We report the results of high frequency acoustic shear impedance measurement on superfluid helium-3 confined in 98% porosity silica aerogel. Using 8.69 MHz continuous wave excitation, we measured the acoustic shear impedance as a function of temperature for the sample pressure of 28.4 and 33.5 bar. We observed the A-B transition on warming in zero magnetic field. Our observations show that the A and B phases in aerogel coexist in a temperature range of about 100 micro-Kelvin in width. We propose that the difference in the relative stability of the A and B phases, arising from anisotropic scattering, can account for our observations.
We present experiments on nematic aerogel oscillating in superfluid $^3$He. This aerogel consists of nearly parallel mullite strands and is attached to a vibrating wire moving along the direction of the strands. Previous nuclear magnetic resonance experiments in $^3$He confined in similar aerogel sample have shown that the superfluid transition of $^3$He in aerogel occurs into the polar phase and the transition temperature ($T_{ca}$) is only slightly suppressed with respect to the superfluid transition temperature of bulk $^3$He. In present experiments we observed a change in resonant properti…
NMR spectra in superfluid A-like phases confined in axially deformed aerogel in presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin precessing mode is rather narrow due to the U(1)LIM effect.
The superfluid state in bulk liquid $^3$He is realized in the form of A or B phases. Uniaxially anisotropic aerogel (nafen) stabilizes transition from the normal to the polar superfluid state which on further cooling transitions to the axipolar orbital glass state (Phys. Rev. Lett. {\bf 115}, 165304 (2015)). This is the case in nafen aerogel preplated by several atomic layers of $^4$He. When pure liquid $^3$He fills the same nafen aerogel a solid-like layer of $^3$He atoms coats the aerogel structure. The polar state is not formed anymore and a phase transition occurs directly to the axipolar …
Longitudinal sound attenuation measurements in superfluid 3He in 98% aerogel were conducted at pressures between 14 and 33 bar and in magnetic fields up to 4.44 kG. The temperature dependence of the ultrasound attenuation in the A-like phase was determined for the entire superfluid region exploiting the field induced meta-stable A-like phase at the highest field. In the lower field, the A-B transition in aerogel was identified by a smooth jump in attenuation on both cooling and warming. Based on the transitions observed on warming, a phase diagram as a function of pressure (P), temperature (T)…
We present results of nuclear magnetic resonance (NMR) experiments in superfluid 3He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples the superfluid transition of 3He occurred into the polar phase, where no qualitative difference between NMR properties of 3He in these samples was found. The difference, however, has appeared on further cooling, after the transition to the polar-distorted A phase (PdA phase) with …
We have designed an experiment to study the role of global anisotropic quasiparticle scattering on the dirty aerogel superfluid 3He system. We observe significant regions of two stable phases at temperatures below the superfluid transition at a pressure of 25 bar for a 98% aerogel.
We report on orientation of the order parameter in the 3He-A and 3He-B phases caused by aerogel anisotropy. In 3He-A we have observed relatively homogeneous NMR line with an anomalously large negative frequency shift. We can attribute this effect to an orientation of orbital momentum along the axis of density anisotropy. The similar orientation effect we have seen in 3He-B. We can measure the A-phase Leggett frequency, which shows the same energy gap suppression as in the B-phase. We observe a correlation of A - B transition temperature and NMR frequency shift.
It was found that NMR properties of both superfluid phases of $^3$He in anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It was also shown that by a proper squeezing it is possible to get the aerogel sample with isotropic NMR properties.
Results of experiments with liquid 3He immersed in a new type of aerogel are described. This aerogel consists of Al2O3 strands which are nearly parallel to each other, so we call it as a "nematically ordered" aerogel. At all used pressures a superfluid transition was observed and a superfluid phase diagram was measured. Possible structures of the observed superfluid phases are discussed.
Superfluid 3He confined to high porosity silica aerogel is the paradigm system for understanding impurity effects in unconventional superconductors. However, a crucial first step has been elusive; exact identification of the microscopic states of the superfluid in the presence of quenched disorder. Using a new class of highly uniform aerogel materials, we report pulsed nuclear magnetic resonance experiments that demonstrate definitively that the two observed superfluid states in aerogel are impure versions of the isotropic and axial p-wave states. The theoretically predicted destruction of lon…
We have performed Small Angle X-ray Scattering (SAXS) on uniaxially strained aerogels and measured the strain-induced structural anisotropy. We use a model to connect our SAXS results to anisotropy of the 3He quasiparticle mean free path in aerogel.
It may be possible to stabilize new superfluid phases of $^{3}$He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid $^{3}$He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical $\sim$98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to b…
Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although the A-like phase with axial pairing is extended by any uniaxial deformation, the vortex core states in the two phases depend highly on the type of deformation in aerogel: In a compressed aerogel, the first order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in B-like phase, while no strange vortex core is expected…
Measurements of superfluid $^3$He in 98% aerogel demonstrate the existence of a metastable \emph{A}-like phase and a stable \emph{B}-like phase. It has been suggested that the relative stability of these two phases is controlled by anisotropic quasiparticle scattering in the aerogel. Anisotropic scattering produced by axial compression of the aerogel has been predicted to stabilize the axial state of superfluid $^3$He. To explore this possiblity, we used transverse acoustic impedance to map out the phase diagram of superfluid $^3$He in a $\sim 98$% porous silica aerogel subjected to 17% axial …
Recently, one analog of the Anderson's Theorem for the $s$-wave superconductor has attracted much interest in the context of the $p$-wave polar pairing state of superfluid $^3$He in a model aerogel in the limit of strong uniaxial anisotropy. We discuss to what extent the theorem is satisfied in the polar phase in real aerogels by examining the normal to polar transition temperature $T_c$ and the low temperature behavior of the superfluid energy gap under an anisotropy of a moderate strength and comparing the obtained results with experimental data. The situation in which the Anderson's theorem…
We report the first observation of coherent quantum precession of magnetization (CQP) in superfluid 3He-A in aerogel. The coherent precession in bulk 3He A-phase is unstable due to the positive feedback of spin supercurrent to the gradient of phase of precession. It was predicted that the homogeneous precession will be stable if the orbital momentum of 3He-A could be oriented along the magnetic field. We have succeeded to prepare this configuration by emerging 3He in uniaxially-deformed anisotropic aerogel. The dissipation rate of coherent precession states in aerogel is much larger then one i…
We present results of high magnetic field experiments in pure $^3$He (in the absence of $^4$He coverage) in nematic aerogel. In this case the aerogel strands are covered with few atomic layers of solid paramagnetic $^3$He, which enables the spin-exchange mechanism for $^3$He quasiparticles scattering. Our earlier NMR experiments showed that in low fields, instead of the polar phase, the A phase is expected to emerge in nematic aerogel. We use a vibrating wire resonator with the sample of aerogel attached to it and measure temperature dependencies of resonance properties of the resonator at dif…
The polar phase of superfluid $^3$He is stable in "nematically ordered" densed aerogel. A rotating vessel with the polar superfluid can be filled either by an array of the single quantum vortices or by an array of the half-quantum vortices. It is shown that the inhomogeneous distribution of the spin part of the order parameter arising in an array of half-quantum vortices in strong enough magnetic field tilted to the average direction of aerogel strands leads to the appearance of a satellite in the NMR signal shifted in the negative direction with respect to the Larmor frequency. The satellite …
Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connencted by a Kibble wall in superfluid 3He in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur with no pinning effect due to the aerogel structure in the polar-distorted B (PdB) phase of superfluid 3He. By fully examining the impurity-scattering induced pairing vertex, the emergence of Anderson's Theorem in the p-wave superfluid is verified in the two opposite limits, the isotropic and strongly anisotropic limits. Solving numerically the resulting Ginzburg-…
We report the first observation of superfluid $β$ phase of $^3$He. This phase is realized in $^3$He in nematic aerogel in presence of high magnetic field right below the superfluid transition temperature. We use a vibrating aerogel resonator to detect the transition to the $β$ phase and measure the region of existence of this phase.
We have found a new stable spin state in the A-like phase of superfluid 3He confined to intrinsically anisotropic aerogel. The state can be formed by radiofrequency excitation applied while cooling through the superfluid transition temperature and its NMR properties are different from the standard A-like phase obtained in the limit of very small excitation. It is possible that this new state is formed by textural domain walls pinned by aerogel.
$^3$He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in $^3$He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work we present theoretical and numerical studies of linear NMR in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.
X-ray diffraction experiments show that solid 4He grown in aerogel is highly polycrystalline, with a hcp crystal structure (as in bulk) and a crystallite size of approximately 100 nm. In contrast to the expectation that the highly disordered solid will have a large supersolid fraction, torsional oscillator measurements show a behavior that is strikingly similar to high purity crystals grown from the superfluid phase. The low temperature supersolid fraction is only ~3x10-4 and the onset temperature is ~ 100 mK.
It is shown that in the polar phase of superfluid 3 He, stabilized by nematic aerogel, at the condition of specular reflection of quasi-particles from the strands of aerogel the temperature dependence of the gap in the spectrum of quasi-particles coincides with that in the bulk polar phase without impurities. The analogy with the Anderson theorem for conventional superconductors is discussed.
Porous aerogel is a source of elastic scattering in superfluid 3He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.
The magnetic dipole-dipole interaction does not prevent existence of half-quantum vortices in the polar phase of superfluid He-3 which can be stable in uniaxial anisotropic aerogel. Here we discus this exotic possibility. After developing a phenomenological theory of phase transition from the normal to polar superfluid state and then to axipolar superfluid state we calculate the NMR properties of such type superfluids at the rest or under rotation filled by an array either single quantum or half quantum vortices.
An equation previously proposed to describe the evolution of vortex line density in rotating counterflow turbulent tangles in superfluid helium is generalized to incorporate nonvanishing barycentric velocity and velocity gradients. Our generalization is compared with an analogous approach proposed by Lipniacki, and with experimental results by Swanson et al. in rotating counterflow, and it is used to evaluate the vortex density in plane Couette and Poiseuille flows of superfluid helium.
We report results of low frequency nuclear magnetic resonance (NMR) experiments in the superfluid polar phase of 3He which is stabilized by a new type of "nematic" aerogel - nafen. We have found that an interaction between transverse and longitudinal NMR modes may essentially influence the spin dynamics. Theoretical formulas for NMR resonant frequencies are derived and applied for interpretation of the experimental results.
Formation of fourth-sound shock waves in narrow channels filled with superfluid helium is studied. Physical and mathematical conditions at the surface of discontinuity are established. These conditions differ somewhat from those in case of first- and second-sound waves. The velocity of discontinuity coincides with that of fourth sound. The jumps of temperature and the superfluid velocity are shown to be of the first order as to the pressure jumps.
A new method of obtaining the interaction Hamiltonian of phonons at superfluid helium-solid interface is proposed in the work. Equations of hydrodynamic variables are obtained in terms of second quantization if helium occupies a half-space. The contributions of all processes to the heat flux from solid to superfluid helium are calculated based on the obtained Hamiltonian. The angular distribution of phonons emitted by a solid is found in different processes. It is shown that all the exit angles of superfuild helium phonons are allowed. The obtained results are compared with experimental data a…
The mechanism of the roughening induced partial depinning of gliding dislocations from Helium-3 impurities is proposed as an alternative to the standard "boiling off". We give a strong argument that Helium-3 remains bound to dislocations even at large temperatures due to very long equilibration times. A scenario leading to the similarity between elastic and superfluid responses of solid Helium-4 is also discussed. Its main ingredient is a strong suppression of the superfluidity along dislocation cores by dislocation kinks (D. Aleinikava, et. al., arXiv:0812.0983). These kinks, on one hand, det…
It is shown that the critical velocity of a small sphere oscillating in superfluid helium increases with the square root of the oscillation frequency. This behavior can be described by a simple dimensional argument. The size of the sphere and the temperature of the superfluid are found to have no or only very little effect. Surface properties of the sphere and remanent vorticity may have an influence but have not been under systematic investigation in these measurements
The phenomenon of the spontaneous phase-coherent precession of magnetization in superfluid 3He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different magnon BEC states have been observed: homogeneously precessing domain (HPD); BEC condensation in the spin-orbit potential trap (Q-balls); coherent precession with fractional magnetization; and two modes of the coherent precession in squeezed aerogel. The spin superfluidity effects, like spin Josephson phenomena, spin current vortices, spin phase slippage, long distance magnetiz…
Generation of a quasi-stationary flow of the superfluid helium normal part in the presence of intense first- and second-sound waves is studied. Relevant equations are obtained. The contribution to the process of energy dissipation at the shock front layer and of fluid viscosity is analysed in detail for the case of a second-sound wave. An estimate concerning possible experimental observation of the process is made.
Tungsten filaments used as sources of electrons in a low temperature liquid or gaseous helium environment have remarkable properties of operating at thousands of degrees Kelvin in surroundings at temperatures of order 1 K. We provide an explanation of this performance in terms of important changes in the thermal transport mechanisms. The behavior can be cast as a first-order phase transition.
It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these ideas it was predicted [9] that 3He in high porosity aerogel would become a superfluid glass. We report here our nuclear …
Nearly five decades have elapsed since the seminal 1966 paper of P.W. Anderson on the flow of superfluid helium, $^4$He at that time. Some of his "Considerations" -- the role of the quantum phase as a dynamical variable, the interplay between the motion of quantised vortices and potential superflow, its incidence on dissipation in the superfluid and the appearance of critical velocities, the quest for the hydrodynamic analogues of the Josephson effects in helium -- and the way they have evolved over the past half-century are recounted below. But it is due to key advances on the experimental fr…
Motivated by the disparity between the experimentally observed properties of superfluid 3He in aerogel and predictions of the Abrikosov and Gorkov theory of superconducting alloys we consider effect of correlated pair-breaking impurities on the temperature dependence of the square of magnitude of the average order parameter and related thermodynamic properties of a Fermi superfluid. We show that the correlations, increasing the spectral density of the fluctuations with small wave vectors increase the transition temperature and enhance a temperature region below Tc where fluctuations of the ord…
We explore the possibility that the fast and exotic negative ions in superfluid helium are electrons bound to quantized vortex structures, the simplest being a ring. In the states we consider, the electron energy is only slightly below the conduction band minimum of bulk helium. To support our proposal we present two calculations. In the first, we show that the electron pressure on the vortex core is insufficient to cavitate the helium and form an electron bubble. In the second, we estimate the equilibrium radius of the vortex ring that would bind an electron and find it is much smaller than t…
System of two-fluid hydrodynamics of superfluid helium with the account of electric field is obtained. These equations are obtained in kinetic approach using quasi-equilibrium distribution function of quasi-particles, which vanishs collision integral of quasi-particles, and contains dependence on electric field by means of phenomenological parameter α. Using experimental data at temperature range of 1,4 - 2 K, where basic role plays roton hydrodynamics, the value of phenomenological parameter, is obtained.
A complete study of the propagation of waves (namely longitudinal density and temperature waves, longitudinal and transversal velocity waves and heat waves) in turbulent superfluid helium is made in three situations: a rotating frame, a thermal counterflow, and the simultaneous combination of thermal counterflow and rotation. Our analysis aims to obtain as much as possible information on the tangle of quantized vortices from the wave speed and attenuation factor of these different waves, depending on their relative direction of propagation with respect to the rotation vector.
One of the most spectacular discoveries made in superfluid $^3$He confined in a nanostructured material like aerogel or nafen was the observation of the destruction of the long-range orientational order by a weak random anisotropy. The quenched random anisotropy provided by the confining material strands produces several different glass states resolved in NMR experiments in the chiral superfluid $^3$He-A and in the time-reversal-invariant polar phase. The smooth textures of spin and orbital order parameters in these glasses can be characterized in terms of the randomly distributed topological …
The new mode of magnetization precession in superfluid 3He-A in a squeezed aerogel has been recently reported. We consider this mode in terms of the Bose-Einstein condensation (BEC) of magnons. The difference between magnon BEC states in 3He-A and in 3He-B is discussed.
We proceed from the premise that the spectrum of elementary excitations in the normal component in Landau's theory of superfluidity should depend on the superfluid helium temperature. This leads to generalization of the Landau superfluidity criterion. On this basis, taking into account available experimental data on inelastic neutron scattering, it is shown that, in addition to phonon--roton excitations, there is one more type of elementary excitations in superfluid helium, which we called helons. The energy spectrum with such a momentum dependence was first proposed by Landau. The helon energ…
An analysis of experimental data shows that, in addition to phonon--roton excitations in superfluid helium, there necessarily exist at least one branch of elementary excitations whose energy spectrum strongly depends on temperature. On this basis, the Landau superfluidity criterion is generalized for several branches of elementary excitations, taking into account that the critical velocity should vanish during the phase transition of liquid helium from the superfluid state to the normal state. We suppose that a new spectrum of excitations with a gap, depending on interparticle interaction, cor…
Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of 3He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at Tc, is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure 3He, with the disappearanc…
Superfluid $T_c$ of liquid helium-3 and its pressure dependence are calculated by using a relation obtained from our macro-orbital microscopic theory. The results agree closely with experiments. This underlines the accuracy of our relation and its potential to provide superfluid $T_c$ of electron fluid in widely different superconductors and renders experimental foundation to our conclusion related to the basic factors responsible for the formation of (q, -q) bound pairs of fermions and the onset of superfluidity in a fermionic system.
Using an optical interferomertric method, the homogeneous cavitation density of superfluid helium at $T=0.96\,$K is measured and found to be $ρ_{cav}=0.1338\pm0.0002\rm\,g.cm^{-3}$. A well established equation of state for liquid helium at negative pressures converts this to the cavitation pressure $P_{cav}=-5.1\pm0.1\,$bar. This cavitation pressure is consistent with a model taking into account the presence of quantized vortices, but disagrees with previously published experimental values of $P_{cav}$.
By large-scale quantum Monte Carlo simulations we show that grain boundaries in Helium-4 crystals are generically superfluid at low temperature, with a transition temperature of the order of ~0.5K at the melting pressure; insulating grain boundaries are found only for special orientations of the grains. We also find that close vicinity to the melting line is not a necessary condition for superfluid grain boundaries, and a grain boundary in direct contact with the superfluid liquid at the melting curve is found to be mechanically stable and the grain boundary superfluidity observed by Sasaki et…
We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile rece…
We argue that classical transitions can be the key to explaining the long standing puzzle of the fast A-B phase transition observed in superfluid Helium 3 while standard theory expects it to be unobservably slow. Collisions between domain walls are shown to be capable of reaching phases inaccessible through homogenous nucleation on the measured timescales. We demonstrate qualitative agreements with prior observations and provide a definite, distinctive prediction that could be verified through future experiments or, perhaps, a specific analysis of existing data.
The quasi-one-dimensional system of surface electrons over superfluid helium with negative charge on substrate is investigated. The temperature dependence of conductivity is ladder-like which is observed at temperature lower 1.3 K. The parameters of ladder have been different in different experiments. The observed dependence isn't explained by classical models of carry with account to the usual scatters in channel. It is supposed the dependence have been connected with quantum character of electron transport in narrow channels.
The fact that superfluid helium always leaks out of an open container is usually explained by the phenomenon of wetting. In the present paper it is demonstrated that this explanation is unconvincing. The fact can be readily explained from the viewpoint of the interpretation of superfluidity proposed earlier by the author according to which superfluidity is an equilibrium state of liquid helium where the symmetry is spontaneously broken because of an intrinsic superflow. Experiments on the thickness of moving helium films that have given rise to much controversy are discussed as well. Some expe…
We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by the interaction with quantized vortices terminating at the free surface. We identify two types of particle trajectories and the associated vortex structures: vertical linear vortices pinned at the bottom of the container and half-ring vortices travelling along the free surface of the liquid.
We comment on the paper by M. Sýkora, M. Pavelka, M. La Mantia, D. Jou, and M. Grmela "On the relations between large-scale models of superfluid helium-4," Physics of Fluids, 33(12):127124(2021), where the authors have developed a formalism for describing a coarse-grained flow of superfluid helium. This formalism is greatly based on the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) model. We strongly disagree with the use of the HVBK equation approach for the case of the three-dimensional quantum turbulence and expose our objections in this comment. We discuss the HVBK method and also criticize the…
This article presents a phenomenological dynamic phase transition theory -- modeling and analysis -- for liquid helium-3. We derived two new models, for liquid helium-3 with or without applied field, by introducing three wave functions and using a unified dynamical Ginzburg-Landau model. The analysis of these new models leads to predictions of existence of 1) a unstable region, 2) a new phase C in a narrow region, and 3) switch points of transition types on the coexistence curves near two triple points. It is hoped that these predictions will be useful for designing better physical experiments…
