The charge localization of single electrons on mesoscopic metallic islands leads to a suppression of the electrical current, known as the Coulomb blockade. When this correction is small, it enables primary electron thermometry, as it was first demonstrated by Pekola et al. (Phys Rev Lett 73:2903, 1994). However, in the low temperature limit, random charge offsets influence the conductance and limit the universal behavior of a single metallic island. In this work, we numerically investigate the conductance of a junction array and demonstrate the extension of the primary regime for large arrays, even when the variations in the device parameters are taken into account. We find that our simulations agree well with measured conductance traces in the submillikelvin electron temperature regime.

Fragile quantum effects such as single electron charging in quantum dots or macroscopic coherent tunneling in superconducting junctions are the basis of modern quantum technologies. These phenomena can only be observed in devices where the characteristic spacing between energy levels exceeds the thermal energy, kBT, demanding effective refrigeration techniques for nanoscale electronic devices. Commercially available dilution refrigerators have enabled typical electron temperatures in the 10 to 100 mK regime, however indirect cooling of nanodevices becomes inefficient due to stray radiofrequency heating and weak thermal coupling of electrons to the device substrate. Here, we report on passing the millikelvin barrier for a nanoelectronic device. Using a combination of on-chip and off-chip nuclear refrigeration, we reach an ultimate electron temperature of Te = 421 ± 35 μK and a hold time exceeding 85 h below 700 μK measured by a self-calibrated Coulomb-blockade thermometer.

The frontiers of quantum electronics have been linked to the discovery of new refrigeration methods since the discovery of superconductivity at a temperature of around 4 K, enabled by the liquefaction of helium. Since then, advances in cryogenics have led to discoveries such as the quantum Hall effect and new technologies such as superconducting and semiconductor quantum bits. Presently, nanoelectronic devices typically reach electron temperatures of around 10-100 mK by use of commercially available dilution refrigerators. However, cooling electrons via the encompassing lattice vibrations, or phonons, becomes inefficient at low temperatures. Further progress toward lower temperatures requires new cooling methods for electrons on the nanoscale, such as direct cooling with nuclear spins, which themselves can be brought to microkelvin temperatures by adiabatic demagnetization. Here we introduce indium as a nuclear refrigerant for nanoelectronics and demonstrate that solely on-chip cooling of electrons is possible down to 3.2±0.1mK, limited by the heat leak via the electrical connections of the device.