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Japanese Journal of Applied Physics

Magnetoresistance in a Superconducting Single-Electron Transistor with a Multiply Connected Coulomb Island

Hideki Sato, Mitsuru Kimura, Shingo Katsumoto

Published Jun 1, 1997• 0 citations
Publisher

Abstract

The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.

DOI
10.1143/jjap.36.4022

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The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.
The number of Cooper pairs on a small superconducting island coupled to superconducting leads by a Josephson junction fluctuates due to tunneling of Cooper pairs through the junction. On the other hand, the impedance of the circuit surrounding the island tends to suppress these fluctuations and to restore charge quantization. We consider the influence of the electromagnetic environment within a two-state approximation for the charge on the island. The average charge and the slope of the steps of the Coulomb staircase are calculated for a realistic environmental impedance and finite temperatures in the range of current experimental studies. It is shown that even a low-frequency environment may lead to a considerable reduction of charge fluctuations provided the integrated total impedance is large enough.
We investigate how coherent Cooper-pair tunneling depends on the competition between Josephson coupling energy E J and charging energy E C. Measurements were performed on a circuit consisting of two dc-SQUIDs in series, with a gate capacitively coupled to the central island. As the E J/E C ratio decreased, coherent Cooper pairs tended to tunnel incoherently. Measured data show good agreement with theoretical calculations in strong and weak coupling limits. This experiment implies the manifestation of Heisenberg's uncertainty principle in a superconductor.
This thesis presents measurements of quantum coherence in a single Cooper pair box, where quantum oscillations of charge between a reservoir and a small superconducting island have been observed. The single Cooper pair box (SCB) consists of a small metallic island which is connected to a reservoir via a tunnel junction. In the superconducting state, Cooper pairs are free to tunnel to and from the island, whose potential can be controlled by a gate voltage. A graded gap method was used to prevent quasiparticles from tunneling onto the island. For this purpose, a magnetic field suppressed the superconducting gap in the SCB leads more than in the island. This created an additional energy barrier for quasiparticles to tunnel to the island, making the gate voltage modulation periodic in Cooper pair charge. For a limited range of gate voltage, the SCB was found to behave as a model two-level quantum mechanical system. A non-adiabatic change in the induced island charge was used to bring two charge states into resonance. The resulting time evolution showed clear charge oscillations between the ground and excited state, with a frequency given by the energy level separation divided by Planck's constant. These oscillations had a longest coherence time of T2=9 ns at a point where the pure charge states are degenerate. The coherence time at this point was found to be limited by the relaxation rate, ?1. Away from this point, the coherence time was limited by the dephasing rate, ??. Away from the charge degeneracy, the dependence of T2 on gate charge suggested that low frequency fluctuators were the main source of dephasing. The charge of the Cooper pair box was measured by coupling the SCB capacitively to a radio frequency single electron transistor (RF-SET). The RF-SET was used as an electrometer by measuring the amount of reflection from a resonant microwave circuit in which a single electron transistor (SET) was embedded. A best charge sensitivity of 2.3·10-6 e/sqrt(Hz) and a 7 MHz bandwidth was reached in an improved setup. Another part of this thesis concerns an investigation of electrical filters for use in single electronics experiments. The characteristics of seven different types of cryogenic filters were evaluated.
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.
The single Cooper pair josephson transistor is a device that exhibits at the same time charge quantization and phase coherence. Coherent quantum phase slip phenomenon is “dual” the Josephson phase coherence, while the charge quantization is dual to the flux quantization. We present the experimental demonstration and the theoretical description of a new superconducting device–single flux transistor, which is dual to the single Cooper pair transistor. Our transport measurements show the periodic modulation of the critical voltage by the external magnetic field. The obtained current-voltage characteristics show the hysteretic behavior, which we attribute to the intrinsic self-heating of charge carriers.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.