Anomalous transmission phase of a Kondo-correlated quantum dot

We study phase evolution of transmission through a quantum dot with Kondo correlations. By considering a model that includes nonresonant transmission as well as the Anderson impurity, we explain the unusually large phase evolution of about $\pi$ across the resonant peak through the Kondo valley observed in recent experiments. We argue that this anomalous phase evolution is a universal property that can be found in the high-temperature Kondo phase in the presence of the time-reversal symmetry.

Figure 1

(a) The magnitude and (b) the phase of the transmission amplitude $t_{LR}$ for $\phi =0$ and $\mid t_b\mid =0.08$ with the temperatures $T=0$ (solid lines), $0.02{\Gamma }_{\mathrm{eff}}$ (dashed lines), $0.5{\Gamma }_{\mathrm{eff}}$ (dotted lines). (c) The magnitude and (d) the phase for $t_b=0$ with the temperatures $T=0$ (solid lines), $0.02{\Gamma }_{\mathrm{eff}}$ (dashed lines), $0.5{\Gamma }_{\mathrm{eff}}$ (dotted lines).

Figure 2

Trajectories in the complex plane for the numerically obtained transmission amplitudes in Fig. 1 for (a) $\mid t_b\mid =0.08$, $\phi =0$, and for (b) $t_b=0$.

Figure 3

The same as Figs. 1a, 1b, except that the results are from the NRG calculations and for finite $U$. $U=20{\Gamma }_{\mathrm{eff}}$, $W=0.065D$ $(\mid t_b\mid =0.2)$, $V=0.2D$, and $T∕{\Gamma }_{\mathrm{eff}}=0,{10}^{-4},{10}^{-3.5},{10}^{-3},\dots ,{10}^{-0.5}$ from top to bottom in (a) and bottom to top in (b).