We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy
EC≪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
Qx=CVg with period
2e.
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 Josephson current through a superconducting grain coupled by two tunnel junctions to macroscopic superconducting leads. As a result of the Coulomb blockade we predict the critical Josephson current to have a threshold behavior when the superconducting gap is suppressed below the charging energy by a magnetic field. This effect is a direct consequence of a discrimination by the superconducting ground state between odd and even number of electrons on the grain. The critical current is periodically modulated by the voltage of a gate electrostatically coupled to the grain. We find a characteristic change in this modulation at the threshold.
We investigate Cooper-pair tunneling in a circuit consisting of two dc-superconducting quantum interference devices in series, with a gate capacitively coupled to the central island. Measurements cover a wide range of values of the ratio between Josephson coupling energy
EJ and charging energy
EC. The
ECEJ ratio dependence of the supercurrent is well described by the orthodox theory provided that strong fluctuations of the Josephson phase due to the electromagnetic environment are taken into account. Our data can be interpreted in terms of squeezing of the charge fluctuations with decreasing
ECEJ ratio.
We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.
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
G between the grain and the electrode, the charge
Q as a function of the gate voltage
Vg changes in steps. The step height is
e if $\ensuremath{\Delta}<{E}_{c}$, where $\ensuremath{\Delta}$ and
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
Q on
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 while the differential capacitance,
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.