Tunable Andreev reflection in an Aharonov-Bohm interferometer

Using the nonequilibrium Green’s function technique, we investigate quantum transport properties of an Aharonov-Bohm interferometer due to Andreev reflections. It is found that the Andreev current can be expressed as the product of the probability of an incoming electron with spin $\sigma$ through the interferometer and that of a reflected hole with the spin-$\sigma$, and exhibits two periods of the oscillation ($h∕e$ and $h∕2e$). The physical reasons originate from the interference of the different paths for both incoming electrons and reflected holes. Since the Andreev reflection coefficient is an even function of the magnetic flux $\phi$, the time-reversal symmetry is kept in the Andreev reflection process and the reciprocity relation for conductance $G\left(\phi \right)=G(-\phi )$ holds in normal-metal/superconductor hybrid mesoscopic systems. By adjusting systematic parameters, such as the gate voltages of the quantum dots and the magnetic flux $\phi$ in the interferometer, we can obtain extremely narrow resonant current peak and antiresonance Andreev current dip. This result provides a mechanism for a very sensitively controlled Andreev current switch. The shot noise is also discussed and the noiseless spectrum corresponds to the resonant and antiresonant Andreev reflection cases respectively.

Figure 1

Aharonov-Bohm interferometer in NS hybrid systems.

Figure 2

The coherent process for electrons with spin $\sigma =\uparrow$ from quantum dots 1 to 4 (a), and the reflected holes with spin $-\sigma =\downarrow$ from quantum dots 4 to 1 (b).

Figure 3

The Andreev reflection coefficient $T_A$ versus $\epsilon \equiv ({\epsilon }_2+{\epsilon }_3)∕2\Gamma$ and $\delta \epsilon \equiv ({\epsilon }_2-{\epsilon }_3)∕\Gamma$ with the arbitrarily chosen magnetic flux $\phi =\pi ∕10$. The symmetric parameters are set as follows: ${\Gamma }_L={\Gamma }_R=\Gamma$ and $t_{Lu}=t_{Ru}=t_{Ld}=t_{Rd}=2.5\Gamma$.

Figure 4

The Andreev conductance $G$ versus the magnetic flux $\phi$. The bare energy levels are set ${\epsilon }_2=-{\epsilon }_3=5\Gamma$.

Figure 5

The Andreev conductance $G$ versus the dimensionless bare energy level $\overline{\epsilon }\equiv {\epsilon }_2∕\Gamma =-{\epsilon }_3∕\Gamma$ with the magnetic flux $\phi =\pi ∕10$.

Figure 6

The shot noise spectrum $S$ in the unit $e^{3}V$ versus the magnetic flux $\phi$. Other parameters are the same as those in Fig. 3.