Phase Coherence of Conduction Electrons Below the Kondo Temperature

Abstract

We have measured the phase decoherence rate, τ deviates from theory with a flatter T -dependence. We speculate that this latter behavior is due to incomplete screening of the s=2 Fe impurities by the conduction electrons.PACS numbers: 72.15. Qm, 73.20.Fz The Kondo problem is a paradigm many-body problem in condensed matter physics. In recent years, Kondo physics has been observed in semiconducting quantum dots [1] and carbon nanotubes, while Kondo lattices play a major role in some strongly-correlated materials [2]. The original problem that motivated Kondo's 1964 paper [3] was the increase in resistivity at low temperature of metals containing magnetic impurities. Although Kondo solved this puzzle, his perturbation theory diverged in the limit of zero temperature. Wilson [4] showed that, at temperatures far below the Kondo temperature T K , the magnetic impurity forms a spin-singlet with the surrounding conduction electrons and behaves as a nonmagnetic scatterer with cross section given by the unitarity limit.The brief history given above might leave the impression that the the behavior of dilute magnetic impurities in metals is completely understood. That is, however, not the case. An important aspect of the Kondo problem concerns the distinction between elastic and inelastic scattering. This distinction is extremely important in the context of quantum transport and mesoscopic physics, where it is known since 1979 that elastic scattering from static disorder preserves quantum phase coherence, whereas inelastic scattering destroys it. 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 . In the presence of magnetic impurities, τ −1 φ contains the additional contribution γ m , which peaks at T ≈ T K . In order to observe this peak in γ m while keeping the magnetic impurity concentration low enough to avoid interactions between impurities, one must choose a system with T K below about 10 K; otherwise τ −1 φ is dominated by electronphonon scattering. In order to acquire data far below T K , however, it is important to keep T K as high as possible. The optimal range for T K is a few Kelvins, which is achieved with Fe impurities in Ag [14].We fabricated Ag wires of dimensions L = 780 µm, w = 0.1 − 0.2 µm and t = 47 nm on oxidized Si...

Magnetic field dependence of dephasing rate due to diluted Kondo impurities

“…2,3,5,15,16 More recently, high-precision experiments using ion-implanted Fe impurities in Ag wires allowed a quantitative comparison with our theory for spin-1/2 impurities, see Refs. 15 and 16 for a critical discussion.…”

“…͑11͒ becomes nonuniversal, yielding temperature-independent corrections of order one, which may be important for the interpretation of highprecision experiments. 16,15 In Ref. 13 we have calculated the leading corrections to Eq.…”

Electronic excitation spectra of the five-orbital Anderson impurity model: From the atomic limit to itinerant atomic magnetism

“…Fe impurities in noble metal environments such as bulk Au or Ag surfaces are classical examples of multiorbital quantum impurity systems [44] and are still widely studied [11,35,38,39,[45][46][47][48]. Fe in Au and Ag displays a lowtemperature resistance minimum, which has been interpreted in terms of Kondo physics [13]: an impurity spin couples antiferromagnetically to the conduction electrons and is screened around the Kondo temperature, which is here on the order of 5-40 K [38,45,46].…”

Inelastic scattering from quantum impurities

“…These energy relaxation experiments could be well explained in terms of the orthodox theory of electron-electron interaction in one-dimensional wires [11], and/or inelastic scattering mediated by magnetic impurities [12,13,14,15]. Parallel to, and partially triggered by these experiments, a systematic study of the inelastic scattering from magnetic impurities has also been carried out recently, where inelastic scattering from magnetic impurities at energies down to well below the Kondo scale has also been studied [16,17,18].…”