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Soviet Journal of Low Temperature Physics

Quantum mechanical analysis of a single contact superconducting interferometer at low temperatures

Ya. S. Grinberg

Published Apr 1, 1982• 0 citations
Publisher

Abstract

The behavior of a single-contact superconducting interferometer at low temperatures, when its energy of zero point quantum vibrations ℏ(LC)−1/2 is comparable to the thermal energy kT, is studied. Hysteresis-free and hysteretic regimes of operation of the interferometer are examined. It is shown that taking into account quantum corrections leads to effects which, probably, can be observed experimentally.

DOI
10.1063/10.0030691

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The behavior of a single-contact superconducting interferometer at low temperatures, when its energy of zero point quantum vibrations ℏ(LC)−1/2 is comparable to the thermal energy kT, is studied. Hysteresis-free and hysteretic regimes of operation of the interferometer are examined. It is shown that taking into account quantum corrections leads to effects which, probably, can be observed experimentally.
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We analyze the thermal escape behavior of the metastable zero-voltage state in biased symmetric hysteretic interferometers in external magnetic fields. An effective single degree of freedom equation of motion for the system with small loop inductance is derived and used to evaluate the two necessary parameters, energy barrier and attempt frequency, for the successful application of Kramers theory for thermal escape from metastable states. The slightly revised theory, resulting in a double pendulum model of the interferometer, is outlined and numerical simulation results are used to validate the approach. Recent experimental reports of excessive thermal escape temperatures for interferometers are discussed and interpreted.
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We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy EC≪ΔE_C \ll ΔEC​≪Δ. We consider a small superconducting grain of finite capacity connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is supposed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system may be described as quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima which become degenerate at the phase difference on the leads equal to πππ, the tunneling amplitude between them being controlled by the gate voltage at the grain. We find the Josephson current and its low-frequency fluctuations and predict their periodic dependence on the induced charge Qx=CVgQ_x=C V_gQx​=CVg​ with period 2e2e2e.
We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q x =CV g .