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Journal of the Physical Society of Japan

Tunable Parity Effect in Coupled Superconducting Single-Electron Transistors

Shingo Katsumoto, Mitsuru Kimura

Published Dec 15, 1996• 2 citations
Publisher

Abstract

We report the current-voltage characteristics of a single-electron circuit, in which the Coulomb island of a single-electron transistor is connected to the source electrode of another transistor. The Josephson-like current of one of the transistors was tuned by adjusting the gate voltage of the other, reflecting the uncertainty relation between the phase difference and the particle number. We found that the “parity effect” or “even-odd asymmetry” was also affected by the gate voltage of the other transistor. A possible explanation for this asymmetry-tuning is presented.

DOI
10.1143/jpsj.65.3704

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We report the current-voltage characteristics of a single-electron circuit, in which the Coulomb island of a single-electron transistor is connected to the source electrode of another transistor. The Josephson-like current of one of the transistors was tuned by adjusting the gate voltage of the other, reflecting the uncertainty relation between the phase difference and the particle number. We found that the “parity effect” or “even-odd asymmetry” was also affected by the gate voltage of the other transistor. A possible explanation for this asymmetry-tuning is presented.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
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 supercurrent branch of a superconducting single electron transistor as a function of gate charge, temperature, and magnetic field. At low temperature and magnetic field, the switching current goes from a minimum to a maximum when the gate charge is varied from 0 to e, as expected for an island in the ground state with an even electron number. When the odd electron number ground state becomes populated by an increase of temperature or field, the Josephson tunneling is strongly suppressed, in agreement with theoretical predictions.
In a system where two small-area (100 nm x 100 nm) superconducting tunnel junctions are connected in series, the Josephson effect which tends to impose the phase competes with the charging effects in the central electrode (the "island" of the device) which tend to set the charge of the island. By applying a voltage on an electrode capacitively coupled to the island (the "gate" electrode) one can arbitrate this competition in favour of either effect. This is can be seen in particular on the supercurrent which can flow through the junctions : it is modulated periodically by the gate voltage (hence the name of "transistor" given to the system). This modulation shows sharp peaks when two charge states of the island are degenerate with respect to the electrostatic energy. The system is then in a state which has no classical description : it is in a coherent superposition of states. In this thesis we demonstrate experimentally the behaviour of this transistor and we analyse the theoretical and practical problems which can prevent the observation of the coherent superposition of states through the modulation of the supercurrent. In particular we show that the parity of the electron number in the island must be rigorously controlled and that the impedance connected to the circuit plays a crucial role in setting the magnitude of the measured supercurrent.
We have experimentally studied Coulomb oscillation in a superconducting single-electron transistor, where electromagnetic-environment impedance was controlled using a one-dimensional array of superconducting quantum interference devices. By decreasing environment impedance, the Coulomb oscillation exhibited a crossover from 2e2e2e to 1e1e1e periodicity. In addition, the 1e1e1e component was enhanced when additional noise was introduced by connecting a potential meter to the central island of the transistor. We propose a theoretical analysis for this parity effect that includes the effect of fluctuations arising from the finite noise temperature of the electromagnetic environment.
The transport properties of a small superconductor--normal-metal--superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current Ic{\mathit{I}}_{\mathit{c}}Ic​ through such a system as a function of the gate voltage Vg{\mathit{V}}_{\mathit{g}}Vg​ taking into account parity effects in the superconductors. The dependence Ic{\mathit{I}}_{\mathit{c}}Ic​(Vg{\mathit{V}}_{\mathit{g}}Vg​) shows resonant singularities and has a qualitatively different character for \ensuremath{\Delta}EC{\mathit{E}}_{\mathit{C}}EC​ and \ensuremath{\Delta}>EC{\mathit{E}}_{\mathit{C}}EC​, \ensuremath{\Delta} being the superconducting gap and EC{\mathit{E}}_{\mathit{C}}EC​=e2{\mathit{e}}^{2}e2/2C being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.