Coherent transport in disordered metals out of equilibrium

We derive a formula for the quantum corrections to the electrical current for a metal out of equilibrium. In the limit of linear current-voltage characteristics our formula reproduces the well known Altshuler-Aronov correction to the conductivity of a disordered metal. The current formula is obtained by a direct diagrammatic approach, and is shown to agree with what is obtained within the Keldysh formulation of the non-linear sigma model. As an application we calculate the current of a mesoscopic wire. We find a current-voltage characteristics that scales with $eV/kT$, and calculate the different scaling curves for a wire in the hot-electron regime and in the regime of full non-equilibrium.Comment: 16 pages, 13 figure

Persistent current induced by magnetic impurities

We calculate the average persistent current in a normal conducting, mesoscopic ring in the diffusive regime. In the presence of magnetic impurities, a contribution to the persistent current is identified, which is related to fluctuations in the electron spin density. Assuming a spin-flip scattering rate which is comparable to the Thouless energy E_c and low temperature, this new contribution to the persistent current is of the order $I\sim E_c^2/(kT\phi_0)$, which is considerably larger than the persistent current induced by the electron-electron interaction.Comment: 19 pages, 7 figures, accepted by Z. Phys.

Coherent transport in disordered metals: zero dimensional limit

We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches

Quasiclassical theory of charge transport in disordered interacting electron systems

We consider the corrections to the Boltzmann theory of electrical transport arising from the Coulomb interaction in disordered conductors. In this article the theory is formulated in terms of quasiclassical Green's functions. We demonstrate that the formalism is equivalent to the conventional diagrammatic technique by deriving the well-known Altshuler-Aronov corrections to the conductivity. Compared to the conventional approach, the quasiclassical theory has the advantage of being closer to the Boltzmann theory, and also allows description of interaction effects in the transport across interfaces, as well as non-equilibrium phenomena in the same theoretical framework. As an example, by applying the Zaitsev boundary conditions which were originally developed for superconductors, we obtain the $P(E)$-theory of the Coulomb blockade in tunnel junctions. Furthermore we summarize recent results obtained for the non-equilibrium transport in thin films, wires and fully coherent conductors.Comment: 46 pages; review articl

Persistent Currents versus Phase Breaking in Mesoscopic Metallic Samples

Persistent currents in mesoscopic normal metal rings represent, even a decade after their first experimental observation, a challenge to both, theorists and experimentalists. After giving a brief review of the existing -- experimental and theoretical -- results, we concentrate on the (proposed) relationship of the size of the persistent current to the phase breaking rate. In particular, we consider effects induced by noise, scattering at two-level systems, and magnetic impurities.Comment: accepted by JLT

Quantum Coherence in an Exactly Solvable One-dimensional Model with Defects

Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning between nearest-neighbour and next-nearest-neighbour terms. We investigate the finite size corrections to the ground state energy and its dependence on an external flux as a function of a parameter $\nu$, characterizing the strength of the defects. For intermediate values of $\nu$, both quantities become very small, although the ground state wavefunction remains extended.Comment: accepted by Europhys. Lett., latex, 7 pages. A postscript version including the figures is available at: http://www.physik.uni-augsburg.de/theo2/Publications

On localization effects in underdoped cuprates

We comment on transport experiments in underdoped LaSrCuO in the non-superconducting phase. The temperature dependence of the resistance strongly resembles what is expected from standard localization theory. However this theory fails, when comparing with experiments in more detail.Comment: 8 pages, to be published in J. of Superconductivit

Discontinuous hp-Finite Element Methods for Advection-Diffusion Problems

We consider the hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form. This class of equations includes second--order elliptic and parabolic equations, first-order hyperbolic equations, as well as problems of mixed hyperbolic-elliptic-parabolic type. Our main concern is the error analysis of the method in the absence of streamline-diffusion stabilization. In the hyperbolic case, an hp-optimal error bound is derived. In the self-adjoint elliptic case, an error bound that is h-optimal and p-suboptimal by half a power of p is obtained. These estimates are then combined to deduce an error bound in the general case. For element-wise analytic solutions the method exhibits exponential rates of convergence under p-refinement. The theoretical results are illustrated by numerical experiments

Onsager relations in a two-dimensional electron gas with spin-orbit coupling

Theory predicts for the two-dimensional electrons gas with only Rashba spin-orbit interaction a vanishing spin Hall conductivity and at the same time a finite inverse spin Hall effect. We show how these seemingly contradictory results are compatible with the Onsager relations: the latter do hold for spin and particle (charge) currents in the two-dimensional electron gas, although (i) their form depends on the experimental setup and (ii) a vanishing bulk spin Hall conductivity does not necessarily imply a vanishing spin Hall effect. We also discuss the situation in which extrinsic spin orbit from impurities is present and the bulk spin Hall conductivity can be different from zero.Comment: Accepted versio

Density functional theory for a model quantum dot: Beyond the local-density approximation

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. For weak interaction, however, accurate results are achieved within the optimized effective potential method, while for intermediate interaction strengths a method combining the exact diagonalization of small clusters with density functional theory is very successful. Results obtained from the latter approach yield very good agreement with density matrix renormalization group studies, where the full Hamiltonian consisting of the dot and the attached leads has to be diagonalized. Furthermore we address the question whether static density functional theory is able to predict the exact linear conductance through the dot correctly - with, in general, negative answer.Comment: 8 page