Anisotropy of Superfluid 3He Near Free Surface Investigated by Surface State Electrons

We have measured the resistivity of a Wigner solid formed on the free surface of superfluid ³He in the A and B phases under magnetic fields. The mobility of the Wigner solid is limited by the collisions of thermally excited quasiparticles in ³He, and hence is very sensitive to the distribution of quasiparticles in momentum space. The observed resistivity of the Wigner solid in the A phase asymptotically approaches the temperature-square dependence at low temperatures, reflecting the A phase gap with point nodes. Its temperature dependence is well explained by the vector being uniformly aligned normal to the surface. The resistivity in the B phase, in contrast, exhibits an exponential decrease at low temperatures. The resistivity in the small field well agrees with the behavior expected for the isotropic gap in the BW state. The resistivity increases in high magnetic fields, which is explained by the combination of the distortion of the gap in the BW state by the field and the orientation of the order parameter caused by the free surface.      

Electrons on the Surface of Superfluid 3He

A review of recent investigations of transport properties of surface state electrons on superfluid ³He is given. The surface state electrons in this temperature region form the Wigner solid (WS), a triangular lattice of electrons with a typical lattice constant of 1 μm. The WS is accompanied with a shallow corrugation of He surface commensurate with the WS. A model is introduced to interpret the observed WS resistivity. The model takes into account specular quasiparticle (QP) reflection from the moderately corrugated free surface, and treats the QP as if it is a quasiclassical particle. After adopting anisotropic properties of superfluid ³He order parameter and QP energy, the model provides satisfactory account of the observed properties. Preliminary results of mobility measurements of ions trapped below superfluid ³He-B are also given.     

Anomalous Resonance Phenomena in Two-Dimensional Electrons on the Surface of 3He-4He Liquid Mixtures

No Heading We report on anomalous resonance phenomena observed in a two-dimensional electron system on ³He-⁴He liquid mixtures. The resonance is observed in a Corbino conductivity measurement, in which a magnetic field B is applied prependicular to the electron sheet. We have detected the resonances for ³He concentrations n₂ from 0.475% to 10.20%, and at temperatures below 800 mK. The resonance frequency f_r is inversely proportional to B. In a preliminary study we found that f_r and the resonance amplitude increases when the electron sheet is not parallel to the electrode, and this made the understanding difficult. Here we have made the systematic measurement keeping the parallelism between the electrons and the electrode. We have observed the resonance only at n₃ > 0.475%. This fact finally leads us to conclude that adding ³He atoms to liquid ⁴He induces the nonuniformity in local electron density, and hence the resonance.PACS numbers: 73.20.–r, 67.60.–g     

Investigation of Microwave Absorption of Surface-State Electrons on Liquid 3He

We report on the experimental study of the resonance microwave absorption of surface-state electrons (SSE) on liquid ³He. The absorption is detected as a variation of the microwave power passing through the experimental cell, or as a resonance-induced change in the electron conductivity. In the latter method a decrease of the conductivity is observed, which points out on the possibility of substantial heating of the electrons by the absorbed microwave power. In a vapor-atom scattering regime the temperature dependence of the linewidth agrees well with the theoretical model, and the absolute value of the measured linewidth is about twice larger than the theoretical one. At very high microwave power the side band absorption peaks are observed.     

Scattering Properties of Spin-Polarized Liquid 3He

In this paper, the scattering properties of spin-polarized liquid ³He (³He^??) are studied using the Galitskii-Migdal-Feynman (GMF) formalism. The effective cross sections??including the total, diffusion and viscosity cross sections??are calculated. It is found that these cross sections tend to decrease with increasing spin polarization f. The S-wave scattering cross section is the most significant partial wave contributing to the total cross section at low energy. This contribution decreases with increasing f; whereas the contribution of the higher angular-momentum waves, especially the P-wave, increases with increasing f. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the cross sections at low temperatures. For comparison purposes, the effective cross sections in the Brueckner-Bethe-Goldstone (BBG) formalism are calculated. These remain zero up to the Fermi momentum, beyond which they are equal to those given by the GMF formalism. We deduce that hole-hole scattering plays an essential role in the scattering properties.     

Surface Magnetism of Liquid 3He on 4He Pre-plated Graphite

No Heading The nuclear susceptibility of liquid ³He in Grafoil pre-plated by 2.5 and 3.5 layers of ⁴He has been studied with a cw NMR method at temperatures between 0.7 and 100 mK under various liquid pressures. The 3.5 layers of ⁴He pre-plating suppresses a formation of the first and second solid ³He layer, eliminating most of surface magnetization at saturated vapor pressure. However, with increasing liquid pressure, a magnetization obeying a Curie Weiss law gradually grows in the same way as in the previous experiment for pure liquid ³He. This magnetization, induced by pressurization, is attributable to the formation of solid ³He layer above the pre-plated ⁴He.PACS numbers: 67.80.Jd, 75.70 Cn, 67.70.+n.     

Fermi Liquid Properties of 3He-4He Mixtures

We calculate microscopically the spectrum of a ³ He impurity atom moving in ⁴ He, determine the Fermi-Liquid interaction between ³ He atoms and then calculate the pressure and concentration dependence of the effective mass and the magnetic susceptibility. The long wavelength limit of the spectrum defines the hydrodynamic effective mass. When k 1.7Å^–1 the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. The calculations of the Fermi-Liquid interaction are based on correlated basis functions (CBF); the relevant matrix elements are determined by the Fermi hypernetted-chain theory. Our theoretical effective masses agree well with recent measurements, ^1,2 but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured ³ Landau parameter F ₀ ^a .     

Ultra-Low Temperature Magnetic Properties of Liquid 3He Films

We report measurements of the nuclear magnetization of submonolayer liquid ³ He films adsorbed on a graphite substrate (Papyex) preplated by a monolayer of ⁴ He. In the submilliKelvin temperature range we observe a substantial enhancement of the nuclear magnetization with respect to the degenerate Fermi Liquid value. The unusual temperature dependence of this new contribution to the liquid ³ He film magnetization agrees well with that expected from the theory of weak disorder in two-dimensional (2D) correlated Fermion systems. The effects of disorder and reduced dimensionality suppress the superfluid transition at least to below 180 K.     

Theory of the Surface Tension Maximum of Liquid 3He

Recently Matsumoto et al. performed very precise measurements of the surface tension of liquid ³He, (T), at low temperatures and found that (T) exhibits a small maximum at about 100 mK. Existing theories are unable to explain this anomaly. On the basis of a local approximation for the entropy in which the Fermi liquid effect is included, we can evaluate the variation of (T), (T)=(T)–(0), as a function of T and of the number density (or the interaction strength). It is found that (T) consists of two terms; a T² term and T⁴ ln T term. We predict that, for the density of real liquid ³He, exhibits a tiny minimum and a small but relatively larger maximum. This prediction explains qualitatively and quantitatively all salient features of the observed (T).     

Surface Tension of Liquid 3He Under 8 T Magnetic Field

Surface tension of liquid ³ He was measured using the capillary rise method. A 8 T magnetic field was applied to study the magnetic response. We found that the temperature dependence of the surface tension in 8 T magnetic field was almost the same as that found in zero field by Suzuki et al [Europhysics Letters 5, 333 (1988)]. The surface tension stayed almost constant below 120 mK, whereas it behaved as T ² in the higher temperature region. The surface tension difference at 8 T field was measured at several temperatures between 30 mK and 100 mK; it decreased by about 350 ppm and no significant temperature dependence was observed within the experimental error. The susceptibility near the free surface was found to decrease compared to the bulk.     

Surface Superconducting State of Heavy-Fermion Superconductor CeIrIn5 Probed by CeIrIn5-Ag Junctions

The CeIrIn₅-Ag junctions of about 2×10^–9 cm^–2 area have been made using microfabrication techniques, and the surface superconducting state of CeIrIn₅, which has two characteristic temperatures T ₀ and T _c, has been investigated, where T ₀ and T _c are the transition temperature to zero-resistivity state and the bulk, thermodynamic transition temperature, respectively. The temperature, below which superconducting anomalies are observed, varies from junction to junction, and yet it is always well above T _c=0.4 K. This result, together with no indication of transition at T _c, suggests that at least the surface of CeIrIn₅ is in the superconducting state above T _c. The data on the critical current I _c in superconducting anomalies point to the possibility to define a local transition temperature for each junction.     

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.     

Acoustic Properties of Normal Liquid 3He in 98% Aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation and sound velocity measurements in the normal state of liquid ³He in 98% aerogel. The absolute attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, 2 mK<T<200 mK. Due to the scattering off the aerogel, the sound excitation remains as first sound over the entire range of temperatures and pressures studied. Unlike pure liquid ³He, the sound attenuation shows a minimum around 30–50 mK, depending on the pressure. We report our results of absolute sound attenuation measurements at 29 bars of sample pressure.     

Electrons and Cavitation in Liquid Helium-3

We report preliminary results from a study of the effect of electrons on cav-itation in liquid ³ He. We have measured the negative pressure at which electron bubbles explode. The results are in good agreement with theoretical expectations.     

Mobility of Electrons at Liquid Helium Surface under Overheating

Mobility of surface electrons (SE) on liquid helium at low temperatures (T≃0.52 K) is studied as a function of the driving electric field E _∥ in the range 1–25 mV/cm. The experimental conditions correspond approximately to effective electron temperatures T _e ≃1–12 K. The measurements are performed for SE with the surface electron density n _s =1.46×10⁸ cm⁻² at different holding electric fields E _⊥ =200–1400 V/cm. The mobility is observed to be an increasing function of the driving field. The function depends strongly on the holding electric field applied. The experimental results are in reasonable agreement with theoretical curves calculated using the force-balance equation method expressing the mobility in terms of the dynamical structure factor of SE.     

Trapping Electrons in Electrostatic Traps over the Surface of 4He

We have observed trapping of electrons in an electrostatic trap formed over the surface of liquid ⁴He. These electrons are detected by a Single Electron Transistor located at the center of the trap. We can trap any desired number of electrons between 1 and ∼30. By repeatedly (∼10³–10⁴ times) putting a single electron into the trap and lowering the electrostatic barrier of the trap, we can measure the effective temperature of the electron and the time of its thermalisation after heating up by incoherent radiation. E. Rousseau’s present address: Ecole Centrale, Paris, France. D. Ponarine’s present address: Chemistry Dept., North Carolina State Univ., Raleigh, NC 27695, USA.     

Thermodynamic Magnetization of Liquid 3He

We have measured the absolute thermodynamic magnetization of ³ He in all of its liquid phases while using a new calibration technique which relies on the nuclear paramagnetism over the entire temperature range below 1 K as measured by Ramm, et al. We have directly measured the temperature dependence separately of the nuclear paramagnetism via NMR and of the total magnetism via our free-surface modulation technique. We report substantial agreement with Ramm, et al. In consequence, we find that the diamagnetism of liquid ³ He is significantly smaller than expected theoretically, a condensed matter effect not seen previously. We have also remeasured the magnitude of the magnetization discontinuity at the superfluid A-B transition and find close agreement at saturated vapor pressure with NMR-deduced values from Scholz.     

Effect of Spin-dependent Correlation Functions on the Ground State Energy of Liquid 3He

The energy of normal liquid ³ He is obtained using the lowest order constrained variational (LOCV) method with the spin-dependent two-body correlation functions. A functional minimization was performed with respect to both spin singlet and spin triplet correlation functions. It is shown that this dependence increases the binding energy of liquid ³ He by about 8% with respect to spin-independent case and it has the same magnitude as our previous work with angular momentum-dependent correlation functions. The S=0 state has completely different behavior with respect to S=1 state. It is also found that the main contribution from potential energy comes from S=1 state and the effect of S=0 state is almost repulsive. We conclude that this spin-dependet effect can be measured experimentaly. The effective interactions and two-body correlation functions in different spin states are being discussed.     

Magnetic Susceptibility of Liquid 3He

We report measurements of the magnetic susceptibility of liquid ³ He at saturated vapor pressure in the normal state from the superfluid transition temperature up to 1 K. Our results are comparable to those of Ramm, et al.¹ at temperatures above 200 mK, but are systematically higher as T0. We conclude that the zero-temperature limiting susceptibility is approximately 5.9% larger than reported by Ramm, et al. Consequently, the discrepancy in the liquid's diamagnetism between values expected theoretically and our experimentally measured results is essentially eliminated.