Thermal Transport in Nanoelectronic Devices Cooled by On-Chip Magnetic Refrigeration.

On-chip demagnetization refrigeration has recently emerged as a powerful tool for reaching microkelvin electron temperatures in nanoscale structures. The relative importance of cooling on-chip and off-chip components and the thermal subsystem dynamics are yet to be analyzed. We study a Coulomb blockade thermometer with on-chip copper refrigerant both experimentally and numerically, showing that dynamics in this device are captured by a first-principles model. Our work shows how to simulate thermal dynamics in devices down to microkelvin temperatures, and outlines a recipe for a low-investment platform for quantum technologies and fundamental nanoscience in this novel temperature range.

Progress in Cooling Nanoelectronic Devices to Ultra-Low Temperatures.

Here we review recent progress in cooling micro-/nanoelectronic devices significantly below 10 mK. A number of groups worldwide are working to produce sub-millikelvin on-chip electron temperatures, motivated by the possibility of observing new physical effects and improving the performance of quantum technologies, sensors and metrological standards. The challenge is a longstanding one, with the lowest reported on-chip electron temperature having remained around 4 mK for more than 15 years. This is despite the fact that microkelvin temperatures have been accessible in bulk materials since the mid-twentieth century. In this review, we describe progress made in the last 5 years using new cooling techniques. Developments have been driven by improvements in the understanding of nanoscale physics, material properties and heat flow in electronic devices at ultralow temperatures and have involved collaboration between universities and institutes, physicists and engineers. We hope that this review will serve as a summary of the current state of the art and provide a roadmap for future developments. We focus on techniques that have shown, in experiment, the potential to reach sub-millikelvin electron temperatures. In particular, we focus on on-chip demagnetisation refrigeration. Multiple groups have used this technique to reach temperatures around 1 mK, with a current lowest temperature below 0.5 mK.

Fundamental dissipation due to bound fermions in the zero-temperature limit.

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.

Operating Nanobeams in a Quantum Fluid.

Microelectromechanical (MEMS) and nanoelectromechanical systems (NEMS) are ideal candidates for exploring quantum fluids, since they can be manufactured reproducibly, cover the frequency range from hundreds of kilohertz up to gigahertz and usually have very low power dissipation. Their small size offers the possibility of probing the superfluid on scales comparable to, and below, the coherence length. That said, there have been hitherto no successful measurements of NEMS resonators in the liquid phases of helium. Here we report the operation of doubly-clamped aluminium nanobeams in superfluid 4He at temperatures spanning the superfluid transition. The devices are shown to be very sensitive detectors of the superfluid density and the normal fluid damping. However, a further and very important outcome of this work is the knowledge that now we have demonstrated that these devices can be successfully operated in superfluid 4He, it is straightforward to apply them in superfluid 3He which can be routinely cooled to below 100 µK. This brings us into the regime where nanomechanical devices operating at a few MHz frequencies may enter their mechanical quantum ground state.

On-chip magnetic cooling of a nanoelectronic device.

We demonstrate significant cooling of electrons in a nanostructure below 10 mK by demagnetisation of thin-film copper on a silicon chip. Our approach overcomes the typical bottleneck of weak electron-phonon scattering by coupling the electrons directly to a bath of refrigerated nuclei, rather than cooling via phonons in the host lattice. Consequently, weak electron-phonon scattering becomes an advant- age. It allows the electrons to be cooled for an experimentally useful period of time to temperatures colder than the dilution refrigerator platform, the incoming electrical connections, and the host lattice. There are efforts worldwide to reach sub-millikelvin electron temperatures in nanostructures to study coherent electronic phenomena and improve the operation of nanoelectronic devices. On-chip magnetic cooling is a promising approach to meet this challenge. The method can be used to reach low, local electron temperatures in other nanostructures, obviating the need to adapt traditional, large demagnetisation stages. We demonstrate the technique by applying it to a nanoelectronic primary thermometer that measures its internal electron temperature. Using an optimised demagnetisation process, we demonstrate cooling of the on-chip electrons from 9 mK to below 5 mK for over 1000 seconds.

Nanoelectronic primary thermometry below 4 mK.

Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼ 10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron-phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the (3)He/(4)He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.

Magnetic phase transition in a nanonetwork of solid 3He in aerogel.

When immersed in liquid 3He, the nanometer strands of aerogel are coated with a thin layer of solid 3He, forming a network of irregular nanotubes. Owing to its high purity and weak interactions, this system is ideal for studying fundamental processes. We report the first experiments on solid 3He in aerogel at ultralow temperatures, cooled by direct adiabatic demagnetization. Simultaneous nuclear magnetic susceptibility and heat capacity measurements indicate a magnetic phase transition.

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B.

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.

Contrasting mechanical anisotropies of the superfluid 3He phases in aerogel.

There has been much recent interest in how impurity scattering may affect the phases of the p-wave superfluid 3He. Impurities may be added to the otherwise absolutely pure superfluid by immersing it in aerogel. Some predictions suggest that impurity scattering may destroy orientational order and force all of the superfluid phases to have an isotropic superfluid density. In contrast to this, we present experimental data showing that the response of the A-like phase to superfluid flow is highly anisotropic, revealing a texture that is easily modified by flow.

Decay of pure quantum turbulence in superfluid 3He-B.

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.

Emission of discrete vortex rings by a vibrating grid in superfluid 3He-B: a precursor to quantum turbulence.

We report a transition in the vorticity generated by a grid moving in the B phase of superfluid 3He at T<

Interfacial energy of the superfluid 3He a-B phase interface in the zero-temperature limit.

We have measured the surface energy of the interface between the A and B phases of superfluid 3He in the low temperature limit at zero pressure. Using a shaped magnetic field, we control the passage of the phase boundary through a small aperture. We obtain the interphase surface energy from the over- or undermagnetization required to force the interface through the aperture in both directions, yielding values of the surface tension and the interfacial contact angle. This is the first measurement of the interfacial energy in high magnetic fields and in the zero-temperature limit.

Shear flow and Kelvin-Helmholtz instability in superfluids.

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.