Indirect Tunneling Enabled Spontaneous Time-Reversal Symmetry Breaking and Josephson Diode Effect in TiN/Al$_2$O$_3$/Hf$_{0.8}$Zr$_{0.2}$O$_2$/Nb tunnel junctions

Josephson diode (JD) effect found in Josephson tunnel junctions (JTJs) has attracted a great deal of attention due to its importance for developing superconducting circuitry based quantum technologies. So far, the highly desirable electrical control of the JD effect has not been demonstrated in any JTJ prepared by techniques used in semiconductor industry. We report the fabrication of JTJs featuring a composite tunnel barrier of Al$2$O$3$ and Hf${\mathrm{0.8}}$Zr$\mathrm{0.2}$O$_2$ prepared by complementary-metal-oxide-semiconductor (CMOS) compatible atomic layer deposition (ALD). These JTJs were found to show the JD effect in nominally zero magnetic fields with the nonreciprocity controllable using an electric training current, yielding a surprisingly large diode efficiency not achieved previously. The quasiparticle tunneling, through which the Josephson coupling in a JTJ is established, was found to show no nonreciprocity. We attribute these observations to the simultaneous presence of positive and negative Josephson couplings, with the latter originating from indirect tunneling. The resulted spontaneous time-reversal symmetry breaking and the double-minima washboard potential for the ensemble averaged phase difference in the resistively and capacitively shunted junction (RCSJ) model are shown to fully account for the experimentally observed JD effect.

💡 Research Summary

The authors demonstrate a Josephson tunnel junction (JTJ) that exhibits a robust, magnetic‑field‑free Josephson diode (JD) effect and can be electrically programmed using a CMOS‑compatible fabrication route. The device stack consists of a 30 nm TiN bottom electrode, a composite tunneling barrier formed by 0.5 nm Al₂O₃ followed by 0.7 nm Hf₀.₈Zr₀.₂O₂ (both deposited by atomic‑layer deposition, ALD), a 30 nm Al₂O₃ capping layer to protect TiN, and a 100 nm Nb top electrode deposited by sputtering. The use of ALD ensures conformal, pinhole‑free layers, as confirmed by atomic‑force microscopy and the linear scaling of the normal‑state resistance with junction area.

Electrical transport measurements at 3 K reveal a clear zero‑voltage supercurrent with distinct critical (I_c) and retrapping (I_r) currents, indicating an under‑damped junction. Quasiparticle tunneling spectra (dI/dV vs. eV) display four gap‑related peaks: two correspond to the sum and difference of the Nb and TiN BCS gaps (direct tunneling), while the other two match the individual gaps of Nb and TiN, arising from double‑quasiparticle processes that become visible because of the ultra‑thin barrier. The I_c R_N product (~1 mV) agrees with the Ambegaokar‑Baratoff prediction, confirming that the Josephson coupling is governed by conventional Cooper‑pair tunneling.

Crucially, the critical current is non‑reciprocal: I_c⁺ ≠ I_c⁻ even without any applied magnetic field. This diode asymmetry can be dramatically enhanced by a “training” current—an electric current of roughly five times the critical current applied for several minutes either at low temperature or above the superconducting transition (≈10 K). After training with a positive current, I_c⁺ becomes larger than I_c⁻, and the opposite occurs after negative training. The diode efficiency η = |I_c⁺ − I_c⁻|/(I_c⁺ + I_c⁻) reaches 0.39, surpassing previously reported values for non‑magnetic JTJs. The effect disappears above ~3.2 K and is erased when the device is warmed above 10 K, indicating that the training modifies a metastable charge configuration that is stable only at low temperature.

The authors attribute the JD behavior to the coexistence of positive and negative Josephson couplings within the same junction. The Hf₀.₈Zr₀.₂O₂ layer, a high‑κ dielectric known to exhibit ferroelectric‑like behavior at nanometer thicknesses, can host bound interface charges when an electric field is applied. These charges attract opposite mobile carriers, creating localized states that enable indirect Cooper‑pair tunneling with a π‑phase shift, i.e., a negative Josephson coupling. The superposition of the usual (positive) direct coupling and the negative indirect coupling yields a double‑well washboard potential for the phase difference φ. Within the resistively and capacitively shunted junction (RCSJ) model, this double‑minimum potential naturally produces two distinct stable phase states, leading to direction‑dependent critical currents and spontaneous breaking of time‑reversal symmetry (TRS) without any external magnetic field.

A modified RCSJ equation incorporating both sin φ and sin 2φ terms (the latter with a negative coefficient) reproduces the measured I‑V asymmetry and its dependence on training polarity. The retrapping current remains essentially reciprocal because high‑frequency damping, dominated by the external circuitry, masks any asymmetry in the dissipative channel.

The work establishes three key advances: (1) the first demonstration of a CMOS‑compatible Josephson diode with a large, electrically programmable non‑reciprocity; (2) the identification of indirect tunneling‑induced negative Josephson coupling as a new mechanism for spontaneous TRS breaking in JTJs; and (3) a practical route toward non‑volatile superconducting memory elements, where the diode polarity can be written electrically and retained at cryogenic temperatures. The findings open new avenues for integrating superconducting logic, quantum‑computing interconnects, and hybrid ferroelectric‑superconducting devices using standard semiconductor manufacturing infrastructure.