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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.
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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.
Of all parameters, determining the behaviour of a physical system in the laboratory, temperature is one of the most important, if not themost important. The study of solid matter at cryogenic temperatures revealed unexpected phenomena like superconductivity and was closely related to the verification of new and revolutionary concepts in solidstate physics in the last century. The nowadays pursued development of quantum effect devices is closely related to technologies of creating ultralow temperatures on the microand nanometerscale. Achievable electron temperatures in miniaturized electronic devices are currently limited to the millikelvin temperature regime, caused by the technical limits of 3He/4He dilution refrigeration in combination with hot-electron effects, due to a strongly weakening electron-phonon coupling strength in miniaturized electronic conductors with lowering the temperature. New physical and technological concepts, like the use of topological materials for quantuminformation processing, created an interest in reaching lower electron temperatures in nanoelectronic devices than currently possible. For this purpose, a bridge to classical ultralow temperature research, where microkelvin cooling of bulk solids is achieved for several decades, has to be built. This work is dedicated to the goal of enabling cooling of nanoelectronic devices to the yet unreached microkelvin regime. For enabling microkelvin refrigeration of nanodevices, methods for chipscale nuclear magnetic cooling are developed, in order to cool electrons on a chip to microkelvin temperatures by direct spin-spin thermalization with nuclear spins, bypassing the weak electron-phonon interaction. A decisive key for reaching a nuclear cooling power in miniaturized volumes, which is sufficient to refrigerate a nanoelectronic circuit to microkelvin temperatures, is the utilization of nonequidistant nuclear level splitting by nuclear quadrupole interaction in the nuclear refrigerant. The metal indium is proposed and utilized as nuclear refrigerant for this purpose, since it combines a strong quadrupolar interaction with a strong hyperfine interaction. The ultilization of indium for magnetic cooling on the micro- and nanoscale is studied by integrating electrochemically deposited indiumfilms onto a Coulomb blockade thermometer. Coulomb blockade thermometry is based on thermally activated single charge transport by tunneling between metallic islands and comprises an ideal and scalable solution for nuclear magnetic cooling and electronic thermometry on a combined, miniaturized platform. By combining indiummicrorefrigerators with an off-chip nuclear magnetic cooling stage, tailor made to couple the chip to an ultracold environment, cooling of a nanoelectronic device to microkelvin temperatures is demonstrated for the first time. With the cooling schemes for miniaturized electronic devices developed in this work, the foundation for quantum nanoelectronics at microkelvin temperatures is laid, opening the door to an experimentally unknown territory in physics.
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Of all parameters, determining the behaviour of a physical system in the laboratory, temperature is one of the most important, if not themost important. The study of solid matter at cryogenic temperatures revealed unexpected phenomena like superconductivity and was closely related to the verification of new and revolutionary concepts in solidstate physics in the last century. The nowadays pursued development of quantum effect devices is closely related to technologies of creating ultralow temperatures on the microand nanometerscale. Achievable electron temperatures in miniaturized electronic devices are currently limited to the millikelvin temperature regime, caused by the technical limits of 3He/4He dilution refrigeration in combination with hot-electron effects, due to a strongly weakening electron-phonon coupling strength in miniaturized electronic conductors with lowering the temperature. New physical and technological concepts, like the use of topological materials for quantuminformation processing, created an interest in reaching lower electron temperatures in nanoelectronic devices than currently possible. For this purpose, a bridge to classical ultralow temperature research, where microkelvin cooling of bulk solids is achieved for several decades, has to be built. This work is dedicated to the goal of enabling cooling of nanoelectronic devices to the yet unreached microkelvin regime. For enabling microkelvin refrigeration of nanodevices, methods for chipscale nuclear magnetic cooling are developed, in order to cool electrons on a chip to microkelvin temperatures by direct spin-spin thermalization with nuclear spins, bypassing the weak electron-phonon interaction. A decisive key for reaching a nuclear cooling power in miniaturized volumes, which is sufficient to refrigerate a nanoelectronic circuit to microkelvin temperatures, is the utilization of nonequidistant nuclear level splitting by nuclear quadrupole interaction in the nuclear refrigerant. The metal indium is proposed and utilized as nuclear refrigerant for this purpose, since it combines a strong quadrupolar interaction with a strong hyperfine interaction. The ultilization of indium for magnetic cooling on the micro- and nanoscale is studied by integrating electrochemically deposited indiumfilms onto a Coulomb blockade thermometer. Coulomb blockade thermometry is based on thermally activated single charge transport by tunneling between metallic islands and comprises an ideal and scalable solution for nuclear magnetic cooling and electronic thermometry on a combined, miniaturized platform. By combining indiummicrorefrigerators with an off-chip nuclear magnetic cooling stage, tailor made to couple the chip to an ultracold environment, cooling of a nanoelectronic device to microkelvin temperatures is demonstrated for the first time. With the cooling schemes for miniaturized electronic devices developed in this work, the foundation for quantum nanoelectronics at microkelvin temperatures is laid, opening the door to an experimentally unknown territory in physics.
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.
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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.
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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.
