Emergence of a negative charging energy in a metallic dot capacitively coupled to a superconducting island

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 $(+2\mid e\mid )$ followed by negative ones $(-\mid e\mid )$ 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.

Figure 1

Schematic view of a normal island $\left(N\right)$ coupled to a Cooper pair box composed of a Josephson junction connecting superconducting reservoir 2 and island $S$, and gate 10. For strong capacitive coupling (controlled by 3 and 9), $S$ imposes an attractive interaction among electrons tunneling between island $N$ and its reservoir (defined between 7 and 8). Detection is made by sweeping the gate voltage 4 and measuring the island voltages using quantum point contacts for both $N$ (5,6,7) and $S$ (1,11,12).

Figure 2

Charge stability (or honeycomb) diagram for $b=1$, (a) $r=0.2$, (b) $r=0.5$, (c) $r=0.8$, and (d) $r=1$. The insets show the charging curves for $N$. In case (c), the charging staircase (inset) exhibits charge-skipping effects.

Figure 3

Charging staircase: (i) (full line) perturbative solution in $E_J$ for $r=0.8$, $b=1$, $E_J∕E_{CS}=0.5$, $k_{B}T∕E_{CS}=3\times {10}^{-2}$, and $R_N∕R_K=10$; (ii) (dotted line) adiabatic solution for $E_J∕E_{CS}=2$, the other parameters being unchanged.

Figure 4

Phase diagram in the $b,r$ plane. The unphysical gray region is excluded. Charge skipping and NDCA occur above the dotted line from bottom to top: $E_J∕E_{CS}=0$ (analytic), 1, 2, and 4 (adiabatic calculation). All other parameters are the same as in Fig. 3.