Giant electrical fluctuations in metallic disordered packings

We have experimentally studied granular arches through electrical measurements. The packing is composed of 2d metallic pentagons and is submitted to small taps. Large electrical fluctuations are observed and they are distributed along power laws. This indicates the presence of long-time memory effects even the packing density remains constant around a value ρ = 0.72±0.02. Large electrical fluctuations should be associated with the breaking/creation of granular arches. Received 3 October 2000     

Low-temperature resistance fluctuation in disordered conductors

At low temperatures the electron elastic mean free path in a disordered conductor can become much smaller than the inelastic mean free path (or more precisely the Thouless length) which in turn may be comparable with, or even larger than the sample size. In this quantum regime, the electrical resistance is dominated by the coherence effects that eventually lead to the now well-known weak or strong localization. Yet another remarkable manifestation of the quantum coherence is that it makes the resistance non-additive in series and, more importantly, non-self averaging, thus replacing the classical Ohm’s law with a quantum Ohm’s law describing statistical fluctuations. In this paper, we report on some of our recent work on the statistics of these “Sinai” fluctuations of residual resistance for one and higher space dimensions (d). In particular we show that the physics at the mobility edge may be dominated by these fluctuations. We also show that an external electric field tends to harness these fluctuations. Some observational consequences such as 1/f-noise at low temperatures are discussed. Our approach is based on invariant imbedding extended by us for this purpose.     

Nuclear spin relaxation in disordered conductors

The relaxation timesT ₁ andT ₂ for nuclear spins interacting with the conduction electrons of disordered metals are calculated. An explicite expression for Warren's relaxation enhancement in terms of electron spectra is obtained, showing in particular that the proportionality ofT ₁ and the conductivity is a universal feature of high resistivity conductors. A formula for an inhomogeneous line width contribution due to disorder induced static Knight shift fluctuations is found. Two dimensional electron spin diffusion is shown to imply various logarithmic line width corrections.     

Magnetoelectric effect in one-dimensional metallic conductors

The effect of a transverse magnetic field on a one-dimensional metallic current carrying conductor is considered. The field produces a transverse electric polarization which is wavevector dependent, and which causes a transverse magnetoelectric field. The magnitude of the effect is estimated for typical one dimensional conductors.     

Anomalous magnetotransport in narrow quantum hall conductors

We present the anomalous magnetotransport observed in a narrow high mobility Hall device; both the peaks and minima in the Shubnikov de Haas oscillations of the longitudinal resistance appear in the quantized plateau region of the Hall resistance. We interpret this feature as a consequence of an inhomogeneous distribution of two dimensional electron gas and provide a quantitative view with a model based on the edge current picture.     

Random matrix model for disordered conductors

We present a random matrix ensemble where real, positive semi-definite matrix elements, x, are log-normal distributed, exp[−log²(x)]. We show that the level density varies with energy, E, as 2/(1+E) for large E, in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson’s Coulomb gas analogy breaks down whenever the confining potential is given by a transcendental function for which there exist orthogonal polynomials.     

Thermodynamics in disordered metallic dots

A general discussion on the signature of the pairing correlations in the behavior of the thermodynamical observables is presented.     

Anomalous transport in disordered dynamical systems

We consider simple extended dynamical systems with quenched disorder. It is shown that these systems exhibit anomalous transport properties such as the total suppression of chaotic diffusion and anomalous drift. The relation to random walks in random environments, in particular to the Sinai model, explains also the occurrence of ageing in such dynamical systems. Anomalous transport is explained by spectral properties of corresponding propagators and by escape rates in these systems. For special cases we provide a connection to quantum mechanical tight-binding models and Anderson localization. New classes of anomalous transport behavior with clear deviations from the behavior of Sinai type are found for generalizations of these models.     

Landau diamagnetism and magnetization of interacting disordered conductors

We show how the orbital magnetization of an interacting diffusive electron gas can be simply related to the magnetization of the noninteracting system having the same geometry. This result is applied to the persistent current of a mesoscopic ring and to the relation between Landau diamagnetism and the interaction correction to the magnetization of diffusive systems. The field dependence of this interaction contribution can be deduced directly from the de Haas-van Alphen oscillations of the free electron gas. Known results for the free orbital magnetism of finite systems can be used to derive the interaction contribution in the diffusive regime in various geometries.     

Coulomb blockade of tunneling between disordered conductors

We determine the zero-bias anomaly of the conductance of tunnel junctions by an approach unifying the conventional Coulomb blockade theory for ultrasmall junctions with the diffusive anomalies in disordered conductors. Both electron-electron interactions within the electrodes and electron-hole interactions between the electrodes are taken into account nonperturbatively. Explicit results are given for one- and two-dimensional junctions, and the crossover to ultrasmall junctions is discussed.     

Residual conductance fluctuations of tiny disordered conductors

Conductances of the equivalent samples differ randomly (Stone 1985). At zero temperature these fluctuations were found to be of the order ofe ²/h for samples of arbitrary size and form (Altshuler 1985; Lee and Stone 1985). Experimentally such fluctuations manifest themselves as e.g. the reproducible aperiodic oscillations of the given sample conductance in magnetic field (Webbet al 1985; Stone 1985). These oscillations can be understood in terms of the correlation function (Lee and Stone 1985; Altshuler and Khmel’nitskii 1985) of the conductances in different fields. The characteristic field scale of the aperiodic oscillations corresponds to the unit magnetic flux through the sample. Conductance fluctuations decrease with the growth of temperature if the sample size is larger than the diffusion length within the timeh/T (Stone 1985; Lee and Stone 1985; Webbet al 1984, 1985; Altshuler and Khmel’nitskii 1985). These fluctuations are proportional toT ^?1/4,T ^?1/2 logT, andT ^?1/2 in the 3-d, 2-d and 1-d cases, respectively (Altshuler and Khmel’nitskii 1985) (the experiments of Webbet al 1984, 1985 correspond to the latter case). Random potential in tiny samples breaks all space symmetries. All effects which are forbidden in the average by these symmetries should manifest themselves by (i) conductance anisotropy, (ii) its dependence on the electric field direction and (iii) giant generation of the second harmonic in the granular sample under light radiation (Altshuler and Khmel’nitskii 1985). Conductance changes aperiodically with variation of the chemical potential (Lee and Stone 1985). Because of this thermopower fluctuations are much larger than its average value (Altshuler and Khmel’nitskii 1985). Conductance fluctuations are very sensitive to the random impurity potential variations (Altshuler and Spivak 1985). For instance, the change of the film conductance due to the shift ofone impurity isfinite for any film size. This effect can be used for the super flow impurity diffusion investigations. Variations of the localized spins realization in spin glasses change the conductance. This can explain (Altshuler and Spivak 1985) the conductance dependence on the magnetic field direction observed by Webbet al (1984, 1985).     

Hopping conduction in disordered carbon nanotubes

We report electrical transport measurements on individual disordered multiwalled carbon nanotubes, grown catalytically in a nanoporous anodic aluminum oxide template. In both as-grown and annealed types of nanotubes, the low-field conductance shows an exp[−(T₀/T)^1/2] dependence on temperature T, suggesting that hopping conduction is the dominant transport mechanism, albeit with different disorder-related coefficients T₀. The electric field dependence of low-temperature conductance behaves as exp[−(ξ₀/ξ)^1/2] at high electric field ξ at sufficiently low T. Finally, both annealed and unannealed nanotubes exhibit weak positive magnetoresistance at . Comparison with theory indicates that our data are best explained by Coulomb-gap variable-range hopping conduction and permits the extraction of disorder-dependent localization length and dielectric constant.