Proximity Effect between a Dirty Fermi Liquid and Superfluid 3He

The proximity effect in superfluid ³He partly filled with high porosity aerogel is discussed. This system can be regarded as a dirty Fermi liquid/spin-triplet p-wave superfluid junction. Our attention is mainly paid to the case when the dirty layer is in the normal state owing to the impurity pair-breaking effect by the aerogel. We use the quasiclassical Green’s function to determine self-consistently the spatial variations of the p-wave order parameter and the impurity self-energy. On the basis of the fully self-consistent calculation, we analyze the spatial dependence of the pair function (anomalous Green’s function). The spin-triplet pair function has in general even-frequency odd-parity and odd-frequency even-parity components. We show that the admixture of the even- and odd-frequency pairs occurs near the aerogel/superfluid ³He-B interface. Among those Cooper pairs, only the odd-frequency s-wave pair can penetrate deep into the aerogel layer. As a result, the proximity-induced superfluidity in a thick aerogel layer is dominated by the Cooper pair with the odd-frequency s-wave symmetry. We also analyze the local density of states and show that it has a characteristic zero-energy peak reflecting the existence of the odd-frequency s-wave pair, in agreement with previous works using the Usadel equation.     

Spin Fluctuations in A-like Superfluid Phase of 3He in Aerogel

The frequency spectrum of the spin fluctuations δ S(t) superimposed on the coherently precessing spin modes in the A-like superfluid phase in aerogel is analysed. It is shown that the low amplitude spin fluctuations could be most easily observed in the case of an uni-axially deformed aerogel. It is demonstrated, in particular, that for axially stretched (radially squeezed) aerogel described by the U(1)LIM model the fourth order harmonic in δ S _z (t) is erased, in contrast with what is expected for the long range Leggett orbital configuration in the ³He-A (ABM state).     

Experiments on 3He–4He Mixtures in Aerogel

We describe experiments on ³ He- ⁴ He mixtures in 98% open aerogel grown by cold-deposition (T80mK) of ⁴ He followed by the deposition of ³ He or alternatively by cooling down a homogenous mixture. The two approaches led to different ⁴ He film morphologies. We will also describe the observation of migration of ⁴ He from or toward the cell below 100 mK. This migration can lead to the exclusion of ⁴ He (other than the localized surface layers) for ⁴ He concentrations between 4% and 11% in the cell.     

Magnetic Susceptibility of the Balian–Werthamer Phase of 3He in Aerogel

The equilibrium superfluid phase of ³He impregnated into high-porosity (98%) silica aerogels appears to be a non-equal-spin-pairing state in zero field at all pressures, which is generally assumed to be the Balian–Werthamer (BW) phase modified by the depairing effects of the aerogel structure. The nuclear magnetic susceptibility played a key role in identifying the B-phase of pure ³He with the BW state. We report theoretical calculations of the nuclear magnetic susceptibility for the BW model of superfluid ³He in aerogel within the framework of the Fermi-liquid theory of superfluid ³He. Scattering of quasiparticles by the aerogel, in addition to Fermi-liquid exchange corrections, leads to substantial changes in the susceptibility of the BW phase. The increase in the magnetic susceptibility of ³He-aerogel compared to pure³He-B is related to the polarizability of the gapless excitations and the impurity-induced local field. The limited data that is available is in rough agreement with theoretical predictions. Future measurements could prove important for a more definitive identification of the ordered phase, as well as for refining the theoretical model for the effects of disorder and scattering on the properties of superfluid ³He.     

Soliton-Like Spin State in the A-Like Phase of 3He in Anisotropic Aerogel

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.      

Observation of Zero-Sound at Atomic Wave-Vectors in a Monolayer of Liquid 3He

The elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid ³He adsorbed on graphite preplated by a monolayer of solid ⁴He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid ³He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk ³He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle-hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid ⁴He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmon excitations in electronic systems).     

3He in Aerogel – an Inhomogeneously Disordered Unconventional Superfluid

We have examined the superfluidity of ³ He in 98.2% porous silica aerogel with up to 34% ⁴ He at 21.6 bar. The mixture is phase-separated for ⁴ He fractions between 11% and 34%. The ⁴ He-rich, phase preferentially occupies the regions of highest silica density in the aerogel, thus modifying the distribution of the correlated disorder seen by superftuid ³ He. The ³ He T _c increases slightly with ⁴ He content while the superfluid fraction decreases rapidly. This behavior is inconsistent with that of ³ He in a homogeneously scattering medium and is analogous to that of a granular superconductor.     

NMR in Superfluid A-Like Phase of 3He Confined in?Globally Deformed Aerogel in?Tilted Magnetic Field

NMR spectra in superfluid A-like phases confined in axially deformed aerogel in the 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 spectrum of high-frequency spin fluctuations accompanying coherently precessing spin modes is constructed.     

Heat Capacity of Liquid 4He Confined in a Nanoporous Glass

We report a preliminary study of heat capacities of ⁴He confined in a nanoporous Gelsil glass that has nanopores of 2.5 nm in diameter. The heat capacity has a broad peak at a temperature far above the superfluid transition temperature obtained by torsional oscillator technique. The heat-capacity peak is attributed to formation of localized Bose-Einstein Condensates in the nanopores, in which the long-range superfluid coherence is destroyed by pore size distribution or random potential inherent to the porous glass.      

Surface Tension Maximum of Liquid 3He—Experimental Study

The surface tension of liquid ³He was measured as a function of temperature by means of the capillary rise method. Suzuki et al. [Europhysics Lett. 5, 333 (1988)] reported that the surface tension was almost temperature independent below 120 mK. Here we have examined it with greater precision and found that it has a small maximum around 100 mK. The surface tension increased with temperature from 35 mK and had a maximum of about 3×10^–4 as a fraction of the surface tension at 0 K. It was found that the surface tension maximum can be attributed mainly to the T⁴ ln T variation which has been theoretically derived by Misawa on the basis of a local approximation for the entropy including Fermi liquid effect.     

Polarization Induced Spin Wave Damping in Spin Polarized Liquid 3He–4He

We have measured the temperature and polarization dependence of Silin spin wave spectra in a saturated ³He–⁴He mixture with a concentration of 9.4% at a pressure of 8 bars. The mixture has been cooled and polarized by a Leiden dilution refrigerator to temperatures in the range 10–15 mK and polarizations as high as 9.2% corresponding to 3.4 times the equilibrium polarization of 2.7% in the external magnetic field of 11.36 T. The analysis takes into account the dipolar interactions and results in the relaxation time τ _⊥ and spin diffusion constant D _⊥ . We find that τ _⊥ and D _⊥ are proportional to where T is the temperature, is the polarization enhancement factor and T _a0 is the anisotropy temperature for the mixture at equilibrium in the external field. Our result T _a0=3.66±0.14 mK is 30% higher than the theoretical prediction for very dilute mixtures and is evidence for the existence of polarization induced relaxation of transverse spin currents.     

Thermodynamics of Liquid–Liquid Criticality in Supercooled Water in a Mean-Field Approximation

In a recent publication, it has been shown how a non-analytic scaling theory of critical phenomena can describe the available experimental information for the thermodynamic properties of supercooled water, when it is assumed to exhibit a liquid–liquid critical point. In this article, we present a mean-field equation of state which also represents the experimental data for supercooled water. Compared to the scaling theory, the mean-field equation has the advantage of simplicity for practical calculations of the properties of supercooled water. The insensitivity to a particular form of a critical equation of state is due to a lack of experimental data asymptotically close to the liquid–liquid critical point. Hence, while the assumed existence of a liquid–liquid critical point in water can account for the observed thermodynamic behavior of supercooled water, the actual location of such a liquid–liquid critical point cannot be determined accurately from the available experimental thermodynamic property data.     

Nuclear Spin Relaxation in Glass States of 3He-A in?Stretched Aerogel

We present results of pulse NMR investigations of superfluid A-like phase of ³He in stretched aerogel. In this case we have anisotropic orbital glass (OG) with two possible types of ordering in spin space??ordered spin nematic (OG-SN) or disordered spin glass (OG-SG) states. It was found that longitudinal relaxation of magnetization is non-exponential in both states and depends on temperature and on inhomogeneity of external steady magnetic field. At the same conditions the relaxation in OG-SG state is more rapid than in OG-SN state. For transverse orientation of the magnetic field relative to anisotropy axis the duration of free induction decay signal was longer than in normal phase. It may be explained by formation of coherently precessing spin state.     

Microwave-Resonance Induced Change in Magneto-Resistivity: Hot Surface Electrons on Liquid 3He

Behaviour of the linear magneto-resistivity σ _xx ⁻¹ of the surface-state electrons (SSE) exposed to the microwave radiation is studied in a wide temperature range which covers both vapor-atom and ripplon scattering regimes. The microwaves induce the resonance transitions of SSE between two lowest Rydberg states, and σ _xx ⁻¹ is observed to vary in the vicinity of the resonance. In the vapor-atom scattering regime (T≳0.5 K), magneto-resistivity decreases at the resonance, while in ripplon scattering regime (T≲0.3 K) it rapidly increases with the microwave power in the given range of the pressing electric field. The observed variation of σ _xx ⁻¹, which under the conditions of our experiment is inversely proportional to the scattering rate, is attributed to the strong heating of SSE. The heating results in the increase of electron temperature well above ambient temperature and in significant thermal population of higher excited states. The theoretical predictions are found to be in good agreement with our experimental results in the whole temperature range.      

Textures of Rotating Superfluid 3He–A in a Single Narrow Cylinder

We have studied textures of the rotating superfluid ³He–A in a single narrow cylinder by NMR measurement. In a narrow cylinder, the characteristic textures such as Mermin-Ho texture (Mermin and Ho in Phys. Rev. Lett. 36:594, 1976) can be formed in order to minimize the free energy of the system determined by the effect of the wall, the magnetic field, the dipole interaction, the flow of the superfluid and so on. We observed three types of NMR absorption spectra dependent on the processes used to form A-phase in a narrow cylinder. A particular texture shows a characteristic spectrum and we can determine the texture from the observed spectrum by comparing the resonance frequency of the peak in NMR spectrum with the calculated one of the spin wave mode. We present the identification and the phase diagram of textures of the rotating superfluid ³He–A in a single narrow cylinder.     

Spin relaxation in normal liquid3He:T 1 in the Fermi liquid (T≪T F) regime

The low-temperature (TT _F) spin relaxation timeT ₁ in normal liquid³He is calculated. First an expression forT ₁ is obtained using the Landau kinetic equation, which is in terms of the perturbations of the scattering amplitudes due to nuclear dipole-dipole interactions. These perturbations are obtained using the induced interaction model, which explicitly includes the effects of many-body correlations arising from the Pauli principle. The results are in good agreement with experiment, as well as with previous calculations.     

??On the Superfluidity of Liquid He3??. Author??s Recollections

The history of the author??s paper (Pitaevskii in J. Exp. Theor. Phys. 37:1794, 1959; Sov. Phys. JETP 10:1267, 1960) on the superfluidity of liquid He³ is presented.     

A Novel Design of a Low Temperature Preamplifier for Pulsed NMR Experiments of Dilute 3He in Solid 4He

Recent experimental studies of solid ⁴He indicate a strong correlation between the crystal defects and the onset of a possible supersolid state. We use pulsed NMR techniques to explore the quantum dynamics of the ³He impurities in the solid ⁴He in order to examine certain theoretical models that describe how the disordered states are related to supersolidity. Because of the very small signal-to-noise ratio at low ³He concentration and the long spin-lattice relaxation time (T ₁), it is essential to significantly enhance the NMR sensitivity to be able to carry out the experiments. Here we present the design of a novel low temperature preamplifier which is built with a low noise pseudomorphic HEMT transistor that is embedded into a cross-coil NMR probe. With a low power dissipation of about 0.7 mW, the preamplifier is capable of providing a power gain of 30 dB. By deploying the preamplifier near the NMR coil below 4 K, the noise temperature of the receiver is reduced to approximately 1 K. This preamplifier design also has the potential to be adapted into a low temperature amplifier with both input and output impedance at 50 Ω or a low temperature oscillator.