Transmission phase shifts of Kondo impurities

TL;DR

This paper develops a many-body scattering theory to analyze transmission phase shifts and conductance in Kondo impurities embedded in quantum dots, revealing universal phase behaviors and the impact of various perturbations.

Contribution

It introduces a novel theoretical framework for calculating transmission properties in Kondo systems, including phase shifts and visibility, applicable to multiple Kondo channels and conditions.

Findings

At low temperatures, the single-channel Kondo phase shift is a/2 with quadratic temperature corrections.

In the two-channel Kondo effect, the phase shift remains a/2 despite non-Fermi liquid behavior.

Zero-temperature visibility is 1/2, indicating half of the conductance is from single-particle processes.

Abstract

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 novel many-body scattering theory which enables us to calculate the conductance through the dot, the transmission phase shift, and the normalized visibility, 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 the transmission phase shift is \pi/2 without any corrections up to order (T/T_K)^2. The visibility has the form 1-(\pi T/T_K)^2. For the non-Fermi liquid fixed point of the two channel Kondo, we find that transmission phase shift is \pi/2 despite the fact that a scattering phase shift is not defined. At zero temperature the visibility is 1/2, thus at zero temperature exactly half of the conductance is carried by single-particle processes. 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.