Measured phase shift using quantum dot interferometer in Kondo regime

Phase measurement was reported by the transport through an Aharonov-Bohm ring with an embedded quantum dot, so-called quantum dot interferometer, with three terminals in the Kondo regime [1]. To evaluate how precisely the phase is measured, we theoretically examine the transport through a double quantum dot (DQD) in parallel, as a tractable model for the interferometer. One of the DQD is in the Kondo regime while the other is transparent with a large line width. We report (i) the formulation of transport through the DQD in terms of Keldysh Green functions for three-terminal setup. The conductance at zero temperature is exactly given using the Bethe Ansatz solution. We find that the Kondo temperature changes with a magnetic flux penetrating the ring. (ii) For the conductance as a function of gate voltage (Coulomb peaks), we show a crossover from an asymmetric shape of Fano-Kondo resonance to a symmetric Kondo plateau with an increase in the number of conduction channels in the leads. (iii) The phase locking at π/2 can be measured around the center of Kondo valley in some conditions for the tunnel couplings between the DQD and three leads, although the measured phase is slightly deviated from the Friedel sum rule.
[1] S. Takada et al., Phys. Rev. Lett. 113, 126601 (2014).