Nonequilibrium Dynamics of Andreev States in the Kondo Regime

The transport properties of a quantum dot coupled to superconducting leads are analyzed. It is shown that the quasiparticle current in the Kondo regime is determined by the nonequilibrium dynamics of subgap states (Andreev states) under an applied voltage. The current at low bias is suppressed exponentially for decreasing Kondo temperature in agreement with recent experiments. We also predict novel interference effects due to multiple Landau-Zener transitions between Andreev states.

Figure 1

Schematic representation of the Andreev state dynamics in two different situations: (a) quantum point contact and (b) S-QD-S in the Kondo regime. The dashed lines correspond to the states for perfect normal transmission. The lower and upper striped regions represent the states in the continuous spectrum. The straight arrows indicate Landau-Zener transitions between AS’s, while the curved arrows represent inelastic transitions between the AS’s and the continuous spectrum (see text).

Figure 2

Low bias $IV$ characteristics of a S-QD-S in the Kondo regime for perfect normal transmission and different values of ${\Gamma }^{*}/\Delta =1$, 2, 3, 4, 5, and 10 from bottom to top. The full lines correspond to the numerical results, while the dashed lines correspond to the approximation given by Eq. (5).

Figure 3

Evolution of the oscillations pattern in the $IV$ characteristics as a function of ${ϵ}_0^{*}$ for ${\Gamma }^{*}/\Delta =5$ and ${ϵ}_0^{*}/\Delta =0$, 0.5, 1.0, 1.5, and 2 from top to bottom. Inset: ${\Gamma }^{*}/\Delta =2$ and ${ϵ}_0^{*}/\Delta =0$, 0.2, 0.4, 0.6, and 0.8.

Figure 4

Zero-bias conductance defined by introducing a finite voltage resolution $e\delta v/\Delta =0.025$. The normal transmission from bottom to top is 0.978, 0.980, 0.982, 0.984, 0.986, 0.99, and 1.0.