Langmuir-type adsorption isotherm with an adsorption constant K=12 mbar −1. The square-root time dependence of ρ is consistent with a diffusion-limited aging mechanism.

Azimuthal mode discrimination in radially chirped concentric-circle-grating distributed feedback lasers

We report a theoretical investigation analyzing the threshold modes of a concentric-circle-grating (CCG) distributed feedback laser with a radially chirped first-order Bragg grating. A numerical coupled-mode analysis of a chirped CCG laser shows improved azimuthal mode discrimination for chirped gratings with linear, quadratic, and square-root radial dependence. Negatively chirped gratings, in which the grating period decreases with radius, result in improved threshold discrimination between the circularly symmetric fundamental mode and higher order modes; positively chirped gratings, in which the grating period increases with radius, result in decreased threshold for higher order modes in general. Also, the intensity for the fundamental mode at the grating center can be reduced by an order of magnitude using linearly chirped gratings.

Magnetic pair breaking in superconductingBa1−xKxBiO3investigated by magnetotunneling

The de Gennes and Maki theory of gapless superconductivity for dirty superconductors is used to interpret the tunneling measurements on the strongly type-II high-Tc oxide-superconductor Ba1-xKxBiO3 in high magnetic fields up to 30 Tesla. We show that this theory is applicable at all temperatures and in a wide range of magnetic fields starting from 50 percent of the upper critical field Bc2. In this magnetic field range the measured superconducting density of states (DOS) has the simple energy dependence as predicted by de Gennes from which the temperature dependence of the pair-breaking parameter alpha(T), or Bc2(T), has been obtained. The deduced temperature dependence of Bc2(T) follows the Werthamer-Helfand-Hohenberg prediction for classical type-II superconductors in agreement with our previous direct determination. The amplitudes of the deviations in the DOS depend on the magnetic field via the spatially averaged superconducting order parameter which has a square-root dependence on the magnetic field. Finally, the second Ginzburg-Landau parameter kappa2(T) has been determined from the experimental data.

Theory of disordered itinerant ferromagnets. I. Metallic phase

A comprehensive theory for electronic transport in itinerant ferromagnets is developed. We first show that the Q-field theory used previously to describe a disordered Fermi liquid also has a saddle-point solution that describes a ferromagnet in a disordered Stoner approximation. We calculate transport coefficients and thermodynamic susceptibilities by expanding about the saddle point to Gaussian order. At this level, the theory generalizes previous RPA-type theories by including quenched disorder. We then study soft-mode effects in the ferromagnetic state in a one-loop approximation. In three-dimensions, we find that the spin waves induce a square-root frequency dependence of the conductivity, but not of the density of states, that is qualitatively the same as the usual weak-localization effect induced by the diffusive soft modes. In contrast to the weak-localization anomaly, this effect persists also at nonzero temperatures. In two-dimensions, however, the spin waves do not lead to a logarithmic frequency dependence. This explains experimental observations in thin ferromagnetic films, and it provides a basis for the construction of a simple effective field theory for the transition from a ferromagnetic metal to a ferromagnetic insulator.

Transient thermal gratings and carrier-induced gratings in diffusion experiments

Complications can arise during measurements of the ambipolar diffusion coefficient, D amb, of charged carriers by the transient grating method (TG) due to the concomitant decay of a transient thermal grating. The thermal diffusion coefficient, D th, of hydrogenated amorphous silicon (a-Si:H) is of the same order of magnitude as D amb, about 10 −2–1 cm 2/s. For calibration purposes we measured the thermal change of refractive index, d n/d T, by optical reflection. We monitored the temperature decay after pulsed laser excitation using transient photoreflectance (TPR). A thermal diffusion process is confirmed by a near square-root time dependence. In grating experiments, the initial temperature and its time dependence can be monitored by TPR. In order to determine D amb a good thermal connection to the substrate and a high quality material is needed.

Copper antiferromagnetic resonance inGd2CuO4:Evidence for coherent crystal-structure distortions

We report on ${\mathrm{Cu}}^{2+}$ antiferromagnetic resonance (AFMR) measurements of gadolinium cuprate ${\mathrm{Gd}}_{2}{\mathrm{CuO}}_{4}$ using far-infrared techniques coupled to high magnetic fields. The experiments were performed in the energy range $10--100 {\mathrm{cm}}^{\ensuremath{-}1}$ at helium temperatures and in magnetic fields up to 13 T. The measurements were carried out in geometry $\mathbf{H}\ensuremath{\Vert}(001)$ plane. The AFMR mode corresponding to ``out-of-plane'' spin vibrations of the copper moments characterized by the gap value ${\ensuremath{\omega}}_{0}^{*}=18.2 {\mathrm{cm}}^{\ensuremath{-}1}$ has been studied. The observed square-root magnetic-field dependence of the resonance frequency of the AFMR mode $\ensuremath{\omega}\ensuremath{\sim}\sqrt{H}$ unambiguously shows the presence of a tilting of copper spins in ${\mathrm{Gd}}_{2}{\mathrm{CuO}}_{4}$ arising from the in-plane oxygen displacements. A value of antisymmetrical exchange interaction of Dzyaloshinskii-Moriya type associated with these distortions of tetragonal structure is determined to be ${H}_{D}=65.5 \mathrm{T}.$ This allows us to infer the canting angle between the copper moments in the ${\mathrm{CuO}}_{2}$ planes equals to $2.4\ifmmode^\circ\else\textdegree\fi{}.$ The observed very narrow signal of copper AFMR displaying a linewidth less than $0.3 {\mathrm{cm}}^{\ensuremath{-}1}$ gives strong evidence for three-dimensional coherent crystal distortions in ${\mathrm{Gd}}_{2}{\mathrm{CuO}}_{4}.$ The effect of considerable enhancement (approximately by a factor of 8) of static magnetic field at the copper position originating from the gadolinium-copper exchange interaction has been detected. In frame of a simple model we discuss the role of the structural distortions in the forming of the magnetic ground state and the dynamic behavior of the complex magnetic system.

Effect of temperature on the inhibition kinetics of phenol biodegradation by Pseudomonas putida Q5.

The temperature-dependent performance of mixed-culture wastewater treatment processes may be strongly influenced by their content of psychrotrophic bacteria. In this work, the effect of temperature on cell growth and phenol biodegradation kinetics of the psychrotrophic bacterium Pseudomonas putida Q5 were determined using both batch and continuous cultures in the range of 10-25 degrees C. The Haldane equation was found to be the most suitable substrate-inhibition model for the specific growth rate. The Haldane parameters mu(max) and K(I) were best modeled by a square-root dependency on temperature. However, the Arrhenius model provided a better prediction of the temperature dependence of K(S). The variation of the yield constant with temperature also was studied experimentally. Comparisons with results of previous workers are presented.

Magnetic breakdown and the Fisher–Kao effect in zinc

A study is made of the decompensation effect in zinc due to magnetic breakdown between the electron and hole orbits near the K point of the Brillouin zone. It is shown that, in contrast to the general case for compensated metals, zinc exhibits the Fisher–Kao effect in a magnetic field which is tilted with respect to the hexagonal axis. The regularities of the changes in the shift of the Fisher–Kao peak in a magnetic field upon changes in the frequency and surface quality are established. It is shown that the field-induced shift is related to the appearance of a subsurface damaged layer. An explanation is proposed for the effect wherein the square-root frequency dependence of the position of the maximum with respect to the field is transformed to a linear function when the state of the surface of the slab is modified.

Spectral theory of a surface-corrugated electron waveguide: The exact scattering-operator approach

We apply the exact surface scattering operator to solve the problem of scalar (electron or sound) wave propagation through a strip with absolutely soft randomly rough boundaries. This approach is nonperturbative in either roughness heights or slopes. We analyzed the roughness-induced dephasing and attenuation of waves both asymptotically and numerically. The analysis proves that the signal is always scattered most effectively into the ``resonant'' waveguide modes, whose transverse wavelength is comparable to the rms roughness height $\ensuremath{\zeta}$ and whose total number is proportional to ${\ensuremath{\zeta}}^{\ensuremath{-}1}.$ According to this integral resonance rule, the dephasing dominates over the attenuation and shows a nonanalytic (square-root) dependence on the dispersion ${\ensuremath{\zeta}}^{2}$ when $(k\ensuremath{\zeta}{)}^{2}\ensuremath{\ll}1 (k$ is the wave number). In the case $(k\ensuremath{\zeta}{)}^{2}\ensuremath{\gg}1,$ the dephasing and attenuation may well compete. We predict another two surprising effects: reentrant transparency and increase of the phase velocity of the wave.

Photocurrents in P3MeT Schottky barrier diodes

Abstract The photocurrent action spectrum of a Schottky diode formed from electrodeposited poly(3-methylthiophene) is shown to follow closely the UV-visible absorption spectrum. At low forward bias, the peak photocurrent asymptotes to the expected square-root dependence on total potential, Vt, across the depletion region. At high reverse bias the superlinear dependence of the photocurrent on Vt suggests that internal photoemission from the rectifying aluminium electrode may be the dominant process.

Dramatic Change of the Magnetic Response inLiV2O4: Possible Heavy Fermion to Itinerantd-Metal Transition

The magnetic relaxation of the $d$-metal oxide ${\mathrm{LiV}}_{2}{\mathrm{O}}_{4}$ has been measured by means of quasielastic neutron scattering. At low temperatures, the observed residual linewidth of 0.5 meV and a square-root temperature dependence of the magnetic relaxation rate are canonical features of heavy-fermion systems. For $Tg40\mathrm{K}$ the magnetic response changes dramatically and can be characterized as a metal close to ferromagnetic order.

A Note on Wind Speed and sea State Dependence of the Heat Exchange Coefficient

Both mean and wave-induced motions generate turbulence in the air flow above sea waves. Assuming a local balance between production of turbulent kinetic energy and its dissipation, an explicit relation for the heat exchange coefficient CH is obtained. It is shown that CH follows a square-root dependence on the drag coefficient CD. However, the proportionality coefficient appears to depend on the sea state, expressed in terms of the coupling parameter. Dependence on the sea state suppresses the CD1/2 wind-speed dependence, and results in a marginal increase of CH with increase in the wind speed.

Laser-induced thermal degradation and ablation of polymers: bulk model

Ablation of organic polymers is described on the basis of photothermal bond breaking within the bulk material. Here, we assume a first order chemical reaction, which can be described by an Arrhenius law. Ablation starts when the density of broken bonds at the surface reaches a certain critical value. In order to understand the ablation behavior near the threshold fluence, φ th, non-stationary regimes are considered. The present treatment reveals several qualitative differences with respect to models which treat ablation as a surface process: (i) Ablation starts sharply with a front velocity that has its maximum value just after the onset. (ii) The transition to quasi-stationary ablation is much faster. (iii) Near threshold, the ablated depth has a square-root dependence on laser fluence, φ− φ th. (iv) With φ≈ φ th, ablation starts well after the laser pulse. (v) The depletion of species is responsible for the Arrhenius tail with fluences φ≤ φ th.

Density-of-states anomaly and tunneling conductance of Au/p-GaAs0.94Sb0.06 contacts near the metal-insulator transition

The tunneling-current anomaly in Au/p-GaAs0.94Sb0.06 contacts at zero bias voltage (V) → 0) is investigated. Epitaxial layers of the solid solution GaAs0.94Sb0.06 are doped with germanium and have a conductivity close to that at the metal-insulator transition. The square-root dependence of the differential conductance G(V)=(dV/dI)−1 at small values of eV>kT TT predicted by the Al’tshuler-Aronov theory of quantum corrections to the density of states at the Fermi level in disordered conductors is observed. Satisfactory agreement between the experimental data and theory is observed at hole densities (p) in the layers greater than the critical density for the metal-insulator transition pc, but the relative magnitude of the anomaly is sharply smaller at p<pc. This confirms the specificity of the condition kFl⩾1 (instead of Open image in new window ) for applicability of the theory for the density-of-states anomaly appearing as a result of electron-electron interactions in a three dimensional electron gas.

Local field dynamics in a resonant quantum tunneling system of magnetic molecules

We observed non-exponential relaxation for a quantum tunneling molecular magnetic system at very low temperatures and argue that it results from evolving intermolecular dipole fields. At the very beginning of the relaxation, the magnetization follows a square-root time dependence. A simple model is developed for the intermediate time range that is in good agreement with the data over 4 decades in time. Detailed numerical calculations as well as measurements are presented which indicate unusual correlation effects in these systems.

Effects of random perturbations in plastic optical fibers

REVIEW The most important feature of an optical fiber waveguide is its bandwidth, which defines its information-carrying capacity. A major limitation on the bandwidth of multimode glass and plastic optical fibers is modal dispersion, in which different optical modes propagate at different velocities and the dispersion grows linearly with length. However, in plastic optical fibers, experimental and theoretical results indicate that the modes are not independent but are highly coupled, which leads to a characteristic square-root length dependence and an unanticipated large enhancement of the bandwidth to gigahertz levels. The ever increasing demands for low-cost, high-bandwidth communications media for voice, video, and data transmission in short- and medium-distance applications are generating a new assessment of multimode optical fibers to serve as high-speed fiber links.

Light scattering by collective excitations in the fractional quantum hall regime

Resonant inelastic scattering methods give access to measurements of low-lying collective excitations of the 2D electron gas at Landau level filling ν= 1 3 . In experiments at finite light scattering wave vectors | k|=k⩽0.15 l 0 −1 , where l 0 is the magnetic length, we find strong light scattering by the collective gap mode of the fractional quantum Hall liquid. Long wavelength spin waves also become allowed in the tilted-field configuration of the present experiments. Such measurements enable the exploration of dispersive charge- and spin-excitations. The energies of the long wavelength collective gap mode at ν= 1 3 display a square-root dependence on perpendicular magnetic field in agreement with current theories of the incompressible quantum fluid. We also consider weaker spectra assigned to light scattering by large wave vector spin wave and collective gap excitation modes. These features are associated with breakdown of wave vector conservation in resonant inelastic light scattering.

Differential resistance of Au/GaAs1−x Sbx tunneling contacts near the zero-bias anomaly. II. Contacts to p-GaAs1−x Sbx

The differential resistance R(V)=dV/dI of Au/p-GaAs1−xSbx tunneling contacts was investigated. Schottky barriers were prepared on epitaxial layers of the solid solution p-GaAs1−xSbx (0.045<x<0.125), which were doped with Ge from 0.01 to 5 at.%. It was shown that substantial features are present in the voltage dependences R(V) for Au/p-GaAs1−xSbx contacts as compared with the data for Au/n-GaAs1−xSbx structures. A square-root voltage dependence was observed for the conductance G(V)5(dV/dI)−1 versus the bias voltage V near the zero-bias anomaly, in agreement with Al’tshuler-Aronov theory for quantum corrections introduced in the density of states at the Fermi level by the characteristic features of the electron-electron interaction in disordered metals.

Differential resistance of Au/GaAs1−x Sbx tunneling contacts in the zero-bias anomaly region. I. Contacts to n-GaAs1−x Sbx

The current-voltage characteristics and the differential resistance R(V)=dV/dI of Au/n-GaAs1−x Sbx tunneling contacts were investigated. Schottky barriers were prepared on n-GaAs1−x Sbx epitaxial layers, which were specially not doped, in the composition range 0.01<x<0.125. It was shown that the curves R(V) in the electron density range 2×1018⩽n⩽7×1018 cm−3 and temperature range 4.2⩽T⩽295 K are described well by the tunneling theory employing a self-consistent calculation of the potential in the Schottky barrier region. A square-root dependence of the conductance G(V)=(dV/dI)−1 on the bias voltage V was observed in the zero-bias anomaly region in accordance with the Al’tshuler-Aronov theory of quantum corrections introduced in the density of states at the Fermi level by the characteristic features of the electron-electron interaction in disordered metals.