Theory of rough surface effects on the anisotropic BCS states

We present a Green's function theory of the rough surface effects on the anisotropic BCS states using the formulation developed in the randomly rippled wall model. It is shown that the randomly rippled wall formulation is general enough to treat rough surface effects from the specular limit to the diffusive limit. We propose a statistical wall configuration such that gives the diffusive limit in the normal state. Within the weak coupling theory, we give a formal solution of the quasi-classical Green's function in a slab geometry and in a semi-infinite geometry with arbitrarily rough surfaces. The formal solution already satisfies the boundary condition. In the diffusive limit, the present theory correctly recovers the linearized gap equation obtained by Kjäldman et al. for the p-wave state in a slab geometry.     

Perturbative Study of Strong Coupling Correction in Superfluid 3He in Aerogel

The AB transition curve of superfluid ³He in aerogel often shows a positive slope dT _AB(P)/dP>0 over the measured pressures P, contrary to that of the bulk liquid. Bearing this behavior in mind suggestive of a unexpectedly strong reduction of the strong coupling (SC) correction due to the aerogel, we examine impurity effects on the SC contributions to the quartic term of the Ginzburg-Landau (GL) functional. Our analysis perturbative both in the repulsive interaction and the impurity scattering suggests that, in agreement with experimental data, the impurity scattering weakens the relative stability of the ABM state to the BW state and notably reduces the SC correction for the ABM phase.     

The paramagnon model and some properties of superfluid 3He

The paramagnon model for the BCS-type state of superfluid ³He is applied to calculate the following properties in the ABM and BW states: the pressure dependence of the initial slope of the normalized superfluid mass density vs. 1 – T/T _c; the pressure dependence of the normalized specific heat jump at T _c; and the temperature dependence of the superfluid mass density at P = 20.7 and 27.6 bar. We also calculate the temperature dependence of the normalized nuclear spin susceptibility in the BW state. We compare our results with the experimental data on the A and B phases of superfluid ³He.Supported in part by grant No. A4630 of the National Research Council of Canada.For a preliminary version of this work see Ref. 1.On leave from the Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo, Japan.     

Effect of Rough Walls on Transport in Mesoscopic 3He Films

The interplay of bulk and boundary scattering is explored in a regime where quantum size effects modify mesoscopic transport in a degenerate Fermi liquid film of ³He on a rough surface. We discuss mass transport and the momentum relaxation time of the film in a torsional oscillator geometry within the framework of a quasiclassical theory that includes the experimentally determined power spectrum of the rough surface. The theory explains the anomalous temperature dependence of the relaxation rate observed experimentally. We model further studies on ³He confined in nanofluidic sample chambers with lithographically defined surface roughness. The improved understanding of surface roughness scattering can be extended to the analogous system of electrons in metals and suggests routes to improve the conductivity of thin metallic films.     

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.     

A–BTransition of Superfluid 3He with a Film Geometry

We have performedcwNMR experiments on superfluid ³ He confined to a parallel-plate geometry with a m scale spacing for a wide pressure range. A static field was applied parallel or perpendicular to the plate surface. The spectra of two absorption signals, a main and a satellite, have been observed below the superfluid transition temperature in a parallel field. As the temperature decreased, the main signal decreased with shifts to higher frequencies, and the satellite grew with shifts to much higher frequencies. From the temperature dependence of these signals and the result in the perpendicular field, it is confirmed that the main signal and the satellite correspond to the A phase signal (ABM state) and the B phase signal (BW state), respectively. The temperature dependence of the two signals indicates that a phase transition from the A phase to the B phase occurs with decreasing temperature. By analyzing these signals, we determine A–B transition temperatures experimentaly. TheA–Btransition temperature normalized by the superfluid transition temperature is 0.95 at 20 bar, and decreased further to 0.70 at 0 bar for a thickness of 0.88 m for pure ³ He. The values of T_AB/T_C were slightly elevated when covering the surface with 4.5 layers of ⁴ He film, which suggests that this transition is also influenced by the surface condition.     

The superflow state of 3He-B at a diffusive wall. Quasiclassical calculations

We report on first computations considering effects of a rough wall on the counterflow state in superfluid ³He-B for high flow velocities. Using the quasiclassical Green's-function formalism supplemented by the boundary conditions for a diffusive wall, we calculate the order-parameter field and the supercurrent near a container wall for various pressures and temperatures. One of our results is that the current density at the wall as a function of the flow has a maximum at the velocity which is about half of the pair breaking velocity.     

Comparison of geometric optics approximation and integral method for reflection and transmission from microgeometrical dielectric surfaces

The effects of incidence angle, geometrical shape, and optical properties of dielectric rough surfaces on reflectivity and transmissivity are discussed. Radiative properties for various surface geometries are calculated. Since the integral method is computationally expensive, a geometric optics approximation is developed. The regions of validity of the approximation compared with the integral method are quantified. Curves are presented that show these radiative properties versus the correlation length at incidence angle for a fixed rms deviation of the surface. The surface geometry, incidence angle, multiple scattering, shadowing effects, and dielectric permittivity contributions to the domains of validity of the approximation method are discussed for both TE and TM polarizations.     

Transport in Fermi Liquids Confined by Rough Walls

I present theoretical calculations of the thermal conductivity of Fermi liquid \(^3\) He confined to a slab of thickness of order \(\sim \) 100 nm. The effect of the roughness of the confining surfaces is included directly in terms of the surface roughness power spectrum which may be determined experimentally. Transport at low temperatures is limited by scattering off rough surfaces and evolves into the known high-temperature limit in bulk through an anomalous regime in which both inelastic quasiparticle scattering and elastic scattering off the rough surface coexist. I show preliminary calculations for the coefficients of thermal conductivity. These studies are applicable in the context of electrical transport in metal nanowires as well as experiments that probe the superfluid phase diagram of liquid \(^3\) He in a slab geometry.     

Theoretical modeling of a diode-pumped Nd:YAG laser with a solid nonfocusing pump light collector

We report theoretical modeling for a diode-side-pumped Nd:YAG laser in which the laser rod is fixed in a solid nonfocusing (prismatic) light collector. The geometry provides for pumping the rod from four sides, which gives a relatively uniform gain profile across the transverse section of the rod and enables a high tolerance of the laser output to resonator and pump diode misalignment. The numerical model is developed to illustrate how the pumping uniformity and the transfer efficiency are affected when changes in the collector and lasing materials are made. We use small-signal gain measurements to test the predictions of the model and to examine the extent to which surface scattering from the rough rod barrel further spatially averages the deposited pump energy. The effects of the different refractive indices of the rod, collector, and fixant and the absorption properties of the laser material on optical transfer efficiencies are discussed.     

The influence off-wave pairing fluctuations on sound propagation in superfluid3He-A

The theory of sound propagation in pair-correlated Fermi liquids developed previously by Wölfle, with additionalf-wave pairing fluctuations, is applied to the ABM state. Expressions for the anisotropic sound absorption and velocity at arbitrary temperature and frequency in the collisionless limit are derived. Thef-wave pairing fluctuations give a large effect on the normal-flapping mode frequency at low temperatures. The corresponding shift in the sound attenuation peak of this collective mode provides a sensitive probe of thef-wave pair coupling constantg ₃. There is also a pronounced effect on the super-flapping mode attenuation peak, which becomes well defined whenf-wave pairing fluctuations are considered.     

Density and temperature dependence of the momentum distribution in liquid helium 4

Deep inelastic neutron scattering measurements on liquid⁴He have been carried out for temperatures from 0.35 K to 4.2 K and densities from 0.125 to 0.200g/cm³ at a momentum transfer of 23 Å^–1. These measurements are at large enough momentum transfer that deviations from the Impulse Approximation are accurately described by current theories and information on the single particle momentum distribution may be extracted from the measured scattering. The scattering exhibits non-Gausian behavior in both the normal liquid and superfluid phases. A distinct change in the scattering, marked by a reduction in the width and increased deviations from the classical Gaussian shape, occurs at the suerfluid transition. We present a comparison of our experimental results with recent calculations at a variety of temperatures and densities and show that theory and experiment are in excellent agreement. We also present model scattering functions, obtained by correcting for instrumental resolution and final state effects, that represent the scattering in the IA limit. Finally, we present values for the average kinetic energy and the Bose condensate fraction over a broad range densities and temperatures.     

An experimental investigation of YBa2Cu3O7 films at millimeter-wave frequencies

We have measured the millimeter-wave (100 GHz) surface resistance of high-quality laserdeposited YBa₂Cu₃O₇ films on SrTiO₃ and LaA10₃ substrates. Due to finite film thickness, radiation losses are important in the normal state and in the superconducting state nearT _c. These effects are calculated andR _s characteristic of the ohmics losses in the film are extracted from the data. The surface resistanceR _s drops rapidly atT _c, and a detailed comparison with calculations which include finite mean free path effects suggests a gap which exceeds the weak coupling BCS limit.     

Radiative Properties of Gold Surfaces with One-Dimensional Microscale Gaussian Random Roughness

The radiative properties of engineering surfaces with microscale surface textures depend on the incident wavelength, optical properties, and temperature as well as the topography of the reflective surface. In the case of slightly rough surfaces, the traditional Kirchhoff theory on rough surface scattering may be applicable. In this study, a direct numerical solution of Maxwell’s equations was developed to understand scattering from weakly to very rough surfaces. The method is the finite-difference time-domain method. The problem of interest is a set of gold surfaces with Gaussian random roughness distributions. Highly accurate experimental data are available from the earlier work of Knotts and O’Donnell in 1994. Due to the negative real component of the complex dielectric constant at the infrared light source wavelengths of 1.152 and 3.392 μm, the convoluted integral was used to convert the frequency domain electrical properties to time-domain properties in order to obtain convergent solutions. The bi-directional reflectances for both normal and parallel polarizations were obtained and compared with experimental data. The predicted values and experimental results are in good agreement. The highly specular peak in the reflectivity was reproduced in the numerical simulations, and the increase of the parallel polarization bi-directional reflectance was found to be due to the effect of a variation in the optical constant from 1.152 to 3.392 μm.     

Mechanism of the anisotropic distribution of molecules freely moving in a channel with rough walls

A mechanism of the anisotropic distribution of molecules with respect to their directions of motion in a channel with rough walls is proposed. Based on a solution of the kinetic equation with a model collision integral and with allowance for the multiple scattering of gas molecules from the rough channel walls, it is shown that a flow driven by pressure gradient is governed by the Fick’s law with an effective diffusion coefficient determined by the geometry of surface inhomogeneities.     

The Coherent Scattering Cross-section of a Slightly Rough Sphere

In the case of scalar waves and impenetrable material, the coherent scattering cross-section of a nearly spherical particle is calculated, where the surface irregularities are described statistically by a correlation function. The results are valid up to the second order of hk (k is the wavenumber,h² the mean-square deviation from a smooth sphere), but for any value of the size parameter f = kR₀ (RR₀ is the radius of the sphere). The limits for small particles (f 1) and for large particles (f d 1) are derived, and it is shown that for f d 1 the scattering pattern outside the diffraction peak coincides with the result obtained by means of the Rayleigh-Rice approach, i.e. by applying scattering results for planar rough areas locally to the curved surface of the scattering body.     

Perturbed gap functions in superfluid 3He

New forms of the Balian-Werthamer (BW) and of the Anderson-Brinkman-Morel (ABM) gap solutions for superfluid ³He are found in the presence of perturbations. Using the perturbed form of the BW solution, a discrepancy is found between the static and dynamic magnetic susceptibilities, which is shown to be in reasonable agreement with the experimental measurements of Sager and Webb. A self-consistent diagrammatic Green's function approach is used.     

Spin-independent transport parameters for superfluid3He-B

The scalar kinetic equation for Bogoliubov quasiparticles in the B phase of superfluid³He is discussed and the collision integral is represented in a compact form. For the cases of shear and second viscosity and diffusive thermal conductivity the problem is reduced to solving one-dimensional integral equations. The quasiparticle interaction enters via weighted angular averages of the normal state scattering amplitude. The effect of strong coupling renormalization of the gap function is accounted for. The transport coefficients are exactly related to relaxation parameters that describe how the system tends toward local equilibrium. For low temperatures the transport parameters are evaluated exactly, including corrections of orderT/T _c. The results are compared with those of a previous paper in which an approximate form of the collision operator was used, as well as with results of a variational approach and with recent experimental data.