Liquid 4He Research Articles

On the Origin and the Amplitude of T‐Square Resistivity in Fermi Liquids

AbstractIn 1937, Baber, Landau, and Pomeranchuk postulated that collisions between electrons generates a contribution to the electric resistivity of metals with a distinct T2 temperature dependence. The amplitude of this term is small in common metals, but dominant in metals hosting either heavy carriers or a low concentration of them. The temperature dependence is set by the size of the scattering phase, but the microscopic source of dissipation is not straightforward. To explain how electron–electron collisions lead to momentum leak, Umklapp events or multiple electron reservoirs have been invoked. This interpretation is challenged by several experimental observations: the persistence of T‐square resistivity in dilute metals (in which the two mechanisms are irrelevant), the successful extension of Kadowaki–Woods scaling to dilute metals, and the observation of a size‐dependent T‐square thermal resistivity () and its WiedemannFranz correlation with T‐square electrical resistivity. This paper argues that much insight is provided by the case of normal liquid 3He where the T‐square temperature dependence of energy and momentum diffusivity is driven by fermionfermion collisions. The amplitude of T‐square resistivity in 3He and in metals share a common scaling. Thus, the ubiquitous T‐square electrical resistivity ultimately stems from the Fermi‐liquid temperature dependence of momentum diffusivity.

Effects of incipient pairing on nonequilibrium quasiparticle transport in Fermi liquids

Abstract The low-temperature properties of a wide range of many-fermion systems spanning metals, quantum gases and liquids to nuclear matter are well understood within the framework of Landau’s theory of Fermi liquids. The low-energy physics of these systems is governed by interacting fermionic quasiparticles with momenta and energies near a Fermi surface in momentum space. Nonequilibrium properties are described by a kinetic equation for the distribution function for quasiparticles proposed by Landau. Quasiparticle interactions with other quasiparticles, phonons, or impurities lead to internal forces acting on a distribution of nonequilibrium quasiparticles, as well as collision processes that ultimately limit the transport of mass, heat, charge, and magnetization, as well as limiting the coherence times of quasiparticles. For Fermi liquids that are close to a second-order phase transition, e.g., Fermi liquids that undergo a superfluid transition, incipient Cooper pairs—long-lived fluctuations of the ordered phase—provide a new channel for scattering quasiparticles, as well as corrections to internal forces acting on the distribution of nonequilibrium quasiparticles. We develop the theory of quasiparticle transport for Fermi liquids in the vicinity of a BCS-type superfluid transition starting from Keldysh’s field theory for nonequilibrium, strongly interacting fermions. The leading corrections to Fermi-liquid theory for nonequilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. Our theory is applicable to quasiparticle transport in superconductors, nuclear matter, and the low-temperature phases of liquid 3He. As an implementation of the theory we calculate the pairing-fluctuation corrections to the attenuation of zero sound in liquid 3He near the superfluid transition and demonstrate quantitative agreement with experimental results.

Cooling low-dimensional electron systems into the microkelvin regime

Two-dimensional electron gases (2DEGs) with high mobility, engineered in semiconductor heterostructures host a variety of ordered phases arising from strong correlations, which emerge at sufficiently low temperatures. The 2DEG can be further controlled by surface gates to create quasi-one dimensional systems, with potential spintronic applications. Here we address the long-standing challenge of cooling such electrons to below 1 mK, potentially important for identification of topological phases and spin correlated states. The 2DEG device was immersed in liquid 3He, cooled by the nuclear adiabatic demagnetization of copper. The temperature of the 2D electrons was inferred from the electronic noise in a gold wire, connected to the 2DEG by a metallic ohmic contact. With effective screening and filtering, we demonstrate a temperature of 0.9 ± 0.1 mK, with scope for significant further improvement. This platform is a key technological step, paving the way to observing new quantum phenomena, and developing new generations of nanoelectronic devices exploiting correlated electron states.

Viscosity to entropy density ratio ($\\eta$/s) in nanoliquid

ABSTRACT We present the coefficient of viscosity (), entropy (S) and viscosity to entropy density (s) ratio () for aqueous silver nanoparticle (AgNP) solution at temperatures T = 273–300 K performing experiments and examining the same with discrete dipole approximation (DDA) simulation. The experimental UV-Visible dipole extinction spectra of the nanoliquid, matched with simulations, explore cluster morphologies. The latter is used for the calculation of (cluster volume fraction ~ 4–10%; NP, cluster radii 8–15 nm and 35–55 nm, respectively). In addition, dimer (AgNP-AgNP) formation free energy and S are explored at those T’s. We determine ratio exploiting nanoparticle behaviour. The value of is found lower than that of water and similar to strongly correlated liquid He4, owing to higher S for NP agglomeration. Our results of , S and are also corroborated from hard sphere model calculation. This, to the best of our knowledge, is the first attempt to determine in NP.

The AB Transition in Superfluid $$^3$$He

The discovery of superfluidity in 3He in 1971, published in 1972, [1, 2] has influenced a wide range of investigations that extend well beyond fermionic superfluids, including electronic quantum ma- terials, ultra-cold gases and degenerate neutron matter. Observation of thermodynamic transitions from the 3He Fermi liquid to two other liquid phases, A and B-phases, along the melting curve of liquid and solid 3He, discovered by Osheroff, Richardson, and Lee, were the very first indications of 3He superfluidity leading to their Nobel prize in 1996. This is a brief retrospective specifically focused on the AB transition.

2 K Cryogenic system with the thermal switch for measuring electrical properties of insulation materials

A cryogenic system has been established to measure electrical properties of insulation materials. The cryostat in the system contains two operating modes: 4.2 K and 1.65 K. A G-M cryocooler is used as cold source in these two modes. In 4.2 K mode, samples were directly cooled by the copper plates connected to the second stage of the cryocooler. In the 1.65 K mode, the helium gas is liquefied. The superfluid 4He (He-Ⅱ) of 1.65 K was obtained by throttling and depressurizing the liquid 4He (He-Ⅰ). The thermal switch in the 1.65 K mode can reduce the precooling time by 11.6 h and saved 22.5 L of helium. The transforming of the two modes is controlled by four threaded rods which are connected to the first and the second stage flange. The electrical test unit is designed, including the breakdown strength test and the flashover characteristics test with the voltage from 0 to 100 kV, which realizes the coupling of low temperature and high voltage.

A superfluid He4 version of a test on QG versus CG: feasibility with demonstrated methods

A field, which mediates entanglement between two quantum systems, must be of quantum nature. Attempts to witness this way quantumlike features of the gravitational field with tabletop experiments are actively studied recently, in particular by considering to look at two masses in a superposition in two locations, each in one interferometer. Entanglement intervention is probed when the interferometers are put side by side. If the masses interact only via Newtonian attraction, and still some degree of entanglement is found, than the gravitational field must be quantum like, or at least non-classical. The masses considered are mesoscopic, 10–14 Kg to 10–12 Kg, and in one proposal Mach–Zehnder interferometry is considered. Liquid He4 is superfluid below 2.17 K, and shows macroscopic quantum behaviour, in particular matter interferometry, as in the Superfluid He Quantum Inteference Device—SHeQUID. With its Josephson junctions as slits, the SHeQUID parallels a Mach–Zehnder. In this case the matter quantities involved are macroscopic, 10–8 Kg. We propose and analize the feasibility of a scheme on the lines of the above, where the matter field is given by superfluid He4, and the Mach–Zehnder’s are two SHeQUID, put side by side. We find that the proposed experiment is feasible, using only well demonstrated methods and technologies, with no need to extensions beyond the current frontiers.

Splitting of the Superfluid Transition in Liquid 3He Induced by a Nematic Aerogel

Role of inhomogeneous perturbations of nematic aerogel on the form of the order parameter emerging at the transition of liquid $^3$He in the superfluid state is considered. It is shown that a region of stability of the polar distorted ABM phase can begin right from the transition temperature. The symmetry argument is given, which selects the most favorable aerogel for stabilization of pure polar phase.

Driving Force of Molecular/Ionic Superfluid Formation

Driving Force of Molecular/Ionic Superfluid Formation

Entropic evidence for a Pomeranchuk effect in magic-angle graphene.

In the 1950s, Pomeranchuk1 predicted that, counterintuitively, liquid 3He may solidify on heating. This effect arises owing to high excess nuclear spin entropy in the solid phase, where the atoms are spatially localized. Here we find that an analogous effect occurs in magic-angle twisted bilayer graphene2-6. Using both local and global electronic entropy measurements, we show that near a filling of one electron per moiré unit cell, there is a marked increase in the electronic entropy to about 1kB per unit cell (kB is the Boltzmann constant). This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons-such as the absence of a thermodynamic gap, metallicity and a Dirac-like compressibility-and others associated with localized moments, such as a large entropy and its disappearance under a magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump has an onset at a temperature of about 30kelvin, the bandwidth of magnetic excitations is about 3kelvin or smaller. The hybrid nature of the present correlated state and the large separation of energy scales have implications for the thermodynamic and transport properties of the correlated states in twisted bilayer graphene.

Evidence for 4D XY Quantum Criticality in 4He Confined in Nanoporous Media at Finite Temperatures

$^4$He confined in nanoporous media is a model Bose system that exhibits quantum phase transition (QPT) by varying pressure. We have precisely determined the critical exponent of the superfluid density of $^4$He in porous Gelsil glasses with pore size of 3.0 nm using the Helmholtz resonator technique. The critical exponent $\zeta$ of the superfluid density was found to be 1.0 $\pm$ 0.1 for the pressure range 0.1 < P < 2.4 MPa. This value provides decisive evidence that the finite-temperature superfluid transition belongs to the four-dimensional (4D) XY universality class, in contrast to the classical 3D XY one in bulk liquid 4He, in which $\zeta$ = 0.67. The quantum critical behavior at a finite temperature is understood by strong phase fluctuation in local Bose-Einstein condensates above the superfluid transition temperature. $^4$He in nanoporous media is a unique example in which quantum criticality emerges not only at 0 K but at finite temperatures.

Particle approximation of the two-fluid model for superfluid 4He using smoothed particle hydrodynamics

This paper presents a finite particle approximation of the two-fluid model for liquid 4He using smoothed particle hydrodynamics (SPH). In recent years, several studies have combined the vortex filament model (VFM), which describes quantized vortices in superfluid components, with the Navier–Stokes equations, which describe the motion of normal fluids. These studies led us to assume that coupling both components of the two-fluid model instead of using the VFM to describe the superfluid component enables us to approximate the system. In this study, we formulated a new SPH model that simultaneously solves both equations of motion of the two-fluid model. We then performed a numerical simulation of the rotating liquid 4He using our SPH. The results showed that the two major phenomena, the emergence of multiple independent vortices parallel to the circular axis and that of the so-called rigid-body rotation, can be reproduced by solving the two-fluid model using SPH. This finding is interesting because it was previously assumed that only a single vortex emerges when addressing similar problems without considering quantum mechanics. Our further analysis found that the emergence of multiple independent vortices can be realized by reformulating the viscosity term of the two-fluid model to conserve the angular momentum of the particles around their axes. Consequently, our model succeeded in reproducing the phenomena observed in quantum cases, even though we solve the phenomenological governing equations of liquid 4He.

Non-Conventional Dynamical Bose Condensation

The paper presents a review of results concerning the non-conventional dynamical condensation versus conventional Bose-Einstein condensation, including the case of generalised van den Berg-Lewis-Pul\'e condensate. The review is based on detailed discussion of two models: a simple toy model and the Bogoliubov Weakly Imperfect Bose-Gas model, which was invented for explanation of superflfluidity of liquid 4He, but which is also instructive for analysis of non-conventional condensation regarding some recent interpretations of experimental data.

Superfluid quantum criticality in liquid He3 in anisotropic aerogel

In the novel superfluid polar phase realized in liquid 3He in highly anisotropic aerogels, a quantum transition to the polar-distorted A (PdA) phase may occur at a low but finite pressure Pc(0). It is shown that a nontrivial quantum dynamics of the critical fluctuation of the PdA order is induced by the presence of both the columnar-like impurity scattering leading to the Anderson's Theorem for the polar phase and the line node of the quasiparticle gap in the state, and that, in contrast to the situation of the normal to the B phase transition in isotropic aerogels, a weakly divergent behavior of the compressibility appears in the quantum critical region close to Pc(0).

Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid 3He. The comparison of electrons in antimony and fermions in 3He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.

Trapping Multielectron Bubbles Using a Point Paul Trap

We demonstrate an experimental setup to trap multielectron bubbles in bulk liquid He4 using a point Paul trap. The experimental configuration is based on dc and rf electric fields applied to planar electrodes such as to trap the bubbles at a certain location. We have performed numerical simulations to estimate the experimental parameters at which stable trapping can occur, which matched with the experimental results. Compared to the linear Paul traps reported earlier by our group, point Paul traps allow more efficient loading and better optical access for viewing the trapped bubbles, and will allow simultaneous storage and investigation of multiple electron bubbles in the future.

Critically Charged Superfluid 4He Surface in Inhomogeneous Electric Fields

We have studied the spatial distribution of charges trapped at the surface of superfluid helium in the inhomogeneous electric field of a metallic tip close to the liquid surface. The electrostatic pressure of the charges generates a deformation of the liquid surface, leading to a “hillock” (called “Taylor cone”) or “dimple”, depending on whether the tip is placed above or below the surface. We use finite element simulations for calculating the surface profile and the corresponding charge density in the vicinity of the tip. Typical electric fields E are in the range of a few kV/cm, the maximum equilibrium surface deformations have a height on the order of (but somewhat smaller than) the capillary length of liquid 4He (0.5 mm), and the maximum number density of elementary charges in a hillock or dimple, limited by an electrohydrodynamic instability, is some 1013 m−2. These results can be used to determine the charge density at a liquid helium surface from the measured surface profile. They also imply that inhomogeneous electric fields at a bulk helium surface do not allow one to increase the electron density substantially beyond the limit for a homogeneous field, and are therefore not feasible for reaching a density regime where surface state electrons are expected to show deviations from the classical behavior. Some alternative solutions are discussed.

The critical velocity of transition to turbulence in 3He–4He liquid solutions

The transition between laminar and turbulent flows around a quartz tuning fork vibrating with frequency ω in superfluid 4He and concentrated solutions (5 and 15% 3He in 4He) in the temperature range 0.3–2.3 K has been studied. The temperature dependences of the amplitude of the critical transition velocity vcr are obtained. The relationship vcr ∼ √(ηω/ρ) is shown to be applicable for the description of these dependences in concentrated solutions of 3He in 4He with density ρ and viscosity η, but this formula does not hold for the temperature dependence of vcr in pure 4He over the entire temperature range explored. It is also shown that in contrast to pure 4He temperature has virtually no effect in concentrated 3He–4He solutions on the drag coefficient in both laminar and turbulent regimes. The concentration dependences of the drag coefficient in the laminar regime normalized to the effective cross section of the vibrating body are plotted in the temperature range 0.5–1 K. The calculated dependences show that for low concentrations of a solution with x3 &amp;lt; 1% 3He the normalized drag coefficient weakly depends on the concentration of 3He and can be qualitatively described by the formula λ/S∼ρηω. In the x3 &amp;gt; 1% 3He concentration range, this coefficient increases sharply, and the reason for such a growth is currently not clear. Overall, the results of the study show that an increase in the 3He concentration in the solution enhances its stability with respect to the development of turbulence as the exciting force of a quartz tuning fork increases.

Erratum to: Spin Diffusion in Liquid 3He Confined in Planar Aerogel

Erratum to: Spin Diffusion in Liquid 3He Confined in Planar Aerogel

Superfluid 3He in a Nematic Aerogel

In nematic aerogels, their constituent fibers are oriented along the same direction. In liquid 3He filling such aerogels, the scattering of Fermi quasiparticles at ultralow temperatures becomes anisotropic. This makes it possible to obtain new superfluid phases of 3He, which are not observed in bulk 3He. In this article, results of NMR investigation of these new superfluid phases of 3He in aerogels with different porosities are compared. We describe the methods for identifying these phases and consider some topological defects observed in them.