Vanishing quasiparticle density in a hybrid Al/Cu/Al single-electron transistor

The achievable fidelity of many nanoelectronic devices based on superconducting aluminum is limited by either the density of residual nonequilibrium quasiparticles $n_{\mathrm{qp}}$ or the density of quasiparticle states in the gap, characterized by Dynes parameter $\gamma$. We infer upper bounds $n_{\mathrm{qp}}<0.033\mu {\mathrm{m}}^{-3}$ and $\gamma <1.6\times {10}^{-7}$ from transport measurements performed on Al/Cu/Al single-electron transistors, improving previous results by an order of magnitude. Owing to efficient microwave shielding and quasiparticle relaxation, a typical number of quasiparticles in the superconducting leads is zero.

Figure 1

(a) Large scale electron micrograph of a sample showing the electrical connections to the active region in the middle. Portions of the ground plane, covered by an insulating Al${\text{O}}_x$ layer of 25 nm thickness, are also visible. (b) Active area of one of the measured samples, consisting of two Al/Al${\text{O}}_x$/Cu/Al${\text{O}}_x$/Al SETs that are coupled capacitively by a Cr wire located underneath the insulating layer. Arrows illustrate the monitored in- and out-tunneling events at the lower SET (green and red, respectively), and the macroscopic electrometer current (yellow) in a configuration where the upper SET is used as the electrometer. Shadow-evaporated leads terminate at ohmic Au/Al contacts beginning $10\mu \mathrm{m}$ away from the junctions (not shown).

Figure 2

Bandwidth-corrected single-electron tunneling rates as a function of $V_{\mathrm{ds}}$ at charge degeneracy measured in different setups at base temperature: PT (18 mK, open upward triangles), PDR1 (50 mK, open circles), and PDR2 (50 mK, open squares). For PDR1, data from higher temperatures is also given: 131 mK (filled stars) and 158 mK (filled diamonds). All these measurements were performed with the same sample employing Au/Al contacts for quasiparticle trapping. The two thin solid lines represent thermally activated rates calculated for the known sample parameters at 158 mK and 135 mK. The dashed line is the theoretical rate for $\gamma =1.6\times {10}^{-7}$ at $T_S=T_N=50\mathrm{mK}$, and the horizontal thick line represents the rate induced by $n_{\mathrm{qp}}=0.033\mu {\mathrm{m}}^{-3}$. Open downward triangles: Base temperature data from a reference sample without Al/Au contacts measured in PDR1. For ease of comparison, tunneling rates from the reference sample have been scaled by the ratio of junction conductances $\frac{G_L+G_R}{G_L^{\mathrm{ref}}+G_R^{\mathrm{ref}}}$.

Figure 3

(a) Measured width of the Coulomb staircase steps as a function of bath temperature for different bias voltages of the DUT. (b) Observed zero-bias tunneling rates at base temperature for different detector currents, and a linear fit to the data. The plotted current is the mean value of the detector trace from which the transition rate was determined.