Nuclear spin ferromagnetic phase transition in an interacting two dimensional electron gas

Topographic Control of Order in Quasi-2D Granular Phase Transitions

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting granular liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-solid one. The interplay of boundary inelasticity and geometry, either order promoting or inhibiting, controls whether it is the granular crystal or the granular fluid which makes contact with the edge. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

Cryogen-free one hundred microkelvin refrigerator

A temperature below 100 µK is achieved in a customized cryogen-free dilution refrigerator with a copper-nuclear demagnetization stage. The lowest temperature of conduction electrons of the demagnetization stage is below 100 µK as measured by using a pulsed platinum nuclear magnetic resonance thermometer, and the temperature can remain below 100 µK for over 10 h. A demagnetization magnetic field of up to 9 T and a research magnetic field of up to 12 T can be controlled independently, provided by a coaxial room-temperature-bore cryogen-free magnet.

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.

Spin liquid mediated RKKY interaction

We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid exists such an interaction could leave a fingerprint by ordering underlying localised moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. We demonstrate that the interaction is predominately shaped by the lattice symmetries of the underlying spin liquid. As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin orderings minimise the RKKY-type energy induced by the KHAF but are unstable due to a zero-energy flat magnon band in linear spin-wave theory. Despite this we show that a small magnetic field is able to gap out this magnon spectrum resulting in an intricate nuclear magnetism.

Comparison of cryogenic low-pass filters

Low-temperature electronic transport measurements with high energy resolution require both effective low-pass filtering of high-frequency input noise and an optimized thermalization of the electronic system of the experiment. In recent years, elaborate filter designs have been developed for cryogenic low-level measurements, driven by the growing interest in fundamental quantum-physical phenomena at energy scales corresponding to temperatures in the few millikelvin regime. However, a single filter concept is often insufficient to thermalize the electronic system to the cryogenic bath and eliminate spurious high frequency noise. Moreover, the available concepts often provide inadequate filtering to operate at temperatures below 10 mK, which are routinely available now in dilution cryogenic systems. Herein we provide a comprehensive analysis of commonly used filter types, introduce a novel compact filter type based on ferrite compounds optimized for the frequency range above 20 GHz, and develop an improved filtering scheme providing adaptable broad-band low-pass characteristic for cryogenic low-level and quantum measurement applications at temperatures down to few millikelvin.

Magnetic cooling for microkelvin nanoelectronics on a cryofree platform

We present a parallel network of 16 demagnetization refrigerators mounted on a cryofree dilution refrigerator aimed to cool nanoelectronic devices to sub-millikelvin temperatures. To measure the refrigerator temperature, the thermal motion of electrons in a Ag wire-thermalized by a spot-weld to one of the Cu nuclear refrigerators-is inductively picked-up by a superconducting gradiometer and amplified by a SQUID mounted at 4 K. The noise thermometer as well as other thermometers are used to characterize the performance of the system, finding magnetic field independent heat-leaks of a few nW/mol, cold times of several days below 1 mK, and a lowest temperature of 150 μK of one of the nuclear stages in a final field of 80 mT, close to the intrinsic SQUID noise of about 100 μK. A simple thermal model of the system capturing the nuclear refrigerator, heat leaks, and thermal and Korringa links describes the main features very well, including rather high refrigerator efficiencies typically above 80%.

Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase

We study a one-dimensional interacting electronic liquid coupled to a 1D array of classical magnetic moments and to a superconductor. We show that at low energy and temperature the magnetic moments and the electrons become strongly entangled and that a magnetic spiral structure emerges. For strong enough coupling between the electrons and magnetic moments, the 1D electronic liquid is driven into a topological superconducting phase supporting Majorana fermions without any fine-tuning of external parameters. Our analysis applies at low enough temperature to a quantum wire in proximity to a superconductor when the hyperfine interaction between electrons and nuclear spins is taken into account, or to a chain of magnetic adatoms adsorbed on a superconducting surface.

RKKY interaction and intrinsic frustration in non-Fermi-liquid metals

We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such non-Fermi liquids, and gives rise to enhanced frustration when the spins form a lattice. Frustration suppresses the magnetic ordering temperature of the lattice spin system. Furthermore, we find that the spin system with a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a model lead to a first-order phase transition and/or glassy phase. This may explain some recent experiments where glassy behavior was observed in stoichiometric heavy fermion material close to a ferromagnetic quantum critical point.

Metallic Coulomb blockade thermometry down to 10 mK and below

We present an improved nuclear refrigerator reaching 0.3 mK, aimed at microkelvin nanoelectronic experiments, and use it to investigate metallic Coulomb blockade thermometers (CBTs) with various resistances R. The high-R devices cool to slightly lower T, consistent with better isolation from the noise environment, and exhibit electron-phonon cooling [proportional] T(5) and a residual heat-leak of 40 aW. In contrast, the low-R CBTs display cooling with a clearly weaker T-dependence, deviating from the electron-phonon mechanism. The CBTs agree excellently with the refrigerator temperature above 20 mK and reach a minimum-T of 7.5 ± 0.2 mK.

Geometric influence on Ruderman-Kittel-Kasuya-Yosida interactions in zigzag carbon nanotubes

We derive an analytic description of the spin susceptibility in finite length zigzag carbon nanotubes (CNT) with chirality (n, 0). The spin susceptibility is proportional to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions which describes indirect carrier mediated exchange coupling between localized magnetic moments. We show that the strongest RKKY interactions are along the edges of the nanotube and in the thermodynamic limit at half filling with spin symmetry the shape of the susceptibility curve about the edge of the CNT can be determined solely by the lattice geometry represented by the parameter n and a parameter L which describes the nanotube length. We also show that the introduction of Zeeman splitting or doping may have no effect on the spin susceptibility, provided n is small. A detailed knowledge of magnetic interactions, such as RKKY interactions, in CNT is of vital importance to the development of nanotechnology applications.

Absence of spontaneous magnetic order of lattice spins coupled to itinerant interacting electrons in one and two dimensions

We extend the Mermin-Wagner theorem to a system of lattice spins which are spin coupled to itinerant and interacting charge carriers. We use the Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature. Our proof applies to a wide class of models including any form of electron-electron and single-electron interactions that are independent of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI) magnetic order is not excluded and intimately connected to equilibrium spin currents. However, in the special case when Rashba and Dresselhaus SOIs are tuned to be equal, magnetic order is excluded again. This opens up a new possibility to control magnetism electrically.

Method for cooling nanostructures to microkelvin temperatures

We propose a new scheme aimed at cooling nanostructures to microkelvin temperature based on the well established technique of adiabatic nuclear demagnetization: we attach each device measurement lead to an individual nuclear refrigerator, allowing efficient thermal contact to a microkelvin bath. On a prototype consisting of a parallel network of nuclear refrigerators, temperatures of ∼1 mK simultaneously on ten measurement leads have been reached upon demagnetization, thus completing the first steps toward ultracold nanostructures.

Nuclear magnetism and electronic order in 13C nanotubes

Single wall carbon nanotubes grown entirely from 13C form an ideal system to study the effect of electron interaction on nuclear magnetism in one dimension. If the electrons are in the metallic, Luttinger liquid regime, we show that even a very weak hyperfine coupling to the 13C nuclear spins has a striking effect: The system is driven into an ordered phase, which combines electron and nuclear degrees of freedom, and which persists up into the millikelvin range. In this phase the conductance is reduced by a universal factor of 2, allowing for detection by standard transport experiments.