Identification of superfluid phases of 3He in uniformly isotropic 98.2% aerogel

Superfluid ^{3}He 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 long-range orbital order (Larkin-Imry-Ma effect) in the impure axial state is not observed.     

Phase diagram of the A and B phases of superfluid 3He in aerogel

We report the first measurements of the A-B phase transition of superfluid 3He confined within 98% silica aerogel in high magnetic fields and low temperatures. A disk of aerogel is attached to a vibrating wire resonator. The resonant frequency yields a measure of the superfluid fraction rho(s)/rho of the 3He within the aerogel. The inferred rho(s)/rho value increases substantially at the A-to- B transition of the confined superfluid, allowing us to map the A-B phase diagram as a function of field and temperature. At 4.8 bars, the B-T transition curve looks very similar to that in bulk with a simple reduction factor of order 0.45 for both transition field and temperature.     

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).     

Interfacial pinning in the superfluid 3He A-B transition in aerogel

Continuous-wave NMR studies of 3He in the presence of 99.3% porosity silica aerogel at 34.0 bars and in a magnetic field of 28.4 mT reveal a first-order phase transition between A-like and B-like superfluid phases on both warming and cooling. NMR spectra show that the phases on warming are the same as the phases on cooling, and the interface between them is found to be strongly pinned, even close to T(c,aero). The observed behavior is consistent with spatial variation of pinning strengths within the aerogel.     

Gauge group and phases of superfluid 3He

The p-wave phases of superfluid ³He are classified without the unitary constraint or the constraints on the net nuclear magnetization and the magnetic susceptibility.     

Phase diagram of superfluid 3He in 99.3% porosity aerogel

We report on continuous-wave NMR measurements of the energy gaps of the A-like and B-like superfluid phases of 3He at 28.4 mT confined to a 99.3% porosity silica aerogel. The gaps are suppressed by the presence of the aerogel in a temperature-independent manner, but the suppression is considerably stronger than expected from the suppression of T(c). We then use our measurements to calculate the free energy ratio between the A-like and B-like phases. The equilibrium AB transition temperature, derived from where this ratio reaches unity, is consistent with previous measurements of the initial displacement of the pinned AB interface on warming. On this basis, we present for the first time the equilibrium phase diagram of the A-like and B-like phases of superfluid 3He in aerogel.     

Phenomenological phase diagram of superfluid 3He in a stretched aerogel

Highly anisotropic “nematically ordered” aerogel induces global uniaxial anisotropy in superfluid ³He. The anisotropy lowers symmetry of 3He in the aerogel from spherical to axial. As a result, instead of one transition temperature in a state with an orbital moment l = 1, there are two, corresponding to projections l _z = 0 and l _z = ±1. This splitting has a pronounced effect on the phase diagram of superfluid ³He and on the structures of the appearing phases. Possible phase diagrams obtained phenomenologically on the basis of Landau expansion of the thermodynamic potential in the vicinity of the transition temperature are presented here. The order parameters corresponding to each phase and their temperature dependences are found.     

Some comments on superfluid 3He placed in globally deformed aerogel

New experimental results focused on the behavior of the superfluid A-like phase placed in globally deformed aerogel environment are considered. We compare experimental data collected by using optically attested axially stretched silica aerogel, on the one hand, and “nematically ordered” aerogel consisting of nearly parallel Al₂O₃ · H₂O polymer strands, on the other. In the case of axially stretched silica aerogel the point of view was adopted according to which the orbital anisotropy axis l? is long-ranged. The experiments were carried out by pulsed NMR techniques in keeping the direction of an externally applied magnetic field normal to aerogel stretching axis. We have generalized the dipole-locked configuration for arbitrary angle of inclination of the magnetic field with respect to aerogel stretching axis. The experimental data collected in using “nematically ordered” aerogel cannot be reconciled with above-mentioned results.     

Thermal conductivity of liquid 3He in aerogel: a gapless superfluid

We have measured the thermal conductivity of liquid 3He in 98% aerogel at ultralow temperatures. Aerogel introduces disorder on a scale comparable to the superfluid coherence length. At low pressures the liquid in the aerogel shows normal-state behavior with conductivity linear in temperature. At pressures above approximately 6 bars the onset of superfluidity suppresses the conductivity and the thermal conductivity again tends towards linear behavior in the very low temperature limit, providing strong evidence that here the liquid 3He in the aerogel is behaving as a gapless superfluid.     

Vortex-lattice phases of superfluid (3)He in rapid rotation

Superfluid 3He in the angular velocity of 0.01 Omega(c2) < or = Omega < or = Omega(c2) is studied theoretically, where Omega(c2) is the upper critical field of order (1 - T/T(c)) x 10(7) rad/s. Five different phases have been found in the pressure-Omega plane. Especially, it is shown that the A-phase-core vortex experimentally found in the B phase originates from Schopohl's polar state at Omega(c2) via an A-phase mixed-twist lattice with polar cores and the normal-core lattice of Ohmi, Tsuneto, and Fujita [Prog. Theor. Phys. 70, 647 (1983)].     

Scaling of the superfluid fraction and T(c) of 3He in aerogel

We have investigated the superfluid transition of 3He in different samples of silica aerogel. By comparing new measurements on a 99.5% sample with previous observations on the behavior of 3He in 98% porous aerogel, we have found evidence for a scaling of the transition temperature and superfluid density of 3He to the correlation length of the aerogel.     

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.     

A1 and A2 transitions in superfluid 3He in 98% porosity aerogel

Superfluid 3He in high porosity aerogel is the system in which the effects of static impurities on a p-wave superfluid can be investigated in a systematic manner. We performed shear acoustic impedance measurements on this system (98% porosity aerogel) in the presence of magnetic fields up to 15 T at the sample pressures of 28.4 and 33.5 bars. We observed the splitting of the superfluid transition into two transitions in high fields in both bulk and liquid in aerogel. The field dependence of the splitting in aerogel resembles that of the bulk superfluid 3He caused by the presence and growth of the A1 phase. Our results provide the first evidence of the A1 phase in superfluid (3)He/aerogel.     

Longitudinal resonance and identification of the order parameter of the A-like phase of superfluid 3He in aerogel

Interpretation of the recent experiments of Dmitriev et al. on longitudinal resonance in the A-like phase based on specific properties of the “robust” order parameter is proposed. The text was submitted by the author in English.     

Currents in superfluid 3He

In the Ginsburg-Landau region the hydrodynamic variables for superfluid ³He are defined by means of the Lie algebra of the gauge group SO(3) x SO(3) x U(1) for the order parameter. The equilibrium of two different superfluid phases of ³He is considered within the framework of this method. At the surface, dividing the two regions filled with these phases, we consider joint conditions on currents and topological structures.