Many-body Josephson diode effect in superconducting quantum interferometers

Abstract

We propose a many-body mechanism for a strong Josephson diode effect (JDE) in an interacting nanoscale SQUID formed by two parallel quantum dots coupled to superconducting leads. Unlike conventional diode behavior, where nonreciprocity originates from a skewed current-phase relation within a single, continuously evolving ground state, the JDE reported here is \emph{branch selected}: the positive and negative critical currents are optimized on different many-body branches across the $0$-$π$ phase boundary, yielding a substantial enhancement of the diode efficiency. We further show that a \emph{nonlocal} Cooper-pair tunneling channel, which binds the two electrons on different arms, is essential: it reshapes the $0$-$π$ boundary and produces a pronounced ``diode band'' in parameter space, in sharp contrast to the fragile hotspot obtained when only local Cooper-pair transfer is available. While the key physics is captured by an effective model in the superconducting atomic limit, our conclusions remain robust for realistic finite-gap devices, as demonstrated within a generalized atomic-limit framework.

Figures (5)

• Figure 1: (a) Current phase relation (CPR) and critical currents $I_{c\pm} = \max \{ \pm I(0 \le \Delta \phi < 2\pi) \}$. (b) Schematic of the SQUID model, which contains two quantum dots connected in parallel to the superconducting leads. (c) Local and non-local transport channels for Cooper pairs tunneling.
• Figure 2: Absolute critical current asymmetry $\Delta I_c = I_{c+} - I_{c-}$ in the $(d\epsilon,U)$-plane for (a) $\zeta = 0.0$ and (b) $\zeta = 1.0$, respectively. (c) $\Delta I_c$ in $(d\epsilon,\zeta)$-plane at $U=5.0$. Calculations are performed at zero temperature with $\Phi = 1.13$. Nonlocal Cooper pairing continuously develops a significant "diode band" over a wide interaction range, see main text.
• Figure 3: (a) $\Delta I_c = I_{c+} - I_{c-}$ (black solid line) vs detuning $d\epsilon$ for $U = 5.0$ at zero temperature ($\zeta = 1.0$ model). The magenta and violet dashed lines are for $\pm I_{c\pm}$, respectively. The diode peak evolves through four distinct stages, labeled 1 to 4, with the corresponding CPRs displayed in the middle panels. Insets depict the GS energy for the singlet and double states. (b) Ground state sectors for $I_{c\pm}$: Lightblue and grey regions indicate where both $I_{c\pm}$ reside in the $0$- and $\pi$-phase, respectively. The orange region highlights the branch selected regime, where $I_{c+}$ and $I_{c-}$ are located on different branches.
• Figure 4: (a) Projection of the GS ($\zeta = 1.0$) at $\Delta \phi_\pm$ onto the local $| \uparrow\downarrow,0 \rangle$, $| 0,\uparrow\downarrow \rangle$ and nonlocal $\frac{1}{\sqrt{2}}[| \uparrow,\downarrow \rangle - | \downarrow,\uparrow \rangle]$ singlet states. (b) $0$-$\pi$ phase diagram in $(\Delta\phi, \zeta)$-plane with $U=5.0$ for various $d\epsilon$. The heatmap in the singlet phase indicates the weight of the nonlocal singlet state.
• Figure S1: Schematic of the SQUID model, consisting of two parallel quantum dots coupled between two superconducting leads. The leads are assumed to be identical s-wave superconductors, differing only in their macroscopic phases. An external magnetic field modulates the electron tunneling phases between the dots and the leads through the Peierls substitution.