Magnetic cooling and on-chip thermometry for nanoelectronics below 10 mK

Cooling of electronic devices below 1 mK is a challenging task, since the thermal coupling with the dilution refrigerator becomes weak at low temperatures and electronic devices are extremely susceptible to external heat leaks such as microwave radiation and electrical noise. Despite these technological challenges, there is a completely new world of physics which can be explored once low temperatures are achieved.
To reach such ultra-low temperatures, we implemented a parallel network of Nuclear Refrigerators, to adapt magnetic cooling to electronic transport measurements. The cooling scheme relies on the cooling of each individual lead by its own nuclear refrigerator to transfer cooling power down to the sample. Here, we present the implementation of a parallel network of nuclear refrigerators for the first time on a cryo-free system. One challenge is the increased vibrations level compared to the wet cryostat, but a careful damping of the vibrations is possible, thus enabling low temperature experiments. The setup successfully cools the electronic temperature of the nuclear refrigerant down to 150 microK and limits a residual heat leak of few nW per mole of copper, allowing to stay below 1 mK for several days. A simple thermal model capturing the demagnetization process, the heat leak, the coupling between electron and nuclei as well as the efficiency of the process typically above 80%.
To characterize the cooling capacity of our system, we cool several electronic devices well below 10 mK. We cool a normal metal-insulator-superconducting tunnel junction down to 7.3 mK. Further lowering temperatures might be limited by the heat release of the socket. However, a theoretical estimate shows that such a device has the potential to reach 1 mK, since the overheating effects turn out to be negligible. Indeed, by using the thermal broadening of sub-gap current steps, we demonstrate the cooling of the tunnel junction down to 4 mK. These steps are novel features which are weakly-coupled and more robust than the conventional NIS thermometry, and we can model them as Andreev bound states enhanced by disorder and the geometry of the junction. Additionally, other physical properties of the junction are investigated experimentally and numerically, such as two-particle sub-gap tunneling current promoted by the disorder and the geometry of the junction and magnetic field suppression of a minigap.
Further improvement on the cooling of the electronic device is achieved by on-chip magnetic refrigeration. We demonstrate magnetic cooling of an array of Coulomb Blockade Thermometers with huge copper islands. The lowest temperature reached is 2.8 mK, which is the lowest temperature measured to date in a solid state electronic device. The reduction in temperature is roughly a factor 8 during the demagnetization process, showing an improved efficiency of the cooling technique compared to the previous experiments. The temperature might possibly be further reduced below 1 mK, by introducing non-inductive filters and damping more the vibrations, which would lead to a lower precooling temperature and an improved efficiency of the on-chip magnetic cooling.