Superconducting Diode Effect in Double Quantum Dot Device

Superconducting diode effect (SDE) is theoretically examined in double quantum dot coupled to three superconducting leads, $L$, $R1$ and $R2$. Lead $L$ is commonly connected to two quantum dots (QD1, QD2) while lead $R1$ ($R2$) is connected to QD1 (QD2) only. The phase differences $\varphi_{1}$ between leads $L$ and $R1$ and $\varphi_{2}$ between leads $L$ and $R2$ are tuned independently. The critical current into lead $R1$ depends on its direction unless $\varphi_{2} = 0$, $\pi$, which is ascribable to the formation of Andreev molecule between the QDs. In the absence of electron-electron interaction $U$ in the QDs, the spectrum of the Andreev bound states forms Dirac cones in the $\varphi_{1}-\varphi_{2}$ plane if the energy levels in the QDs are tuned to the Fermi level in the leads. The SDE is enhanced to almost 30\% when $\varphi_{2}$ is set to the value at the Dirac points. In the presence of $U$, the SDE is still observed when $U$ is smaller than the superconducting energy gap in the leads. Our device should be one of the minimal models for the SDE since a similar device with a single QD does not show the SDE.