He superfluidity in the presence of aerogel

Aerogels introduce disorder into the p-wave-paired superfluid ³He and suppress T_c. Quantifiable (by small angle X-ray scattering) differences in the long-range structure of two identical density aerogels are primarily responsible for their different transition temperatures. We also demonstrate that alteration of the short-range correlations by the addition of ⁴He does not strongly affect T_c. Acoustic measurements of the fast and slow modes of ³He in aerogel are described. These can be used to explore the superfluid component. We also outline future prospects.     

Quantitative theory of thermal fluctuations and disorder in the vortex matter

A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.     

Critical scaling properties at the superfluid transition of 4He in aerogel

We study the superfluid transition of 4He in aerogel by Monte Carlo simulations and finite size scaling analysis. Aerogel is a highly porous silica glass, which we model by a diffusion limited cluster aggregation model. The superfluid is modeled by a three dimensional XY model, with excluded bonds to sites on the aerogel cluster. We obtain the correlation length exponent nu=0.73+/-0.02, in reasonable agreement with experiments and with previous simulations. For the heat capacity exponent alpha, both experiments and previous simulations suggest deviations from the Josephson hyperscaling relation alpha=2-dnu. In contrast, our Monte Carlo results support hyperscaling with alpha=-0.2+/-0.05. We suggest a reinterpretation of the experiments, which avoids scaling violations and is consistent with our simulation results.     

Torsional oscillator and synchrotron X-Ray experiments on solid 4He in aerogel

X-ray diffraction experiments show that solid 4He grown in aerogel is highly polycrystalline, with an 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 approximately 3 x 10(-4), and the onset temperature is approximately 100 mK.     

Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel

It has been shown by the example of ³He in aerogel that the correlation in the position of impurities may have a considerable effect on the transition temperature T _c of a Fermi fluid to an unconventional superfluid or superconducting state if the correlation radius of the system of impurities exceeds the correlation length ξ₀ of the emerging superfluid phase. A decrease in T _c of ³He in aerogel has been expressed in terms of the structure factor of aerogel. Taking into account the fractal structure of aerogel provides a simple formula that satisfactorily describes the observed decrease in T _c.     

Relation between quantum and thermal fluctuations

A relation between quantum and thermal fluctuations, called the generalized uncertainty relation, is derived and discussed. It is given in the terminology of thermo field dynamics. The relation enables us to separate the purely thermal fluctuation from the total fluctuation.     

Phonons, rotons, and layer modes of liquid 4He in aerogel

We report the first observation of two-dimensional layer modes in both fully filled and partially filled aerogel. Using complementary high-energy resolution and high statistical precision neutron scattering instruments, and two different 87% porous aerogel samples, we show that the three-dimensional (3D) phonon-roton excitation energies and lifetimes of liquid 4He in aerogel are the same as in bulk 4He within current precision. The layer modes are the excitations that distinguish aerogel from the bulk rather than a difference in the 3D roton energy.     

High-frequency acoustics of 3He in aerogel

High-frequency ( approximately 15 MHz) acoustics were performed on 3He in 98% porous silica aerogel using an acoustic cavity technique. Measurements of the sound attenuation in the normal Fermi liquid and superfluid display behavior quite different from the bulk owing to strong elastic scattering of quasiparticles. The transition from first-to-zero sound is completely obscured with a quasiparticle mean-free path estimated to be in the range of 200-300 nm. No collective mode attenuation peak was observed at or below the superfluid transition.     

Heat capacity of 3He in aerogel

The heat capacity of pure 3He in low density aerogel is measured at 22.5 bars. The superfluid response is simultaneously monitored with a torsional oscillator. A slightly rounded heat capacity peak, 65 microK in width, is observed at the 3He-aerogel superfluid transition, T(ca). Subtracting the bulk 3He contribution, the heat capacity shows a Fermi-liquid form above T(ca). We can fit the heat capacity attributed to superfluid within the aerogel with a rounded BCS form accounting for 0.30 of the nonbulk fluid in the aerogel, or by assuming a substantial reduction in the superfluid order parameter. Both approaches are consistent with earlier superfluid density measurements.     

Interplay between disorder and quantum and thermal fluctuations in ferromagnetic alloys: the case of UCu2Si2-xGex

We consider, theoretically and experimentally, the effects of structural disorder, quantum fluctuations, and thermal fluctuations in the magnetic and transport properties of certain ferromagnetic alloys. We study the particular case of UCu2Si2-xGex. The low temperature resistivity, rho(T,x), exhibits Fermi liquid behavior as a function of temperature T for all values of x, which can be interpreted as a result of the magnetic scattering of the conduction electrons from the localized U spins. The residual resistivity, rho(0,x), follows the behavior of a disordered binary alloy. The observed nonmonotonic dependence of the Curie temperature, T(c)(x), with x can be explained within a model of localized spins interacting with an electronic bath. Our results clearly show that the Curie temperature of certain alloys can be enhanced due to the interplay between quantum and thermal fluctuations with disorder.     

Singularity in the thermal boundary resistance between superfluid (4)He and a solid surface

We report new measurements in four cells of the thermal boundary resistance R between copper and (4)He below but near the superfluid-transition temperature T(lambda). For 10(-7)< or =t identical to 1-T/T(lambda))< or =10(-4) fits of R = R(0)t(-x(b))+R(B) to the data yielded x(b) approximately equal to 0.18, whereas a fit to theoretical values based on the renormalization-group theory yielded x(b) = 0.23. Alternatively, a good fit of the theory to the data could be obtained if the amplitude of the prediction was reduced by a factor close to 2. The results raise the question whether the boundary conditions used in the theory should be modified.     

Ultrasound attenuation of superfluid 3He in aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B phase of superfluid 3He in 98% porosity aerogel down to the zero temperature limit for a wide range of pressures at zero magnetic field. The absolute attenuation was determined by direct transmission of sound pulses. Compared to the bulk fluid, our results revealed a drastically different behavior in attenuation, which is consistent with theoretical accounts with gapless excitations and a collision drag effect.     

Dissipation mechanisms near the superfluid 3He transition in aerogel

We have investigated the dissipation (Q-1) using the torsion pendulum technique for pure 3He and 3He-4He mixtures in silica aerogel near the 3He superfluid transition (T(c)) in aerogel. With pure 3He the Q-1 decreases at the onset of superfluidity. When phase separated 3He-4He mixtures are introduced into the aerogel, the Q-1 does not decrease as rapidly and eventually increases for the highest 4He content. We provide a model for the related attenuation of transverse sound alpha that takes into account elastic and inelastic scattering processes and exhibits a decrease in alpha at T(c).