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 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.
We consider the hybrid setup formed by a metallic dot, capacitively coupled to a superconducting island
S connected to a bulk superconductor by a Josephson junction. Charge fluctuations in
S act as a dynamical gate and overscreen the electronic repulsion in the metallic dot, producing an attractive interaction between two additional electrons. As the offset charge of the metallic dot is increased, the dot charging curve shows charge-skipping positive steps $(+2\ensuremath{\mid}e\ensuremath{\mid})$ followed by negative ones $(\ensuremath{-}\ensuremath{\mid}e\ensuremath{\mid})$ signaling the occurrence of a negative differential capacitance. A necessary condition for such an effect is that the capacitance coupling the two islands should be larger than the Josephson junction capacitance. A proposal for experimental detection is given, and potential applications in nanoelectronics are outlined.
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.