JOURNAL OF LOW TEMPERATURE PHYSICS Vol. 188, Nos. 5/6 March 2000

Enhancement of Josephson quasiparticle current in coupled superconducting single-electron transistors

D. C. Dixon, C. P. Heij, P. Hadley, and J. E. Mooij
Department of Applied Physics and DIMES, TU-Delft, Delft, The Netherlands

Superconducting single-electron transistors (SSET's) are small islands of superconducting material isolated from an external circuit by tunnel barriers (Josephson junctions). The normal tunnel barrier resistances (R > h/4e2 ~ 6.5 kW) are sufficient to make the SSET's charge a good quantum number, so that the excess charge on the island is constrained to integer multiples of e. At equilibrium, adding an extra charge to the island costs a "charging energy" Ec = e2/2C, where C  is the island's total capacitance.

At zero voltage bias, a supercurrent may flow coherently through the SSET, while for a large voltage bias (|eV| > 4D), the current is dominated by successive charging and discharging of the island by quasiparticles. Within a range of moderate bias (2D + Ec < |eV| < 2D + 3Ec), current flows via a hybrid transport mechanism termed the ''Josephson quasiparticle cycle'' (JQP). 1 In each turn of the cycle, a Cooper pair (CP) resonantly tunnels onto the SSET through one junction, followed by two successive quasiparticle (QP) tunneling events through the other junction, shuttling a charge of 2e between source and drain. The effective CP tunneling rate is typically slower than either QP tunneling rate, so the current is limited by the Josephson coupling.2

Here we show some intriguing measurements of the JQP current flowing through a SSET that is strongly coupled to a nearby, independently voltage-biased SSET. The two SSET's are coupled by a large capacitance Cm supplied by an overlap capacitor instead of a tunnel junction, so there is no direct Josephson coupling between the islands. The strong capacitive coupling ensures that the charge of one island influences the QP and CP tunneling rates for the other island.

The SSET's were formed by the standard procedure of double angle evaporation of Al, with an oxidation step to form Al/AlOx tunnel barriers between each island and the leads. The gate electrodes and the central metal strip coupling the two islands were created in an underlying Au layer, with an intermediate insulation layer of SiO (32 nm). From normal-state measurements,3 the junction capacitances were seen to be in the 0.3 - 0.4 fF range, while Cm ~ 0.6 fF. The series resistances of the SSET's were 7 and 13 MW, so the Josephson energies of the tunnel junctions are expected to be very small (EJ <  0.1 meV) compared to the charging energy (Ec ~ 80 meV).

Measurements of the device were carried out at low electron temperature (27 mK) in a helium dilution refrigerator. The source-drain voltage biases for the two SSET's (Vb1, Vb2) were applied asymmetrically, with one lead from each SSET tied to ground. During our experiments, the left SSET was biased to the onset of JQP (eVb1 = 2D + Ec = 435 meV). When Vb2 was grounded, sweeping the gate voltage Vg1 produced a series of small peaks (~ 0.5 pA) periodic in gate charge of e (DVg1 = e/Cg1 ~ 3.8 mV).

The effects of biasing the other SSET are shown in Figure 2, where the current I is plotted as a function of Vg1, for various values of Vb2. Vg2was counterswept to cancel the cross-capacitance from the gate to the right SSET, fixing the induced charge of this SSET in each gate sweep. Capacitive effects due to the changing bias voltage were not cancelled, however, resulting in a slight leftward shift of the peaks for increasing Vb2.

The additional peaks in Fig. 2 arise due to charging of the right SSET, since an extra charge on that SSET induces a polarization charge (~ 0.24 e) on the left SSET due to the presence of Cm. This shifts the CP tunneling resonance to a different Vg1, allowing a new peak to be visible. Each peak can thus be indexed by the charge of the right SSET (n2), indicated by the dotted lines in Fig. 2. For small Vb2, only one or two peaks are visible per period. Beginning at a bias of about 470 mV, up to four peaks are seen per period. This bias is too small to allow successive QP tunneling, so this appearance of extra peaks may indicate a JQP cycle in the right SSET. As an example of the complex behavior seen in this regime, at Vb2 = 570 mV (Fig. 2(b)), peaks corresponding to an even n2 are all larger than those with odd n2. The four-peak structure continues up to Vb2 ~ 800 mV. At higher biases the peaks disappear one by one, then re-emerge with up to three times their original amplitude. The peak heights continue to increase for even higher Vb2; no saturation in the peak height was seen in similar experiments where the bias voltage was swept up to 5 mV. Although we cannot presently account for each peak's behavior, it is clear that the left SSET can be used to detect charge state populations in the right SSET. The peak height could be considered a measure of the probability that a certain charge state n2 is occupied, modified by the conductivity of the left SSET.

The increase in peak height is not presently understood, and in fact runs counter to expectations. Since JQP current is bottlenecked by the coherent CP tunneling step, it is hard to see how the stochastic fluctuations of n2 would increase this rate. Part of the explanation must take into account events involving the simultaneous transfer of charge in both SSET's. For example, a Cooper pair may tunnel into one of the SSET's while a quasiparticle tunnels out of the other SSET. However, preliminary calculations using the combined density matrix predict a suppression of the JQP current, not an enhancement, when the right SSET conducts a current of quasiparticles.

References