Excitation of Single Quasiparticles in a Small Superconducting Al Island Connected to Normal-Metal Leads by Tunnel Junctions

We investigate the dynamics of individual quasiparticle excitations on a small superconducting aluminum island connected to normal metallic leads by tunnel junctions. We find the island to be free of excitations within the measurement resolution. This allows us to show that the residual heating, which typically limits experiments on superconductors, has an ultralow value of less than 0.1 aW. By injecting electrons with a periodic gate voltage, we probe electron-phonon interaction and relaxation down to a single quasiparticle excitation pair, with a measured recombination rate of 16 kHz. Our experiment yields a strong test of BCS theory in aluminum as the results are consistent with it without free parameters.

Figure 1

(a) Scanning electron micrograph of the sample studied. It is biased with voltage $V_b$ and a gate offset voltage $V_g$ is applied to a gate electrode (not shown) to obtain a gate offset charge $n_g=C_g{V}_g/e$, where $C_g$ is the gate-island capacitance. (b) Measured source-drain current $I$ as a function of bias and gate voltages. (c) Calculated current based on sequential single-electron tunneling model. (d) Measured current at $n_g=0$ is shown as black dots. Black line is calculated assuming a quasiparticle generation rate of 2 kHz, and the red line is calculated assuming a vanishing generation rate.

Figure 2

(a),(b) Measured current of sample A against gate voltage amplitude $A_g$ at $f=4$ and 1000 kHz at bias voltage values $V_b=120$, 200, $280\mu \mathrm{V}$ shown as blue, red, and green dots, respectively. Black lines show simulations assuming an elevated temperature on the superconducting island. (c) Similar measurement for sample B at $f=1\mathrm{MHz}$. (d) The electron-phonon heat flux in the superconducting state normalized by that in the normal state extracted from the measurements (black circles). Temperature is expressed with respect to the critical temperature $T_C=\Delta /1.76k_B$. The theoretical result of Eq. (3) is shown by the black line. Solid and dotted red lines show the recombination and scattering part of Eq. (3) correspondingly. The open gray symbol is from sample B.

Figure 3

Red circles show the measured current for $f=4–1000\mathrm{kHz}$ at $V_b=280\mu \mathrm{V}$. Black lines are simulations based on Eq. (1). Recombination rates are taken to match the heat flux in the regime where the thermal model applies [Eq. (3)]. Dotted blue lines are calculated with vanishing electron-phonon relaxation rate and solid gray lines with the thermal model.