Comment on "Quantum Decoherence in Disordered Mesoscopic Systems"

In a recent paper, Phys. Rev. Lett. 81, 1074 (1998), Golubev and Zaikin (GZ) found that ``zero-point fluctuations of electrons'' contribute to the dephasing rate extracted from the magnetoresistance. As a result, the dephasing rate remains finite at zero temperature. GZ claimed that their results ``agree well with the experimental data''. We point out that the GZ results are incompatible with (i) conventional perturbation theory of the effects of interaction on weak localization (WL), and (ii) with the available experimental data. More detailed criticism of GZ findings can be found in cond-mat/9808053.Comment: 1 page, no figure

Dephasing of a particle in a dissipative environment

The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance $\ell << L$. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit ($\ell >> L$). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.Comment: 18 pages, 2 figures, some textual improvements, to be published in JP

Interaction effects and phase relaxation in disordered systems

This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disordered metals. Using well-controlled perturbation theory with the inverse conductance $g$ as the small parameter, we show that this effect consists of two contributions. First contribution comes from the processes with energy transfer smaller than the temperature. This contribution is responsible for setting the energy scale for the magnetoresistance. The second contribution originates from the virtual processes with energy transfer larger than the temperature. It is shown that the latter processes have nothing to do with the dephasing, but rather manifest the second order (in $1/g$) correction to the conductance. This correction is calculated for the first time. The paper also contains a brief review of the existing experiments on the dephasing of electrons in disordered conductors and an extended qualitative discussion of the quantum corrections to the conductivity and to the density of electronic states in the weak localization regime.Comment: 34 pages, 13 .eps figure

Decoherence of a particle in a ring

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.Comment: 5 pages, 1 figure, proofed version to be published in EP

Geometry dependent dephasing in small metallic wires

Temperature dependent weak localization is measured in metallic nanowires in a previously unexplored size regime down to width $w=5$ nm. The dephasing time, $\tau_{\phi}$, shows a low temperature $T$ dependence close to quasi-1D theoretical expectations ($\tau_{\phi} \sim T^{-2/3}$) in the narrowest wires, but exhibits a relative saturation as $T \to 0$ for wide samples of the same material, as observed previously. As only sample geometry is varied to exhibit both suppression and divergence of $\tau_{\phi}$, this finding provides a new constraint on models of dephasing phenomena.Comment: 6 pages, 3 figure

Magnetolocalization in disordered quantum wires

The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results on magnetolocalization is included.Comment: 22 pages, RevTe