Experimental realization of a Coulomb blockade refrigerator

We present an experimental realization of a Coulomb blockade refrigerator (CBR) based on a single-electron transistor (SET). In the present structure, the SET island is interrupted by a superconducting inclusion to permit charge transport while preventing heat flow. At certain values of the bias and gate voltages, the current through the SET cools one of the junctions. The measurements follow the theoretical model down to $\sim 80$ mK, which was the base temperature of the current measurements. The observed cooling increases rapidly with decreasing temperature, in agreement with the theory, reaching about a 15 mK drop at the base temperature. The CBR appears as a promising electronic cooler at temperatures well below 100 mK.

Figure 1

Principle of the operation of the cooler. (a) Schematic of the energy levels of the device at its operation point. (b) Thermal scheme of the structure.

Figure 2

(a) SEM image of the device, shown together with a schematic of the experimental setup, where the SET island consists of two normal metal islands with a superconducting inclusion in between. (b) Closeup SEM image shows the left part of the SET that is connected to the cooled island through the Al “dot” (see text for more details). Zoom into the Al “dot” with NIN and clean NN contacts is shown in the inset. In the main panel, the NIS probes used to monitor the temperature of the cooled island are highlighted. All normal metal parts are colored red, while superconductors are shown in blue.

Figure 3

(a) Closeup of the measured $I\text{−}V$ of the SET shown as blue dots. The solid red line is the fit for the gate open case. The inset shows the full $I\text{−}V$ of the SET at $\sim 207$ mK (blue dots) together with a full theory fit (solid red line) for both gate open and gate closed positions, utilizing the same $R_T$ and $E_c$ as in the main panel. (b) $I\text{−}V$ curves (orange dots) of one of the probing NIS junctions at various temperatures between 50 and 300 mK. The solid horizontal gray line indicates the 3 pA current bias of the NIS probe (see text for details). The lower inset shows the measured full $I\text{−}V$ at a bath temperature of $\sim 48$ mK. The upper inset shows the voltage calibration obtained from the $I\text{−}V$ curves in the main panel for bias currents of 1, 3, and 14 pA (shown as black, blue, and purple dots from bottom to top, respectively).

Figure 4

Top panels: Temperature $T_1$ over a few gate periods [shown as blue dots in (a) and (d)]. The solid red lines correspond to the theoretical prediction, where the voltage of the SET has a value of $45 \mu \mathrm{eV}$. The base electronic temperatures $T_{e,0}$ are shown as blue dashed lines for data. The two middle panels, (b) and (e), show $T_2$ (green dots) together with the theory (solid red lines), and the base temperatures marked as dashed lines. The two lowest panels, (c) and (f), present the gate dependent current $I$ through the SET, measured simultaneously as the temperatures $T_1$ and $T_2$.

Figure 5

(a) Observed cooling $\Delta T$ (see the inset for definition) for three different voltage bias values over the temperature range from 200 down to 80 mK. The data sets obtained by averaging over all realizations within a $\pm 5 \mu \mathrm{eV}$ range are shown for mean bias values of $60 \mu \mathrm{eV}$ (orange circles), $40 \mu \mathrm{eV}$ (blue squares), and $20 \mu \mathrm{eV}$ (red triangles), from top to bottom. The error bars are calculated as a standard deviation for the data. The theoretical predictions of $\Delta T$ for the three voltage bias values (60, 40, and $20 \mu \mathrm{eV}$) are shown as orange, blue, and red solid lines, respectively. The dashed lines show the theoretical prediction without cotunneling. (b) The theoretical predictions of $T_1$ for the three voltage bias values, as indicated in the legend, in the temperature range of 10–130 mK, are shown as solid lines. The dashed-dotted red line indicated as $20{}^{*} \mu \mathrm{eV}$ is the same as in (a), where in the model we used values of $R_{T,k}$ obtained from the experiment. The solid purple, dark green, and dark blue lines (from top to bottom at $T_{e,0}>20\mathrm{mK})$ are predictions for a CBR with tunneling resistances ten times higher than those in the present measurements.