Micrometre-scale refrigerators

A superconductor with a gap in the density of states or a quantum dot with discrete energy levels is a central building block in realizing an electronic on-chip cooler. They can work as energy filters, allowing only hot quasiparticles to tunnel out from the electrode to be cooled. This principle has been employed experimentally since the early 1990s in investigations and demonstrations of micrometre-scale coolers at sub-kelvin temperatures. In this paper, we review the basic experimental conditions in realizing the coolers and the main practical issues that are known to limit their performance. We give an update of experiments performed on cryogenic micrometre-scale coolers in the past five years

Hybrid single-electron transistor as a source of quantized electric current

The basis of synchronous manipulation of individual electrons in solid-state devices was laid by the rise of single-electronics about two decades ago. Ultra-small structures in a low temperature environment form an ideal domain of addressing electrons one by one. A long-standing challenge in this field has been the realization of a source of electric current that is accurately related to the operation frequency $f$. There is an urgent call for a quantum standard of electric current and for the so-called metrological triangle, where voltage from Josephson effect and resistance from quantum Hall effect are tested against current via Ohm's law for a consistency check of the fundamental constants of Nature, $\hbar$ and $e$. Several attempts to create a metrological current source that would comply with the demanding criteria of extreme accuracy, high yield, and implementation with not too many control parameters have been reported. However, no satisfactory solution exists as yet despite many ingenious achievements that have been witnessed over the years. Here we propose and prove the unexpected concept of a hybrid metal-superconductor turnstile in the form of a one-island single-electron transistor with one gate, which demonstrates robust current plateaus at multiple levels of $ef$ within the uncertainty of our current measurement. Our theoretical estimates show that the errors of the present system can be efficiently suppressed by further optimizations of design and proper choice of the device parameters and therefore we expect it to eventually meet the stringent specifications of quantum metrology.Comment: 5 pages, 3 figure

Heat Transistor: Demonstration of Gate-Controlled Electron Refrigeration

We present experiments on a superconductor-normal metal electron refrigerator in a regime where single-electron charging effects are significant. The system functions as a heat transistor, i.e., the heat flux out from the normal metal island can be controlled with a gate voltage. A theoretical model developed within the framework of single-electron tunneling provides a full quantitative agreement with the experiment. This work serves as the first experimental observation of Coulombic control of heat transfer and, in particular, of refrigeration in a mesoscopic system.Comment: 4 pages, 3 color figure

Primary tunnel junction thermometry

We describe the concept and experimental demonstration of primary thermometry based on a four probe measurement of a single tunnel junction embedded within four arrays of junctions. We show that in this configuration random sample specific and environment-related errors can be avoided. This method relates temperature directly to Boltzmann constant, which will form the basis of the definition of temperature and realization of official temperature scales in the future

Static structure factor of two-dimensional liquid 3He adsorbed on graphite

International audienceLiquid 3He is a model system for strongly correlated Fermi liquids. For this reason, many X-ray and neutron scattering experiments have been performed to understand the structure and dynamics of this quantum fluid. We have recently shown that two-dimensional liquid 3He sustains long-lived zero-sound excitations at large wave-vectors (Nature 483, 576, 2012). Here we show that its static structure factor can be obtained with reasonable accuracy by integrating the experimental S(Q,ω) over a suitable energy range. A good agreement is found between the static structure factor deduced from the experiment and theoretical models: Quantum Monte Carlo simulations and Dynamical Many Body Theory (DMBT). At high wave-vectors, the experimental values are underestimated because of the limited accessible phase space; nevertheless, even at atomic wave-vectors a semiquantitative agreement is observed with the theoretical predictions

Traceable Coulomb Blockade Thermometry

We present a measurement and analysis scheme for determining traceable thermodynamic temperature at cryogenic temperatures using Coulomb blockade thermometry. The uncertainty of the electrical measurement is improved by utilizing two sampling digital voltmeters instead of the traditional lock-in technique. The remaining uncertainty is dominated by that of the numerical analysis of the measurement data. Two analysis methods are demonstrated: numerical fitting of the full conductance curve and measuring the height of the conductance dip. The complete uncertainty analysis shows that using either analysis method the relative combined standard uncertainty (k = 1) in determining the thermodynamic temperature in the temperature range from 20 mK to 200 mK is below 0.5 %. In this temperature range, both analysis methods produced temperature estimates that deviated from 0.39 % to 0.67 % from the reference temperatures provided by a superconducting reference point device calibrated against the Provisional Low Temperature Scale of 2000.Comment: 11 page

Observation of zero-sound at atomic wave-vectors in a monolayer of liquid 3He

International audienceThe elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid3He adsorbed on graphite preplated by a monolayer of solid 4He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid 3He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk 3He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid 4He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmons excitations in electronic systems)

Pair excitations and vertex corrections in Fermi fluids and the dynamic structure function of two-dimensional 3He

International audienceWe use the equations-of-motion approach for time-dependent pair correlations in strongly interacting Fermiliquidsto develop a theory of the excitation spectrum and the single-particle self energy in such systems. We present here the fully correlated équations and their approximate solutions for3He. Our theory has the following properties: It reduces to both, i) the "correlated" random-phase approximation (RPA) for strongly interacting fermions if the two-particle-two-hole correlations are ignored, and, ii) to the correlated Brillouin-Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two firstenergy-weighted sum rules,and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad-hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair-excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization

Two-Dimensional 3He: A Crucial System for Understanding Fermion Dynamics

International audienceNeutron scattering measurements at the Institut Laue-Langevin off quasi-twodimensional 3He have shown, for the first time, a situation where the collective mode crosses the particle-hole continuum and reappears, at a momentum transfer of q≈ 1.55 ˚A−1 as a well-defined collective excitation. The effect is well described by the Fermion generalization of multi-particle fluctuation theory of Jackson, Feenberg, and Campbell that has been so successful for bosonic quantum fluids. We describe the theory briefly and state that it can be mapped onto the form of time dépendent Hartree-Fock theory (TDHF)containing energy dépendent effective interactions; these are obtained from microscopic ground state theory. Our theoretical result has far-reaching consequences: a popular paradigm in discussing the density-density response function of Fermi systems is the "random phase approximation" (RPA), most frequently applied with some static interaction and, perhaps, some effective mass. Such a "phenomenologically modified" RPA can be justified only under severe simplifying approximations and is unable to describe the experimental situation consistently. As soon as one goes beyond the RPA, intermediate states which cannot be described in terms of the quantum numbers of a single (quasi-)particle become essential for capturing the correct physics. In oder to understand the above mentioned experiment, their appropriate inclusion, as presented in this work, is essential

Roton collective mode observed in a two-dimensional Fermi liquid

International audienceUnderstanding the dynamics of correlated many-body quantum systems has been a challenge for modern physics. Due to the simplicity of their Hamiltonian, 4He (bosons) and 3He (fermions) have served as paradigm for strongly interacting quantum fluids. For this reason, substantial efforts have been devoted to their understanding. An important milestone was the direct observation of the collective "phonon-roton" mode in liquid 4He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations ("zero-sound" in 3He, "plasmons" in charged systems) as well as incoherent particle-hole (PH) excitations are observed. At small wave-vectors and energies, both types of excitations are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the PH band, where it is strongly damped. The dynamics of Fermi liquids at high wave-vectors was thus believed to be essentially incoherent. We report here the first observation of a roton-like excitation in a Fermi liquid, obtained in a monolayer of liquid 3He, studied by inelastic neutron scattering. We find that the collective density mode reappears as a well-defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the region outside the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained within a novel dynamic many-body theory