Charge-tunable Cooper-pair diode

Abstract

Superconducting diodes, devices that allow Cooper-pair currents to flow more easily in one direction than the other, are set to become key building blocks for dissipationless electronics. Existing realizations, however, rely on magnetic fields, ferromagnets, or complex heterostructures that hinder integration and scalability. Here we demonstrate a diode effect for Cooper-pairs that arises solely from electron-electron interactions in nanoscale superconducting lead islands. When these islands are driven into the Coulomb blockade regime, Cooper-pair transport occurs through resonant charge states. By tuning the island's electrostatic environment, we controllably break particle-hole symmetry and induce nonreciprocal supercurrents, thereby achieving a gate-switchable superconducting diode without any external magnetic field. Our approach enables robust rectification of superconducting currents and microwave photoresponse, providing a scalable strategy to superconducting logic devices.

Figures (4)

• Figure 1: Resonant Cooper-pair tunneling in Pb islands on graphene. (a) Schematic rendering of the experimental setup: an STM superconducting tip approaches a superconducting Pb island on proximitized graphene. (b) STM image showing Pb islands of different sizes on graphene ($V$ = 0.4 V, $I$ = 10 pA). (c) Voltage-biased $dI/dV$ spectra of a large island, with effective radious $r_{eff} =\sqrt{Area/\pi}= 18.9$ nm, (blue, $V = 5$ mV, $I = 250$ nA, $R=20$ k$\Omega$), showing a Josephson peak at zero bias, and a small island, with $r_{eff} = 13.9$ nm (orange,$V$ = 5 mV, $I$ = 200 nA, $R=25$ k$\Omega$), with symmetric resonant Cooper-pair tunneling (RCT) peaks separated by a voltage gap. Insets: STM images of the two islands. (d) Current-biased $V(I)$ characteristics of the islands in panel c, comparing the zero-voltage Josephson state of the larger (blue) with the voltage step in the smaller (orange), representing the onset for RCT (junction resistances as in c). The orange curve is multiplied by 0.8 to compensate for the different tunneling resistances, allowing comparison of low-resistance plateaus. (e) Dependence of RCT gap on island size, determined from voltage-biased spectra on a set of 12 islands of different areas. The gap increases inversely with effective radius $r_{eff}$, as expected for Coulomb blockade. We identify it as a Cooper pair charging gap, amounting to $4E_C/e$.
• Figure 2: Josephson effect in the presence of Coulomb blockade. (a) Circuit model of the double Josephson Junction and, below, scheme of the two mechanisms of Cooper-pair tunneling described in section S10: direct and via (dis)charging the island. (b) Eigen-energies of the charge Hamiltonian \ref{['charge']} as a function of the gate-induced charge offset $n_0$. Parabolic energy bands for each charge state $\hat{n} = -2, 0,$ and $2$ (dashed lines) overlap and open gaps proportional to $E_J$. Vertical arrows mark Cooper-pair tunneling events that add or remove pairs from the island. A finite fractional charge offset $n_0$ breaks particle–hole symmetry for Cooper-pair tunneling (dashed arrows). (c,d) PoE simulations (orange) of Josephson dI/dV spectra (blue) of (c) a single and (d) double JJs, using $E_C=0.35$ meV in d and a tip-sample capacitance of 5 fF (1 fF) for the simulation in panel c(d). The PoE in d reproduces RCT peaks spaced by a bias gap amounting to twice the charging energy $4E_C$ divided by 2e, the Cooper pair charge, i.e. $4E_c/e$. As the model ignores other transport mechanisms relevant at energies $\sim 4E_C$ (e.g. multiple Andreev reflections, thermal quasiparticle tunneling,..) the negative $\dv*{I}{V}$ dips are overestimated in the simulation.
• Figure 3: Gate voltage dependence of the RCT peaks.a dI/dV spectrum of a $r_{eff} = 13.9$ nm Pb island (STM image in the inset) showing voltage-asymmetric RCT peaks. b Current bias V(I) spectrum of the same island in A, asymmetric in resistance and hysteresis. In gray, the calculated V/I resistance shows a pronounced diode effect. c Set of dI/dV spectra varying the island excess charge $q_0$ from +0.75e to -0.75e with STM voltage pulses (section S5), inducing a gradual shift of the RCT peaks (V = 5 mV, I = 200 nA, R = 25 k$\Omega$). d Set of V(I) spectrum in the same conditons of c. The diode effect gradually switches polarity with $n_0$ (also shown in linear resistance plots in fig. S6). e RCT mechanism in the presence of inversion and particle-hole symmetry breaking. Thicker(thinner) arrows represent the easy(resistive) current polarity.
• Figure 4: Cooper pair rectifier behavior.a$V(I)$ plots of a $r_{eff}=9.5$ nm Pb island in two opposite charge polarities (top, $n_0>0$, bottom $n_0<0$). A simulated sinusoidal current drive around $I=0$ yields an offset non-sinusoidal junction voltage. b Voltage rectification produced by a sinusoidal bias current at drive frequency of 1 applied to each of the two gating configurations of the island in a ($V$ = 5 mV, I = 250 nA, R = 20 k$\Omega$). c Detection of microwave radiation using the Cooper pair diode in voltage-biased mode exposed to a radiofrequency antenna. The experimental zero-voltage current $I(0)$ (dots) increases with incident microwave power, independently of frequency (color). Solid lines are fits of Tien-Gordon theory. Error bars correspond to the uncertainty in $I$. Inset shows its dependence on junction power in the small-signal limit, where it is well approximated by a linear fit giving the sensor responsivity.