Dirty Metal Research Articles

Nuclear spin relaxation in strongly disordered superconductors

The influence of nonmagnetic impurity and spin-orbit scattering on the nuclear spin-lattice relaxation rate in strongly disordered superconductors is presented. Using Anderson's exact-eigenstate formalism, it is shown that there exist two effects of disorder onT1−1. Firstly, nonmagnetic impurity and spin-orbit scattering enhances the magnitude of the relaxation rate in the same manner as in the normal dirty metal due to the diffusive nature of quasiparticle motion. Secondly, the Hebel-Slichter peak becomes suppressed due to the disorder enhancement of the quasiparticle inelastic scattering rate due to phonon, Coulomb, and/or spin-fluctuation interactions. Comparison with the available experimental data is made.

Electron-phonon scattering rates in disordered metallic films below 1 K.

We have studied thin disordered metal films at low temperatures under nonequilibrium conditions. The electron temperature was raised above the lattice temperature by applying a dc bias. The Coulomb anomaly and weak localization were used as thermometers for the electrons. We confirm that at temperatures below 1 K the electron temperatures as derived from either the Coulomb anomaly or weak localization are consistent. The electron-phonon energy relaxation rate was measured to be proportional to ${\mathit{T}}^{3}$. Our results disagree with theoretical calculations of the electron-phonon rates for dirty metals which predict electron-phonon scattering rates proportional to ${\mathit{T}}^{4}$ for three-dimensional phonons.

On the shot noise in dirty metal contacts

The shot noise in metal contacts with small elastic electron mean free path is calculated. In the absence of inelastic scattering its value is three times smaller than that of a tunnel junction with equal resistance. If the contact is sufficiently long at large voltages the emission of phonons by nonequilibrium electrons leads to a nonlinear noise dependence on voltage.

Magnetism in doped Kondo insulators

Abstract We consider the effect of substitution of small amounts of non-magnetic La for Ce in Kondo insulators of the CeNiSn type. In stoichiometric Kondo insulators, it appears that a gap on the scale of the Kondo temperature TK, is opened in the excitation spectrum. Doping with small amounts of La introduces a dilute heavy-hole gas in which we argue that the hole-hole exchange coupling can lead to an antiferromagnetic ground state at relatively low doping levels. For higher doping levels the system becomes a dirty metal and, depending on the value of the effective conduction-electron-f-electron magnetic coupling JK, may revert to a nonmagnetic state. Thus we anticipate the possibility of a ‘tongue’ of antiferromagnetic phase protruding into the non-magnetic region of the phase diagram at low to intermediate doping levels.

Critical currents, grain boundaries and squids in the high temperature cuprate superconductors

A summary of some of the recent findings on the properties of grain boundaries in the high temperature superconductors, particularly in the Y 1Ba 2Ca 3O 7−δ epitaxial films, is presented. We show that some aspects of the behavior of the critical current across the grain boundary can be explained by assuming that the boundary can be presented by a dirty metal. Annealing in ozone at low temperatures decreases both the resistance and 1/f noise of the boundary; implying that the boundary contains charge trapping sites. Finally, the utility of single grain boundary junctions as Josephson elements of a SQUID is described.

Universal long-time relaxation of nuclear spins in a disordered conductor

The influence of fluctuations of the local density of states in dirty metal on the kinetics of nuclear magnetization is investigated. The large-scale fluctuations of the Korringa relaxation rate lead to a deviation from the typical exponential law. The nuclear spin diffusion promotes a new universal exponential regime at long times, when the exponent is independent of the constant of electron-nuclear interaction and is determined by the nuclear spin diffusion coefficient D s and by the electron diffusion coefficient D.

Investigation of the electric-field effect on weak localization using the balance-equation approach.

The electric-field effect on weak localization is studied within the framework of the balance-equation theory. The frictional forces due to direct, lowest-order impurity scattering and all orders of singular impurity backscattering, as well as the energy-loss rate due to phonons, are calculated by the use of the Feynman diagrammatic technique in the formulation of closed-time-path Green's functions. We find that, in addition to the electron heating, there exists the direct influence of a strong dc electric field on the quantum correction to the resistivity for all dimensions. Its physical origin is the same as that of an electric field on the Drude conductivity. Although for typical dirty metals this effect is submerged in the electron heating, it is in principle observable in cleaner, low-dimensional systems.

Weak localization, fluctuation, and superconductivity in thin Nb films and wires.

Weak localization, fluctuation conductivity, and related problems have been investigated based on a comprehensive set of experiments on transition metal Nb films and wires. The temperature dependence of the inelastic scattering rate 1/${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\varphi}}}$ of films with various thicknesses (25--80 \AA{}), estimated from magnetoresistance data above ${\mathit{T}}_{\mathit{c}}$, is well fitted to a function of ${\mathit{C}}_{0}$+${\mathit{C}}_{1}$T+${\mathit{C}}_{3}$${\mathit{T}}^{3}$. The coefficient ${\mathit{C}}_{1}$ is in excellent quantitative agreement with the theoretical prediction of the electron-electron scattering mechanism for two-dimensional dirty metals. The coefficient ${\mathit{C}}_{3}$ shows no thickness dependence and is in semiquantitative agreement with theories of three-dimensional electron-phonon scattering mechanisms. The upper critical field of thin Nb wires with a width of less than 1000 \AA{} exhibits unconventional temperature dependence close to ${\mathit{T}}_{\mathit{c}}$. We also discuss this behavior.

Theory of Landau diamagnetism of dirty metals.

We give a linear-response formulation of the Landau diamagnetism in a dirty metal featuring the disorder-unaveraged diamagnetic susceptibility tensor. Upon averaging over the disorder, we obtain the well-known result that the average susceptibility of a disordered metal is identical to that of a clean metal. We also determine the correlation function of the susceptibility tensor and show that the average mesoscopic fluctuation of the susceptibility can be up to (${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$\ensuremath{\tau}${)}^{2}$ times larger than its average value. We interpret this effect in terms of the diffusive nature of the orbital mass.

Proximity Induced Meissner Effect in Dirty Normal Metals

Temperature dependences of the proximity induced Meissner diamagnetization in dirty normal metals are calculated by use of the Usadel equation. Besides the effect of the normal impurity scattering, that of the magnetic one is investigated. Especially the Kondo effect is examined based on the Anderson Hamiltonian employing a scheme that interpolates magnetic and non-magnetic behaviors, and a crossover between these two has been described.

Electrical resistivity as quantum chaos

The physics of quantum transport is re-examined as a problem in quantum chaos. It is proposed that the “random potential” in which electrons in dirty metals move is not random at all, but rather any potential inducing the electron motion to be chaotic. The Liapunov characteristic exponent of classical electron motion in this potential is identified with the collision rate 1/ T appearing in Ohm's law. A field theory for chaotic systems, analogous to that used to describe dirty metals, is developed and used to investigate the quantum Sinai billiard problem. It is shown that a noninteracting degenerate electron gas moving in this potential exhibits Drude conductivity in the limit h ̷ → 0 .

Spin dephasing in disordered semiconductors and metals.

The spin dephasing time ${T}_{2}$ of electrons in a very dirty metal is calculated. The dephasing is due to weak scattering processes which do not conserve the total electron spin. Two scattering processes which are of particular importance in the impurity band of many-valley semiconductors are considered: nuclear spin flip and intervalley spin orbit. The diffusive nature of the electron motion enhances the spin dephasing rate over the usual rate present in clean metals. Electron-electron interactions are shown to have strong effects upon this diffusive process and lead to an enhanced dephasing rate. To lowest order in the interactions this enhancement is proportional to the enhancement of the spin susceptibility. Quantitative comparison is made with experiments in phosphorus-doped silicon.

Spin fluctuations and magnetoresistance in dirty metals

Effects or strong spin fluctuations induced by the Anderson localization are investigated on the quantum corrections to conductivity and magnetoresistance based on the Hubbard model together with long range Coulomb interactions. The present mechanism predicts a large spin dependent magnetoresistance, which will explain at least the trend observed in the various experiments which has been so far left unanswered.

Spin fluctuations and magnetoresistance in dirty metals

Spin fluctuations and magnetoresistance in dirty metals

Anderson localization and spin fluctuations

Effects of Anderson localization on itinerant magnetism are investigated. It is shown that Anderson localization enhances the tendency toward magnetism and spin fluctuations. Possible experimental consequences are discussed, including superconductivity in dirty metals and impurity conduction in doped semiconductors.

Universal Conductance Fluctuations, Magnetofingerprints, and the Aharonov-Bohm Effect in Metals

The conductance of any metallic sample is shown to fluctuate as a function of chemical potential, magnetic field, or impurity configuration by an amount of order e2/h independent of sample size and degree of disorder at low temperature. Fluctuations of this size are present as long as kT and the inelastic scattering rate are less than the inverse time to diffuse across the sample; at higher T they are reduced as a weak power law of T. This fluctuation effect means that weak localization theory may fail to describe experimental systems in this regime of size and temperature. This provides a quantitative explanation for the observability of sample-specific h/e Aharonov-Bohm oscillations in normal metal rings. The conductance of a given sample is found to be extremely sensitive to very small changes in impurity configuration. This result may provide the basis for a quantitative microscopic theory of low-frequency noise in dirty metals. It also suggests that the sample-specific magnetoresistance patterns ("magnetofingerprints") may provide a useful tool for probing microscopic processes associated with defects in dirty metals. The theory is in good agreement with experiments on small wires, rings and FETs, and also has implications for experiments studying classical wave motion in random media.

Spin Fluctuations and Magnetoresistance in Dirty Metals

Effects or strong spin fluctuations induced by the Anderson localization are investigated on the quantum corrections to conductivity and magnetoresistance based on the Hubbard model together with long range Coulomb interactions. The present mechanism predicts a large spin dependent magnetoresistance, which will explain at least the trend observed in the various experiments which has been so far left unanswered.

Fermi-liquid theory for very dirty metals

Landau's phenomenological Fermi-liquid theory is extended to the case of diffusing electrons.

The minimum metallic conductivity

Abstract Both experiment and theory show that the conductivity of a degenerate electron gas in a ‘dirty metal’ tends continuously to zero in the limit oflow temperatures, as the Fermi energy approaches a mobility edge. A derivation is given in terms of the Kubo-Greenwood formula. This is not the case when the metal-insulator transition is induced by a magnetic field, and then a minimum metallic conductivity σmin can be observed. Doped crystalline semiconductors and amorphous and liquid semiconductors are discussed in this context. A brief account is given of two-dimensional systems.

Anisotropic magnetoconductance in metallic doped Ge:Sb

The dependence of magnetoconductance on the direction of a magnetic field is measured in four valley and stressed single valley lightly metallic Ge:Sb, and is analyzed on the basis of the localization and the interaction theories of dirty metal. Positive magnetoconductance is described fairly well by the localization theory in its anisotropy. The theory is consistent with the experiment also in its magnitude in single valley case but is too large in four valley case. Negative magnetoconductance is analyzed as a sum of the components of orbital and g-factor anisotropy. The latter contribution is found to be dominant, though its magnitude is larger than the interaction theory both in four and single valley cases.