Weak Localization Contribution Research Articles

Crossover from Orthogonal to Unitary Symmetry for Ballistic Electron Transport in Chaotic Microstructures

We study the ensemble-averaged conductance as a function of applied magnetic field for ballistic electron transport across few-channel microstructures constructed in the shape of classically chaotic billiards. We analyse the results of recent experiments, which show suppression of weak localization due to magnetic field, in the framework of random-matrix theory. By analysing a random-matrix Hamiltonian for the billiard-lead system with the aid of Landauer′s formula and Efetov′s supersymmetry technique, we derive a universal expression for the weak-localization contribution to the mean conductance that depends only on the number of channels and the magnetic flux. We consequently gain a theoretical understanding of the continuous crossover from orthogonal symmetry to unitary arising from the violation of time-reversal invariance for generic chaotic systems.

Effect of anisotropy on conductivity and magnetoconductance in heavily doped polyacetylene

The conductivity of iodine doped Shirakawa polyacetylene films with various stretching ratio ( l l 0 = 1∼6 ) was measured as a function of temperature, pressure and magnetic field. Unoriented samples show a power-law temperature dependence of the conductivity, with the characteristic resistivity ratio ρ I ≡ ρ(1.4K)/ρ(300K) ∼ 80, and a positive magnetoreisitance at low temperature. Although the conductivity anisotropy ( σ ∥ σ ⊥ ) increases with stretching up to σ ∥ σ ⊥ ∼ 110 for l l 0 = 6 , the temperature dependence of the conductivity ( ρ r = 3.0 ± 0.3) for stretched sample is nearly independent on the direction and the ratio of stretching. The negative magnetoresistance for the stretched sample indicates that weak localization contribution to the conductivity is dominant at low temperature. The anisotropy of magnetoconductance is close to the conductivity anisotropy implying that the bulk anisotropy originates from partially aligned fibrillar morphology. Application of high pressure decreases ρ r and changes the dominant dephasing mechanism of weak localization from the inelastic electron-electron scattering in the dirty limit to that in clean limit.

Pressure dependence of the conductivity and magnetoconductance in oriented iodine-doped polyacetylene.

The temperature dependences of conductivity and magnetoconductance (MC) have been measured, both parallel and perpendicular to the chain axis, in oriented polyacetylene films doped with iodine. The evolution of anisotropy in conductivity as a function of doping time has been studied. Hydrostatic pressure increases the conductivity for pressures up to 4 kbar; at higher pressure the conductivity gradually decreases. The reduced activation-energy function [W=-T[d(ln\ensuremath{\rho})/dT] is temperature independent in the intermediate temperature region (T\ensuremath{\approxeq}180--60 K) suggesting that the material is just on the metallic side of the critical regime of the disorder-induced metal-insulator transition. However, at 8 kbar, W(T) exhibits a positive temperature coefficient from 180 to 1.2 K, implying that the system is more metallic due to enhanced interchain transport. The ${\mathit{T}}^{1/2}$ dependence of conductivity and the enhanced negative MC, at very low temperatures, indicates that the role of electron-electron interactions is significant. MC measurements have been carried out in all the five different combinations of current with respect to the chain axis and field directions. The sign of MC is positive (negative) when the field is perpendicular (parallel) to the chain axis. The anisotropy in MC is attributed to the anisotropic diffusion coefficient. This is shown by the enhanced positive contribution to the MC at 8 kbar, when the field (current) is parallel (parallel) to the chain axis.At 1.2 K, when both the magnetic field and current are perpendicular to the chain axis, the field-induced crossover from positive to negative MC shows the subtle interplay of weak localization and electron-electron interaction contributions to MC. The inelastic scattering lengths, at 1.2 K, in parallel and perpendicular directions to the chain axis are found to be 1163 and 210 \AA{}, respectively. The ${\mathit{T}}^{\mathrm{\ensuremath{-}}3/4}$ dependence of the inelastic scattering length at low temperatures is consistent with the ${\mathit{T}}^{3/4}$ dependence of conductivity. This indicates that the inelastic electron-electron scattering known to be of importance in disordered metals is the dominant scattering mechanism in iodine-doped oriented polyacetylene.

Effects of spin-orbit scattering in mesoscopic rings: Canonical- versus grand-canonical-ensemble averaging.

Motivated by recent experiments on persistent currents in mesoscopic rings, the effect of spin-orbit scattering on closed electron trajectories is studied. It is shown that for one-dimensional systems within either the grand-canonical ensemble or the canonical ensemble consisting exclusively of even numbers (at zero temperature), there exist universal reduction factors due to spin-orbit scattering. No such universal factors occur in the canonical ensemble for an odd number of electrons. In higher dimensions, it is argued that strong spin-orbit scattering reduces the weak-localization contribution to the paramagnetic persistent current by a factor of 1/4. Enhancement of the paramagnetic behavior due to an additional mechanism is suggested. The relevance of these results to experiments is discussed.

Anisotropic Electron Transport in Cu/Al Multilayers

ABSTRACTWe have measured the anisotropy of the electron diffusivity in a series of Cu/Al multilayers. The Samples were made by magnetron sputtering and characterized by X-Ray diffraction. The low temperature transverse magnetoresistance of each sample was measured for two different orientations of the magnetic field—parallel and perpendicular to the plane of the sample film. The Weak Localization(WL) contribution to the magnetoresistance is sensitive to the component of the electron diffusivity in a plane perpendicular to the magnetic field. We use this fact to calculate the ratio of different components of the diffusivity from the observed dependence of magnetoresistance on the orientation of magnetic field. For our samples, the ratio of the in and out of plane components of the diffusivity, (Dxy/Dz), is seen to range between 1 and 2.2, and the anisotropy is largest for the sample with the highest conductivity.

Non-local effects in transport properties of macroscopic conductors

We discuss a physical system which allows a quantitative calculation of non-local properties of the macroscopic conductivity due to quantum interference effects in a two-dimensional electron gas. The case in question is the weak localization contribution to the magnetoconductivity of a two-dimensional electron gas in an inhomogeneous magnetic field. Changing the phase coherence length of the electronic wave function by lowering the temperature makes it possible to observe the transition from a local to a non-local magnetoconductivity regime. The relation of the results to recent experimental observations is discussed.

Modifications of weak localization contributions to magnetoresistance due to magnetic impurities in amorphous DyxY1−xNi alloys (invited)

High-field magnetoresistance experiments performed on thick amorphous alloys offer a simple way to study three-dimensional (3D) weak localization of conduction electrons. After the precursor work of Fert et al. on nonmagnetic amorphous alloys, we found it interesting to study how these effects would disappear under substitutions of magnetic impurities (1% to 10% of Dy) in a nonmagnetic amorphous alloy (YNi). The experiments, performed between 1.5 to 50 K and in magnetic fields up to 20 T, showed (i) in YNi, characteristic features of the magnetoresistance due to weak localization under strong spin-orbit scattering and (ii) in DyxY1−xNi, a coexistence of weak localization effects with the classical contribution of spin alignment by the applied magnetic field, saturating at negative values. This last contribution dominates the behavior of Dy-richer samples whereas weak localization is clearly observed for x≤3%. In all the samples a dramatic increase of the initial magnetoresistance slope Δρ/ρH2 (where ρ=resistivity and H=applied field) is observed when magnetic impurity concentrations increase. We explain this increase of weak localization effects, in the framework of the available weak localization theory, by an enhancement of the Zeeman spin splitting due to interactions between localized (4f ) and delocalized (d, s) electronic states.

Absence of quantum corrections to the anomalous Hall conductivity.

We discuss quantum corrections to the anomalous Hall conductivity in disordered metallic films containing magnetic moments. Within a model of skew scattering we show that Coulomb-anomaly terms vanish identically. The weak-localization contribution is cut off by the phase-breaking effect of skew scattering. In a dense system of magnetic moments, the internal magnetic field may cause a more rapid destruction of phase coherence. Our findings are in agreement with a recent experiment on ferromagnetic amorphous Fe films.

Limits to weak localization in Ca70Mg30−xAlx

Abstract We use computer simulations of random flights, in combination with measurements of the temperature and magnetic field dependence of resistivity, to estimate the size of the total contribution of quantum interference to the resistivity in a series of CaMgAl alloys. We find that this effect alone is insufficient to explain the negative temperature coefficient in this system, even though it describes the low temperature magnetoresistance better for this system than any other glass studied to date. The techniques presented should allow similar bounds to be estimated for the weak localization contribution to resistivity in other alloys.

Magnetic-field dependence of the hole-hole interaction in fluorine-intercalated graphite fibers.

Magnetoresistance measurements have been performed in high magnetic fields up to 15 teslas in fluorine-intercalated vapor-deposited graphite fibers with concentrations ${\mathrm{C}}_{4.5}$F and ${\mathrm{C}}_{3.6}$F. Previous studies had shown that the intercalation of fluorine, an acceptor in graphite, induces a two-dimensional hole gas in the graphene layers. The fluorine-intercalation process also introduces disorder into the highly ordered pristine fiber, as exhibited by the transport properties. At high magnetic fields, a positive magnetoresistance is observed and is found to vary strongly with temperature. This phenomenon is explained by the effect of the magnetic field on the hole-hole interaction when the spin subbands are split by the magnetic field. A negative magnetoresistance is observed at low fields, and is explained in terms of weak-localization theory. The magnetoresistance data are fitted with the weak-localization contribution in the weak-field regime, then extrapolated to high fields and this contribution is finally subtracted from the measured values to obtain the hole-hole interaction contribution to the magnetoresistance. From a fit to this latter contribution, a value for the screening parameter is found. The relative importance of the weak localization and hole-hole interaction contributions to the logarithmic increase in \ensuremath{\rho}(T) at low temperature is discussed.

Phase coherence in quantum wires in presence of scattering by acoustic phonons

We investigate the destruction of phase coherence of electrons in a disordered quantum wire by acoustic phonon scattering using non-equilibrium Green-function technique. The main subjects of our analysis are the influence of discrete subband structure, the transition to strong localization and the nature of dephasing by acoustic phonons. The results are used to discuss the temperature dependence of phase coherence length and weak localization contribution to conductance in GaAs quantum wires.

Anomalous magnetoconductance beyond the diffusion limit

The weak localization contribution to the conductance depends sensitively on the applied magnetic field. This anomalous magnetoconductance provides a unique tool for the identification of weak localization and other phenomena associated with it. The standard theory of the anomalous magnetoconductance is based on the diffusion approximation, which applies to the case where the number of elastic scattering events is very large during a time of phase coherence in the electronic wave. For a strictly two-dimensional film, an arbitrary number of scattering events is considered and marked deviations are found from the standard theory if this number is not large.

Effect of partial phase coherence on Aharonov-Bohm oscillations in metal loops.

The averaging of Aharonov-Bohm oscillations caused by incomplete phase coherence has been studied in two Sb rings. In these devices, the phase-coherence length ${L}_{\ensuremath{\varphi}}$ can be determined independently from an analysis of the weak localization contribution to the magnetoconductance ($\ensuremath{\Delta}{G}_{C}$) or from the amplitude of the conductance fluctuations. We find that the Aharonov-Bohm oscillations decrease as $\mathrm{exp}(\ensuremath{-}\frac{L}{{L}_{\ensuremath{\varphi}}})$ where $L$ is the sample length. The values of ${L}_{\ensuremath{\varphi}}$ inferred from $\ensuremath{\Delta}{G}_{C}$ qualitatively predict the temperature dependence of the conductance fluctuations.

Temperature Dependent Hall Constant Data in a 100 Å In2O3-x Film

We have observed a ln(1/T) temperature dependence in the Hall constant data of a 100 Å In2O3-x film measured at liquid helium temperatures in a 1.95 Tesla magnetic field. The data was interpreted using the electron-electron interaction theory of Altshuler, et al. The only parameter in the theory was the electron screening constant F; the Hall constant data gave a value of 0.75 for F. Agreement was found between the resistance-temperature data and the theory composed of the interaction contribution and the weak localization contribution.

Scaling behavior of the magnetoconductance of highly disordered In/InO x thin-films superconductors

Magnetoconductance data on composite amorphous In/InO x thin (100 Å)-film superconductors have been analyzed near critical disorder where the mean-field transition temperature T c0 is rapidly suppressed with increasing normal-state sheet resistance. For a factor of 2.5 decrease in T co, from 2.49 K to 0.97 K, the magnetoconductance data are observed to be scale-invariant with respect to the parameter ratios H/ T, the perpendicular magnetic field divided by the temperature, and T/ T c0, the temperature T normalized to T c0. This behavior is consistent with the functional forms of the Aslamazov-Larkin and Maki-Larkin contributions to the magnetoconductance providing the electron diffusivity is constant and the inelastic scattering rate is linear in temperature. These restrictive conditions are found to be valid for independent experimental determinations. Deviations in the scaling behavior are observed when weak localization contributions dominate at high temperature and when data for films with even lower T co are included in the analysis.

Quantum corrections to the resistance in two-dimensional disordered superconductors aboveTc: Al, Sn, and amorphousBi0.9Tl0.1films

Disordered films of superconductors above their transition temperature ${T}_{c}$ show several quantum corrections to the conductance, weak localization (WL), two contributions from the retarded Coulomb interaction, and two contributions from superconducting fluctuations, the Aslamazov-Larkin (AL) and the Maki-Thompson (MT) terms. In a magnetic field, most of them show a magnetoresistance and all are temperature dependent. In this paper the temperature and field dependence of the resistance is measured for Al, Sn, and amorphous ${\mathrm{Bi}}_{0.9}$${\mathrm{Tl}}_{0.1}$ films. This covers the weak-coupling and the extremely-strong-coupling superconductors as well. Of particular interest are the AL and the MT terms. The latter can be reduced by a pair-breaking mechanism. This pair breaking is caused by the inelastic-scattering time of the conduction electrons and can be measured by weak localization. Al has only a small spin-orbit scattering but by covering it with \textonequarter{} atomic layer of Au it can be transformed into a strong spin-orbit scatterer. This allows an independent determination of the inelastic lifetime ${\ensuremath{\tau}}_{i}$ and spin-orbit scattering time ${\ensuremath{\tau}}_{\mathrm{s}.\mathrm{o}.}$ and therefore a complete examination of the theory and its consistency. The agreement between experiment and theory is very good for the magnetoresistance. However, the theory for the temperature dependence of the resistance fails (with the exception of the contribution of WL). For the intermediate- and strong-coupling superconductors the applicability of the existing theories is restricted. The magnetoresistance of amorphous ${\mathrm{Bi}}_{0.9}$${\mathrm{Tl}}_{0.1}$ is essentially determined by the AL contribution.