Dirty Metal Research Articles

Periodicity of transport coefficients with half flux quanta in the Aharonov-Bohm effect

We prove that all transport coefficients of a dirty normal metal in the Aharonov-Bohm geometry are exactly periodic with a period of a half flux quantum. This special periodicity appears only after performing the ensemble average over a symmetric distribution of random potentials. This result indicates how to improve numerical studies of localization by selectively averaging over the ensemble in such a manner as to preserve the special symmetries of the Hamiltonian.

Diffusion near the metal-insulator transition

Some comments are presented on electronic diffusion, in both the very dirty metal and the nearly delocalized insulator. It is concluded that Coulomb interactions appear to play an important role, b...

Localization effects in thin Pt wires

Abstract The resistance of Pt wires with cross-sectional areas (A) as small as 2.6 x 10−12 cm2 ( A =160 A ) has been studied at low temperatures (T). The wires exhibit a resistance rise as the temperature is decreased, and the variation of the rise with A and T is the same as that found previously for thin wires made from other materials. Combining the results for Pt with those of other materials we find that the resistance rise varies approximately linearly with the amount of disorder. This result is inconsistent with theories based on Coulomb interactions. If this result is interpreted in terms of current theories of localization, it implies that the inelastic mean free path is independent of the amount of disorder, a conclusion which is very difficult to reconcile with present ideas concerning inelastic scattering in dirty metals.

Disordered one-dimensional conductors at finite temperature

Abstract Inelastic scattering processes at nonzero temperatures produce a broadening, h/τin, of electronic energies which essentially is equivalent to the imaginary component of the energy one must introduce in order to evaluate the Kubo formula for the d.c. conductivity of a dirty metal. We1) have developed a fast algorithm for evaluating the conductivity of a linear chain, and have used it to study the dependence of the conductivity on the magnitude of the imaginary part of the electron energy. Results for the Anderson model with different degrees of disorder and at different energies can all be scaled onto the same curve, which is of the form expected from the usual theory of localized states. A cross-over is evident between two limiting regimes: in one the damping caused by the complex energy is dominant; in the other, localization of the eigenstates dominates. The universal curve obtained make it possible to connect tight binding model results with the conductivity calculated for an electron in a white noise potential. This curve describes models in which the scattering potentials have finite variance. Similar, but not identical, results are obtained for tight binding chains with a Cauchy distribution of site energies.

Transport at low temperature in amorphous magnetic metals (invited)

The scaling theory of conduction for a noninteracting electron gas in a disordered system at T = 0 is reviewed and the conductivity at various length scales obtained. The concepts of the mean free time between inelastic collisions and the corresponding inelastic length ℓin, are introduced. The conductivity for a dirty metal is obtained as a function of temperature at low temperatures in terms of ℓin(T). For the case of a disordered magnetic metal the effect of the temperature-dependent magnetic disorder is introduced and several possible typical situations schematically analyzed. The effect of electron-electron interactions is briefly discussed, as determining the effective inelastic length and a simple qualitative picture of conduction as a function of temperature suggested. Some cautionary remarks about the testing of these ideas by experiments are made.

An anomalous temperature dependence in superconducting tunnel junctions

Experiments have been carried out on tunneling junctions prepared by Clark's method between pairs of bulk superconductors. The resistance of the junctions has been determined at temperatures between the transition temperatures T 1 and T 2 of the two metals. The resistance was found to be a monotonically increasing function of the temperature. Assuming that the barrier can be considered as a very dirty metal, the results are interpreted in terms of layer of induced gapless superconductivity inside the barrier, thus reducing its effective thickness. The rounding of the discontinuity at T 1 is discussed in terms of Ferrell's paraconductivity. Confirmatory experiments have been performed on junctions in which the barrier is replaced by a layer of germanium, with similar results.

On the fluctuation enhanced conductivity of a superconductor: The correct evaluation of the Maki graph

According to Maki, a particular diagram—the Maki graph—gives a contribution to the fluctuation enhanced conductivity of a superconductor which is infinite in the case of a thin film. It is shown that this result is spurious and that it is due to a breakdown of the standard Green function impurity technique. A new method is developed which is strictly based on the Boltzmann equation. It is shown that the temperature dependent contribution of the Maki graph to the conductivity is negligibly small in a dirty metal.

Theory of resistive anomaly in a superconductor above a second-order critical magnetic field

We use the time-dependent Ginzburg-Landau equation to calculate the effect of thermodynamic fluctuations in lowering the resistance below the normal state value for magnetic fields above a second-order critical field. We consider only dirty metals in the Ginzburg-Landau temperature region and evaluate the conductivity of a bulk specimen along and transverse to the applied field. There is a strong anisotropy in the effect: σzz is proportional to (H - Hc2)−fraction three-twos but σxx is proportional to (H - Hc2)−½, where the z axis is along the magnetic field. The results are in agreement with a recent microscopic calculation by Usadel.

Fluctuations in a superconductor above Tc in the high field region

The singular part of the electric conductivity is calculated for bulk material and for films with a static magnetic field applied. Dirty metals and high magnetic fields are considered only.