In this Letter, we manipulate the phase shift of a Josephson junction using a parallel double quantum dot (QD). By employing a superconducting quantum interference device, we determine how orbital hybridization and detuning affect the current-phase relation in the Coulomb blockade regime. For weak hybridization between the QDs, we find π junction characteristics if at least one QD has an unpaired electron. Notably the critical current is higher when both QDs have an odd electron occupation. By increasing the inter-QD hybridization the critical current is reduced, until eventually a π-0 transition occurs. A similar transition appears when detuning the QD levels at finite hybridization. Based on a zero-bandwidth model, we argue that both cases of phase-shift transitions can be understood considering an increased weight of states with a double occupancy in the ground state and with the Cooper pair transport dominated by local Andreev reflection.
We theoretically study the Fano resonance in Josephson current. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). To treat the Coulomb interaction inside the QD, we employ the Hubbard-I approximation, in which the correlation {δ n ↑ δ n ↓ ) can be taken into account beyond the Hartree-Fock approximation. It is found that the dependence of the Josephson critical current on the QD energy level has an asymmetric resonance, which is similar to the Fano resonance in normal metal systems. Moreover, we find that the sign of the critical current can change around the resonance, and such behavior is not seen without the Coulomb interaction. These results indicate that the cooperation of the Fano effect and the Coulomb interaction induces the 0-π transition.
We theoretically investigate the Fano effect in dc Josephson current at the absolute zero of temperature. The system under consideration is a double-path Josephson junction in which one path is through an insulating barrier and the other one is through a quantum dot (QD). Here the Kondo temperature is assumed to be much smaller than the superconducting gap, and the Coulomb interaction inside the QD is treated by the Hartree-Fock approximation. It is shown that the Josephson critical current exhibits an asymmetric resonance against the QD energy level. This behavior is caused by the interference between the two tunneling processes between the superconductors: the direct tunneling across the insulating barrier and the resonant one through the QD. Moreover, we find that the Josephson critical current changes its sign around the resonance when the Coulomb interaction is sufficiently strong. Our results suggest that $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition is induced by the cooperation of the Fano effect and the Coulomb interaction inside the QD.
We report the transport measurements on the InAs self-assembled quantum dots (SAQDs) which have a unique structural zero-dimensionality, coupled to a superconducting quantum interference device (SQUID). Owing to the SQUID geometry, we directly observe a π phase shift in the current phase relation and the negative supercurrent indicating π junction behavior by not only tuning the energy level of SAQD by back-gate but also controlling the coupling between SAQD and electrodes by side-gate. Our results inspire the future quantum information devices which can link optical, spin, and superconducting state.
A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc current carrying three-body static phase coherence, known as the ``quartet current.'' We calculate the zero-frequency current noise cross correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy ${\ensuremath{\epsilon}}_{0}$ is connected to three superconductors
Sa,Sb, and
Sc with gap $\mathrm{\ensuremath{\Delta}}$, biased at ${V}_{a}=V,\phantom{\rule{0.16em}{0ex}}{V}_{b}=\ensuremath{-}V$, and
Vc=0, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$, which is demonstrated with a semianalytical perturbative expansion of the cross correlations. Noise reveals the absence of granularity of the superflow splitting from
Sc towards
(Sa,Sb) in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, cross correlations measured in the
(Va,Vb) plane should reveal an ``anomaly'' in the vicinity of the quartet line
Va+Vb=0, related to an additional contribution to the noise, manifesting the phase sensitivity of cross correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors ${F}_{\ensuremath{\varphi}}$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors ${F}_{\ensuremath{\varphi}}$ are of order unity in the resonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\lesssim}1$, and they are vanishingly small in the nonresonant dot regime ${\ensuremath{\epsilon}}_{0}/\mathrm{\ensuremath{\Delta}}\ensuremath{\gg}1$.