Comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations".

In a recent Letter [1], Jerez, Vitushinsky and Lavagna (JVL) propose a new theoretical interpretation of the experimental measurements [2] of the transmission phase shift, δABI , through a quantum dot (QD) in the Kondo regime, as deduced from placing the QD in an open double-slit Aharonov-Bohm interferometer (ABI). Describing the QD, which is coupled to two reservoirs via one-dimensional leads, by the single level Anderson model (SLAM) [their Eq. (1)], JVL argue that at zero magnetic field (H = 0) the conductance through the QD is given by G ∝ sin2(δG), with δG = δABI/2. In this Comment we question the validity of this result for the SLAM, since it fails in several exactly known limits. Whether the SLAM succeeds to describe the experiment [2] is irrelevant to the theoretical problem posed here [3]. Without interactions (U = 0), JVL’s SLAM can be solved exactly: assuming the scattering solution Ale + Ble −ikx to the left of the QD, and Are −ikx + Bre ikx to its right, the solution is