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arXiv:cond-mat/9712074 · Physics-Uspekhi

Coulomb effects in a ballistic one-channel S-S-S device

Dmitri A. Ivanov, M. V. Feigel’man

Published Feb 28, 1998• 1 citation
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Abstract

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy $E_C \ll Δ$. 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 $π$, 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 $Q_x=C V_g$ with period $2e$.

DOI
10.1070/pu1998v041n02abeh000363

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•Jan 1, 2006•5 citations
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 .
We study the interplay of controlled quantum-mechanical charge and phase fluctuations by measuring their influence on the supercurrent through a small superconducting grain. The grain is connected to leads by two small Josephson tunnel junctions. The phase fluctuations are controlled by the magnetic flux threading a SQUID that connects the grain to a large superconductor. The charge fluctuations are modulated by a voltage on a gate capacitor. As a function of gate voltage we observe a broadening of the Coulomb resonance of the supercurrent for decreasing phase fluctuations, in agreement with theoretical predictions.
We consider charge quantization in a small superconducting grain that is contacted by a normal-metal electrode and is controlled by a capacitively coupled gate. At zero temperature and zero conductance GGG between the grain and the electrode, the charge QQQ as a function of the gate voltage Vg{V}_{g}Vg​ changes in steps. The step height is eee if $\ensuremath{\Delta}<{E}_{c}$, where $\ensuremath{\Delta}$ and Ec{E}_{c}Ec​ are, respectively, the superconducting gap and the charging energy of the grain. Quantum charge fluctuations at finite conductance remove the discontinuity in the dependence of QQQ on Vg{V}_{g}Vg​ and lead to a finite step width $\ensuremath{\propto}{G}^{2}\ensuremath{\Delta}$. The resulting shape of the Coulomb blockade staircase is of a novel type. The grain charge is a continuous function of Vg{V}_{g}Vg​ while the differential capacitance, dQ∕dVgdQ∕d{V}_{g}dQ∕dVg​, has discontinuities at certain values of the gate voltage. We determine analytically the shape of the Coulomb blockade staircase also at nonzero temperatures.
Spectral density of current fluctuations in a short ballistic superconducting quantum point contact is calculated for arbitrary bias voltages VVV. Contrary to a commonly held view that the supercurrent flow in Josephson junctions is a coherent process without fluctuations, we find extremely large current noise that is caused by the supercurrent coherence. At finite voltages, this noise can be qualitatively understood as the shot noise of the large charge quanta of magnitude $2\ensuremath{\Delta}/V$ equal to the charge transferred through the contact during one period of the Josephson oscillations.
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.
This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning.