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Attractive correlation and charge skipping in a metallic grain capacitively coupled to a superconducting island

Cecilia Holmqvist, D. Feinberg, Alex Zazunov

Published Mar 15, 2007• 0 citations
OpenAlex

Abstract

Capacitively coupling a normal metallic grain to a superconducting island can lead to attractive correlation (negative-U center) in the grain. The considered setup geometry is similar to that of a Cooper pair box coupled to a single-electron transistor, but operates in the regime of strong capacitive coupling. In the Coulomb staircase for the grain, positive steps ($+2e$) skipping odd charge numbers are found to be followed by negative ones ($-e$) signaling the occurrence of a negative differential capacitance. The condition for charge skipping is analyzed as a function of the ratio between the Josephson ($E_J$) and charging energies. The non-monotonous charging curves are calculated in the limits of large and small $E_J$.

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Capacitively coupling a normal metallic grain to a superconducting island can lead to attractive correlation (negative-U center) in the grain. The considered setup geometry is similar to that of a Cooper pair box coupled to a single-electron transistor, but operates in the regime of strong capacitive coupling. In the Coulomb staircase for the grain, positive steps (+2e+2e+2e) skipping odd charge numbers are found to be followed by negative ones (−e-e−e) signaling the occurrence of a negative differential capacitance. The condition for charge skipping is analyzed as a function of the ratio between the Josephson (EJE_JEJ​) and charging energies. The non-monotonous charging curves are calculated in the limits of large and small EJE_JEJ​.
We consider the hybrid setup formed by a metallic dot, capacitively coupled to a superconducting island SSS connected to a bulk superconductor by a Josephson junction. Charge fluctuations in SSS 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.
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.
In the field of nanoelectronics, one seeks to combine quantum mechanical effects with macroscopic entities such as currents in order to find new ways of storing and manipulating information. One possibility to accomplish this is to use the quantum correlations found in superconductors. Teaming superconductors with normal metals and magnetic systems, one can obtain novel correlation and fluctuation effects. \n\nIn the first work of this thesis, we examine how charge correlations in a metallic dot are modified due to the presence of a capacitively coupled superconducting island. It is possible to overcome the Coulomb repulsion between electrons in a hybrid double-dot system consisting of a metallic island coupled capacitively to a Cooper-pair box. The superconducting island S acts as a dynamic gate on the metallic island N and in the strong coupling regime the electric charge of the Cooper pairs in S and their fluctuations are able to overscreen the repulsion between electrons in N. This produces an attractive interaction between two additional electrons in the metallic island and results in a non-monotonous charging curve of the metallic island. \n\nThe second part of the thesis considers how the dynamics of a precessing molecular magnetic moment affects the Josephson current. The precession gives rise to a time-dependent tunnel potential which not only creates different tunneling probabilities for spin-up and spin-down quasiparticles, but also introduces a time-dependent spin-flip term. In particular, we study the effects of the spin-flip term alone on the Josephson current between two spin-singlet superconductors as a function of precession frequency and junction transparency. The system displays a nonequilibrium steady-state solution which depends on the precession frequency of the classical spin.\n\n\n
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 model a Superconducting Single-Electron Transistor operating by repulsive interactions. The device consists of a ring of Hubbard clusters, placed between electrodes and capacitively coupled to a gate potential. In each cluster, a pair of electrons at appropriate filling feels a weak effective interaction which leads to pairing in part of the parameter space. Thus, the system can host many bound pairs, with correlation induced binding. When the charging energy exceeds the pairing energy, single-electron tunneling prevails; in the opposite regime, we predict the Coulomb blockade pattern of two-electron tunneling. This suggests that in tunneling experiments repulsion-induced pairs may behave in a similar way as phonon-induced ones.
The charge on a superconducting island coupled to a superconducting electrode by a Josephson junction is determined in the region where the gap energy and the single-electron charging energy of the island are of comparable magnitude. The Coulomb staircase describing the incremental charging of the island in response to a biasing voltage is studied. The rounding of the staircase corners due to thermal and quantum fluctuations is found to depend on the parity of the island charge in the adjacent tread. This should allow for an experimental disentanglement of the effects of quantum charge fluctuations from thermal fluctuations.