Universal Dephasing Rate due to Diluted Kondo Impurities

Abstract

We calculate the dephasing rate due to magnetic impurities in a weakly disordered metal as measured in a weak-localization experiment. If the density n S of magnetic impurities is sufficiently low, the dephasing rate 1= ' is a universal function, 1= ' n S =fT=T K , where T K is the Kondo temperature and is the density of states. We show that inelastic vertex corrections with a typical energy transfer E are suppressed by powers of 1= ' E / n S . Therefore, the dephasing rate can be calculated from the inelastic cross section proportional to ImT ÿ jTj 2 , where T is the T matrix which is evaluated numerically exactly using the numerical renormalization group. DOI: 10.1103/PhysRevLett.96.226601 PACS numbers: 72.15.Lh, 72.15.Qm, 72.15.Rn, 75.20.Hr Dephasing, i.e., the loss of wave coherence, is a ubiquitous phenomenon in the quantum mechanics of complex systems. It is of relevance to any experiment where both interference and interactions play a role and is, therefore, of profound importance in all areas of nanoscopic and mesoscopic physics.While the basic phenomenon of dephasing as such is of a rather general nature, the concrete definition of a dephasing rate and its experimental determination vary from context to context. In this Letter, we consider the dephasing rate as determined by weak-localization (WL) measurements in metals [1]. In weakly disordered metals, the interference of electronic wave functions on time-reversed paths leads to a characteristic reduction (or enhancement in the presence of spin-orbit interactions) of the conductivity. The magnitude of this effect is controlled by the dephasing time ' -the typical time scale over which electrons get entangled with their environment (phonons, other electrons, or dynamical impurities), thereby losing the ability to interfere. Even small magnetic fields break time-reversal invariance, thus prohibiting the interference of time-reversed paths. Fitting the magnetoresistivity to WL theory is a means to determine the dephasing rate 1= ' with high precision. Surprisingly, most of these experiments [2] show a saturation of the dephasing rate at the lowest accessible temperatures T, while theoretically it is expected that in the limit T ! 0 all inelastic processes freeze out when the system approaches its (time-reversal invariant and unique) ground state. This has led to an intense discussion [2 -5] as to whether quantum fluctuations can induce dephasing at T 0. While we believe that this latter scenario is theoretically excluded for electrons in a disordered metal, the presence of only a few parts per million of dynamical impurities -realized by atomic two-level systems [6] or by magnetic impurities [7-10]-may be an alternative cause of the saturation phenomenon. Indeed, it has been shown experimentally that magnetic impurities lead to an apparent saturation of 1= ' at least in some T range [9]. In contrast, some extremely pure Au and Ag samples with a negligible concentration of impurities [10] show no saturation and seem to follow the predictions of Altshu...

Disorder-quenched Kondo effect in mesoscopic electronic systems

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Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals

“…The Kondo problem is of central importance for understanding low-temperature anomalies in low-dimensional disordered metals [1,2,3,4,5,6,7,8,9,10,11,12], such as the saturation of the dephasing rate [13] and the non-Fermi-liquid behavior of certain magnetic alloys [1,14]. For a clean metal, the screening of a spin-1/2 magnetic impurity is governed by a single energy scale, the Kondo temperature T K .…”

Phase Coherence of Conduction Electrons Below the Kondo Temperature

“…The magnetic impurity contribution to the conduction electron phase coherence rate, τ −1 φ , was first measured explicitly by two groups in 1987 [5,6], and has received renewed attention recently [7,8] in the context of the debate over zero-temperature decoherence in disordered metals [9,10]. Until very recently [11,12], however, there was no theoretical expression for the temperature dependence of the inelastic scattering rate valid for T not too far below T K , and very little reliable data in that temperature range [13].The most reliable estimates of τ −1 φ come from analysis of low-field magnetoresistance data in the context of weak-localization theory. In disordered metals without magnetic impurities, τ −1 φ is dominated by electronphonon scattering at temperatures above about 1 K, and by electron-electron scattering at lower T .…”