Enhanced Sensitivity of the Transmission Phase of a Quantum Dot to Kondo Correlations

The strong sensitivity of the transmission phase through a quantum dot embedded into one arm of a two-wave Aharonov-Bohm interferometer to the Kondo effect is explained. The enhancement takes place because of the buildup of the exchange scattering on the dot due to Kondo correlations even much above $T_K$. The enhanced exchange competes with the potential scattering, which is always weak. Both cases of the Anderson impurity model and a multilevel quantum dot are considered. In the latter case in addition to the description of peculiar phase behavior a mechanism leading to ferromagnetic Kondo coupling in quantum dots is proposed.

Figure 1

The phase $\varphi$ as a function of the depth of the impurity level $-{\epsilon }_d$ for $\Gamma =U/30$. Solid lines show the calculated $\varphi ({\epsilon }_d)$ for $T=\Gamma ,\Gamma /4,\dots ,\Gamma /4^6$. Since the theory is valid only for $T\gg T_K$, the curves are shown only for $T>2T_K({\epsilon }_d)$. The dotted line depicts schematically the expected $\varphi ({\epsilon }_d)$ for $T=\Gamma /1024$. The thin dashed line shows the phase for the sum of two Breit-Wigner resonances and the thick dashed line is the conventional Bethe-ansatz solution for $T\equiv 0$.

Figure 2

The phase $\varphi (V_g)$ for a sequence of valleys $S=1/2,1,1/2$. Dotted line: Breit-Wigner. Solid lines: the phase at different temperatures $T=\Gamma ,\Gamma /8,\dots$. The bottom line shows the schematic conductance of such a dot, and letters $a,b$ indicate, to which level the electron is added.