Transmission phase shifts of Kondo impurities

Assaf Carmi, Yuval Oreg, Micha Berkooz, David Goldhaber-Gordon

Research output: Contribution to journalArticlepeer-review


We study the coherent properties of transmission through Kondo impurities by considering an open Aharonov-Bohm ring with an embedded quantum dot. We develop a many-body scattering theory which enables us to calculate the conductance through the dot G d, the transmission phase shift φ t, and the normalized visibility η in terms of the single-particle T matrix. For the single-channel Kondo effect, we find at temperatures much below the Kondo temperature T K that φ t=π/2 without any corrections up to order (T /T K )2. The visibility has the form η=1- (πT /T K )2. For the non-Fermi-liquid fixed point of the two-channel Kondo, we find that φ t=π/2 despite the fact that a scattering phase shift is not defined. The visibility is η=1/2(1+4λ√πT) with λ∼1/√T K, thus, at zero temperature, exactly half of the conductance is carried by single-particle processes, and coherent transmission may actually increase with temperature. We explain that the spin summation masks the inherent scattering phases of the dot, which can be accessed only via a spin-resolved experiment. In addition, we calculate the effect of magnetic field and channel anisotropy, and generalize to the k-channel Kondo case.

Original languageEnglish
Article number115129
JournalPhysical Review B
Issue number11
StatePublished - 20 Sep 2012

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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