The frontiers of quantum electronics have been linked to the discovery of new refrigeration methods since the discovery of superconductivity at a temperature around 4 K, enabled by the liquefaction of helium. Presently, nanoelectronic devices typically reach electron temperatures around 10 mK to 100 mK by commercially available dilution refrigerators. This led to discoveries such as the quantum Hall effect and new technologies like superconducting and semiconductor quantum bits. However, cooling electrons via the encompassing lattice vibrations, or phonons, becomes inefficient at low temperatures. Further progress towards 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 a record low temperature of 3.2 ± 0.1 mK in an unmodified dilution refrigerator.Quantum electronics relies on the precise control of electronic states in nanostructures, which is possible if the energy level separation is much higher than the thermal energy k B T . Thus, the efficient cooling of electrons is vital for solid state nanoelectronics and is an important design consideration for existing scalable quantum technologies. Access to novel states of matter such as electron-nuclear ferromagnets [1-3], non-Abelian anyons in fractional quantum Hall states [4,5], topological insulators [6] or exotic superconductivity [7-9] requires further progress in the cooling of nanoelectronics, approaching the µK regime.Typical electron temperatures of the order of 10 mK are accessible in semiconductor and metallic nanostructures by mounting the chip containing the devices on an insulating substrate cooled by commercially available dilution refrigerators. The lowest achievable electron temperature is limited by the heat transferred from the electrons at a temperature of T e to phonons at a temperature of T p . The heat flow between conduction electrons and phonons in a metallic volume V isQ ep = ΣV T 5 e order of 10 9 WK −5 m −3 [10,11]. A residual heat leak oḟ Q leak = 10 aW to a well-shielded nanostructure [12] with V = 1 µm 3 then yields T e ≈ 25 mK even as T p approaches zero. Increasing the coupling volume V by electrodeposition of thick metal films and improving thermalization by liquid helium immersion cells led to T e ≈ 4 mK [13][14][15] in specially built dilution refrigerators.The key to reduce the electron temperature further thus involves coupling the electron system to a cold bath without the necessity of heat transport via phonons. This can be achieved by nuclear magnetic cooling. In the limit of small Zeeman splitting compared to k B T n , the magnetization of the nuclear spin system is M ∝ B/T n at a magnetic field of B and a temperature of T n . T n can be reduced by adiabatically lowering the magnetic field from B i to B f . In the ab...

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, k B T , demanding effective refrigeration techniques for nanoscale electronic devices. Commercially available dilution refrigerators have enabled typical electron temperatures in the 10 . . . 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 T e = 421 ± 35 µK measured by a Coulomb-blockade thermometer. With a hold time exceeding 85 hours below 700 µK, we provide a landmark demonstration of nanoelectronics in the microkelvin regime.Accessing the microkelvin regime [1] holds the potential of enabling the observation of novel electronic states, such as topological ordering [2], electron-nuclear ferromagnets [3,4], p-wave superconductivity [5] or non-Abelian anyons [6] in the fractional quantum Hall regime [7]. In addition, the error rate of various quantum devices, including single electron charge pumps [8] and superconducting quantum circuits [9] could improve by more effective thermalization of the charge carriers.The conventional means of cooling nanoelectronic devices relies on the thermal coupling between the refrigerator and the conduction electrons, mediated by phononphonon coupling in the insulating substrate,Q p-p ∝ T 4 p1 − T 4 p2 and electron-phonon coupling in the devicė Q e-p ∝ T 5 e − T 5 p [10, 11], both rapidly diminishing at low temperatures. In a typical dilution refrigerator, T p > 5 mK, and specially built systems reach 1.8 mK [12], which limits T e > T p to the millikelvin regime. The lowest static electron temperature reached with this technique was T e = 3.9 mK [13] in an all-metallic nanostructure, and other experiments reached similar values [14][15][16] in semiconductor heterostructures.This technological limitation can be bypassed by adia- * These authors contributed equally to this work.batic magnetic refrigeration, which relies on the constant occupation probability of the energy levels of a spin system, ∼ exp(−gµBm/k B T ) in the absence of heat exchange with the environment [17]. Here, k B T is the thermal energy at a temperature of T , gµB is the energy split between adjacent levels at a magnetic field of B and m is the spin index. Thus, the constant ratio B/T allows for controlling the temperature of the spin system by changing the magnetic field. Exploiting the spin of the nuclei [18,19], this technique has been utilized to cool bulk metals down to the temperature range of T ∼ 100 pK [20]. If only Zeeman splitting is present, which is linear in B, the ultimate tempe...

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.