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Physical Review Letters

Bloch Diode

Manuel Houzet, Tereza Vakhtel, Julia S. Meyer

Published Mar 12, 2026• 1 citation
Publisher

Abstract

The Josephson diode effect-an asymmetry of critical currents at opposite polarities-has attracted much attention recently. One of its simplest realizations is an asymmetric SQUID with multiple Josephson harmonics tuned away from half-integer flux (in units of the superconducting flux quantum). Here we predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. The dual "Bloch diode effect" manifests itself as an asymmetry of critical voltages at opposite polarities when the Cooper pair transistor is tuned away from half-integer gate charge (in units of the Cooper pair charge). It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a Bloch diode could be implemented using conventional superconducting quantum circuits.

DOI
10.1103/q98p-j4vh

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•Jan 1, 1999•2 citations
The Josephson diode effect-an asymmetry of critical currents at opposite polarities-has attracted much attention recently. One of its simplest realizations is an asymmetric SQUID with multiple Josephson harmonics tuned away from half-integer flux (in units of the superconducting flux quantum). Here we predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. The dual "Bloch diode effect" manifests itself as an asymmetry of critical voltages at opposite polarities when the Cooper pair transistor is tuned away from half-integer gate charge (in units of the Cooper pair charge). It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a Bloch diode could be implemented using conventional superconducting quantum circuits.
In a SQUID tuned away from half-integer flux (in units of the superconducting flux quantum), the concurrence of multiple Josephson harmonics and an asymmetry between the junctions leads to the Josephson diode effect -- a nonreciprocal current-voltage characteristic manifested as an asymmetry of critical currents at opposite polarities. We predict a dual version of this effect in a gate-tunable Cooper pair transistor placed in series with a highly resistive environment. When tuned away from half-integer gate charge (in units of the Cooper pair charge) it shows an asymmetry of critical voltages at opposite polarities -- a dual diode effect we refer to as the Bloch diode effect. It arises from an asymmetry in the dispersion of the transistor's Bloch bands. A highly resistive environment can be realized with a Josephson junction array, suggesting that such a diode could be implemented using conventional superconducting quantum circuits.
We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy EJ{E}_{J}EJ​ embedded in an inductive environment provided by a chain of SQUIDs. Such an environment induces localization of the charge on the junction, which results in an enhancement of the zero-bias resistance of the circuit. We explain this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by charge diffusion in the lowest Bloch band of the Josephson junction as well as by Landau-Zener transitions out of the lowest band into the higher bands. In addition, the frequencies corresponding to the self-resonant modes of the SQUID array exceed the Josephson energy EJ{E}_{J}EJ​ of the tunable junction, which results in a renormalization of EJ{E}_{J}EJ​, and, as a consequence, an increase of the effective bandwidth of the lowest Bloch band.
We investigate the switching current of a Cooper pair transistor with tunable Josephson energy. The junctions are fabricated in a superconducting quantum interference device (SQUID) geometry which allows for an in situ tunable effective Josephson energy by application of a magnetic field. We find a 2e2e2e-periodic switching current versus gate charge. As the magnetic field is increased the switching current stays 2e2e2e-periodic but the magnitude is suppressed. At a magnetic field of half a flux quantum through the SQUID's the switching current is minimum. We can theoretically model the experimental data by assuming a switching current which is proportional to the ideal critical current squarred. We show that such a dependence is expected in the limit where the effect of thermal fluctuations on the system is strong.
We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with R/sub s/=1 k/spl Omega/. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise limits. The critical current of the system was found to be close to its nominal value, that is in accordance with the electromagnetic environment theory. The I-V curves were modulated by the gate with a period of e and a maximum swing of about 2 /spl mu/V. Such rather moderate modulation results from the Josephson-to-charging energies ratio, E/sub J//E/sub C//spl ap/9, in our sample being far from its optimum value (/spl ap/0.3+1).
In superconducting quantum interference devices (SQUIDs), the superconducting diode effect may be generated by interference of multiple harmonic components in the current-phase relationships (CPRs) of different branches forming SQUID loops. Through the inclusion of two gate-tunable Josephson junctions in series in each interference branch of a double-loop SQUID, we demonstrate independent control over both the harmonic content and the amplitude of three interfering CPRs, facilitating significant improvement in the maximum diode efficiency. Through optimized gate-controlled tuning of individual Josephson energies, diode efficiency exceeding 50% is demonstrated. Flux-dependent oscillations show quantitative agreement with a simple model of SQUID operation.
Abstract⎯We have fabricated the Bloch transistor shunted on-chip by a small-sized Cr resistor with Rs ≈ 1 kΩ. The Bloch transistor normally consists of two small Josephson junctions connected in series, which in our case have been replaced by two superconducting interferometer loops, each with two junctions in parallel. A capacitively coupled gate is supplied to control the induced charge of the small intermediate electrode (island) of the transistor. The measured I-V curves show no hysteresis and correspond to the operation of a effective Josephson junction at the high-damping and strong-noise limits. The critical current of the system was found to be close to its nominal value, that is in accordance with the electromagnetic environment theory. The I-V curves were modulated by the gate with a period of e and a maximum swing of about 2 µV. Such rather moderate modulation results from the Josephson-tocharging energies ratio, EJ/EC ≈ 9, in our sample being far from its optimum value ( ≈ 0.3÷1). I.