Impurity Scattering Effect on Superfluidity of 3He in Aerogel

The impurity scattering effect on superfluid ³ He in aerogel is studied on the basis of the standard impurity theory within the weak coupling limit. We discuss the superfluid transition temperature and the superfluid density in the dirty Fermi liquid. The results are compared with recent experiments on the superfluidity of ³ He in aerogel. The low pressure data of the observed superfluid density are shown to be in better agreement with the results for the A-phase than for the B-phase. The B-phase results show considerable disagreement with the low pressure data.     

Sound Propagation and Transport Properties of Liquid 3He in Aerogel

Superfluid ³ He confined in aerogel offers a unique chance to study the effects of a short mean free path on the properties of a well defined superfluid Fermi liquid with anisotropic pairing. Transport coefficients and collective excitations, e.g. longitudinal sound, are expected to react sensitively to a short mean free path and to offer the possibility for testing recently developed models for quasiparticle scattering at aerogel strands. Sound experiments, together with a theoretical analysis based on Fermi liquid theory for systems with short mean free paths, should give valuable insights into the interaction between superfluid ³ He and aerogel.     

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of ³ He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of ³ He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.     

The Thermal Damping of an Aerogel Resonator in Superfluid 3He-B at Ultra Low Temperatures

No Heading We present measurements of the thermal damping of a cylindrical aerogel sample oscillating in superfluid. ³He-B in the low temperature regime. The measurements are made at low pressures where the ³He confined in the aerogel is normal. As in the case of conventional vibrating wire resonators, the thermal damping arises from quasiparticle collisions at the wire surface and is enhanced by many orders of magnitude by Andreev scattering from the superfluid backflow around the resonator. However, in the case of aerogel, incoming quasiparticles must be absorbed and thermalised within the aerogel before being re-emilled.PACS numbers: 67.57.Bc, 67.57.De, 67.57.Hi, 67.57.Pq.     

Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

Thermodynamic Potential for Superfluid 3He in?Aerogel

We present a free energy functional for superfluid ³He in the presence of homogeneously distributed impurity disorder which extends the Ginzburg-Landau free energy functional to all temperatures. We use the new free energy functional to calculate the thermodynamic potential, entropy, heat capacity and density of states for the B-phase of superfluid ³He in homogeneous, isotropic aerogel.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

Thermal Conductivity of Normal Liquid 3He in Aerogel

We report thermal conductivity measurements for normal phase liquid ³He inside 98 and 95% aerogels at dilution refrigerator temperatures (5 to 50 mK). In our measurements we use cylindrical samples of aerogel which have been fabricated inside quartz tubes. Each tube is enclosed at one end by a small chamber to which a known heat input is applied at a measured temperature. The other end is in an open volume of helium which is heat sunk to the refrigerator. Vibrating wire thermometry is used to measure the helium temperatures. The thermal conductivity measurements show clearly the effects of quasiparticle-impurity scattering, from which values of the mean free path are derived. These are 92 nm for the 98% aerogel and 56 nm for the 95% sample.     

Superfluid helium three in aerogel

We report measurements of the superfluid density and transition temperature of³He confined within 98.2% open aerogel. Both the superfluid fraction and the temperature at which the superfluid is manifested are suppressed strongly from their bulk values. The results suggest that the aerogel reduces the order parameter by a mechanism other than as a diffusely scattering surface.     

A Preliminary Heat Capacity Measurement of 3He in Aerogel near its Superfluid Transition

We report simultaneous heat capacity and torsional oscillator measurement of ³ He in aerogel near the superfluid transition. The heat capacity has a peak at the temperature T_c where the torsional oscillator shows the onset of superfluid decoupling. The coincidence of these signatures suggests that ³ He in aerogel does undergo a true thermodynamic transition.     

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.      

Novel Oscillating Aerogel Experiments in Superfluid 3He at Ultralow Temperatures

We present novel experiments on a disk of 98% aerogel oscillating in superfluid ³ He at ultralow temperatures. The aerogel dik is attached to a goal post shaped vibrating wire resonator and immersed in liquid ³ He cooled by a Lancaster style nuclear cooling stage. At low pressures we see no evidence for superfluidity within the aerogel down to our base temperature of below <0.11T_c. At higher pressures we observe large temperature dependent frequency shifts, reminiscent of torsional oscillator experiments. We find the transition temperature at 5 bar to be around 600K. The response of the resonator is highly non linear when the helium in the aerogel is superfluid. The resonant frequency decreases strongly with increasing wire amplitude. This offers an exciting new technique for measuring the superfluid properties of ³ He in aerogel in the ultralow temperature regime.     

Vortex Core Transitions in Superfluid 3He in Uniaxially Anisotropic Aerogel

Vortex core transitions (VCTs) in the superfluid phases of liquid ³He in uniaxially stretched and compressed aerogels are theoretically investigated. Uniaxial deformation imposed on the aerogel alters superfluid pairing symmetries in aerogels and the axial and polar pairing states are favored. In this study, we examine whether the effects of the uniaxial anisotropy on the pairing symmetries are reflected in core states of a single vortex extending along the deformation axis. By numerically solving the Ginzburg-Landau equations, we find that in the compressed aerogel, the first order VCT appears at any pressure in the B-like phase, while in the stretched aerogel, the VCT in the B-like phase is lost. Further, the vortices in the A-like phase in the stretched aerogel, have a polar core state in place of the A-phase core of the nonsingular Mermin-Ho vortex.     

Excitations of Liquid 4He in Disorder

We discuss the effect of disorder and confinement on the excitations in superfluid and normal liquid ⁴ He. Neutron scattering measurements of the excitations to date are limited to helium in aerogel. There the phonon-roton energy and width are slightly modified by disorder but there is no evidence for additional excitations at low energy nor of a gap in the phonon energy at long wavelengths. Experimental difficulties are discussed. In a recent path-integral Monte-Carlo study, in which a high density of point impurities are introduced at random positions, a significant broadening and energy shift are found together with additional low-energy excitations.     

Phase separation of3He-4He mixture in aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures confined in aerogel show evidence of a well defined phase separation region. This region is detached from the superfluid transition line, opening up a region of miscible superfluid mixture at high ³ He concentration.     

Non-linear Mechanical Response of the A-like Phase of Superfluid 3He in Aerogel

We present measurements of the response of the A-like phase of superfluid ³He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid ³He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.     

Effective Heat Conductivity and Relaxation Processes in Superfluid Mixtures of 3He-4He

The effective thermal conductivity coefficient'ceff in superfluid ³He-⁴He mixtures with concentration of 9.8% ³He has been studied experimentally between 100 and 500 mK, where the main contribution to the kinetic processes is made only by phonons and ³He impurity excitations. In this case the effective thermal conductivity is a combination of diffusivity, thermal conductivity and thermal diffusion. The κ _eff value was found from stationary measurements of the temperature gradients caused by the thermal flow and from the temperature relaxation kinetics. Both the methods provide consistent resugts which also agree with those on effective thermal conductivity calculated in terms of the kinetic theory of phonon-impuriton system.     

Effect of Strong Magnetic Fields on Superfluid 3He in 98% Porosity Aerogel

No Heading We report our results of shear acoustic impedance measurements performed on superfluid ³He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on ³He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.PACS numbers: 67.57Pq, 67.80Mg     

Thermal convection and thermal conductivity of nondilute3He-4He mixtures

We present measurements of the critical temperature difference for the onset of thermal convection and the effective thermal conductivity in two³He-superfluid-⁴He mixtures. The mixtures were 6.8% and 9.8% by molar volume of³He in⁴He and the measurements were made from 0.65 K to just above the superfluid transition temperature for each mixture. The measurements were made as part of an effort to visualize convective flow patterns in helium mixtures using optical shadowgraph techniques. We discuss the implications of our results for this effort.     

Measurements on a Dynamic A-B Phase Boundary in Superfluid 3He at Very Low Temperatures

We present preliminary measurements of the dynamics of a moving A-B phase interface in superfluid ³ He at temperatures below 0.2T _c We initially stabilise the interface at low temperatures with a shaped magnetic field. We can then move the interface in a controlled manner by applying small additional time-dependent fields. The interface is created inside a quasiparticle radiator consisting of a cylindrical chamber in weak thermal contact with the refrigerant. Vibrating wire resonators inside the radiator allow us to monitor the temperature of the superfluid and to infer the heat generated by the interface motion. When we oscillate the interface at low frequencies, we measure spectacular oscillatory swings of the liquid temperature arising from the enormous change in the low lying density of states as the volume of the A-phase superfluid is alternately compressed and expanded. We have also observed hysteresis in the transition as a function of magnetic field. In particular, we observe a small history-dependent super-magnetisation of the B-phase prior to A-phase nucleation in the experimental chamber. When the system is in the metastable super-magnetised state we are able to observe a higher nucleation probability of the A-phase when the cryostat is exposed to neutrons.