Normal Fluid Density Research Articles

Vortex properties of a resonant superfluid

The properties of a vortex in a rotating superfluid Fermi gas are studied in the unitary limit. A phenomenological approach based on Ginzburg-Landau theory is developed for this purpose. The density profiles, including those of the normal fluid and superfluid, are obtained at various temperatures and rotation frequencies. The superfluid and normal fluid densities can be identified from the angular momentum density. The total free energy and angular momentum of the vortex are also obtained.

Decay of Pure Quantum Turbulence in SuperfluidHe3−B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.

Exact summation of vertex corrections to the penetration depth ind-wave superconductors

A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this result to be relevant to the $ab$-plane penetration depth in high-purity single crystals of underdoped YBCO.

On superflow in solidHe4

Kim and Chan have recently observed Non-Classical Rotational Inertia (NCRI) for solid $^4$He in Vycor glass, gold film, and bulk. Their low $T$ value of the superfluid fraction, $\rho_{s}/\rho\approx0.015$, is consistent with what is known of the atomic delocalization in this quantum solid. By including a lattice mass density $\rho_{L}$ distinct from the normal fluid density $\rho_{n}$, we argue that $\rho_{s}(T)\approx\rho_{s}(0)-\rho_{n}(T)$, and we develop a model for the normal fluid density $\rho_{n}$ with contributions from longitudinal phonons and ``defectons'' (which dominate). The Bose-Einstein Condensation (BEC) and macroscopic phase inferred from NCRI implies quantum vortex lines and quantum vortex rings, which may explain the unusually low critical velocity and certain hysteretic phenomena.

Optical conductivity of a superfluid density wave

We present a calculation of the low-frequency optical conductivity of a superconductor in the presence of quenched inhomogeneity in both the superfluid and normal fluid densities. We find that inhomogeneity in the superfluid density displaces spectral weight from the condensate to a frequency range that depends critically on the spatial correlation of normal and superfluid density fluctuations.

Superfluid [formula omitted] in the zero-temperature limit

The properties of superfluid 3 He in the regime of negligible normal fluid density is both of fundamental interest and yet very simple. The behaviour is dominated by the properties of the condensate, and several phenomena, otherwise masked by the normal fluid, become observable. We discuss the techniques needed to cool the superfluid to T⪡0.1 T c . We discuss some examples of the unique low temperature behaviour; quasi-persistent spin precession, possible orbital precession, imaging turbulence, nucleation and the phase diagram in aerogel.

Models for enhanced absorption in inhomogeneous superconductors

We discuss the low-frequency absorption arising from quenched inhomogeneity in the superfluid density rho_s of a model superconductor. Such inhomogeneities may arise in a high-T_c superconductor from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. Using standard classical methods for treating randomly inhomogeneous media, we show that both mechanisms produce additional absorption at finite frequencies. For a two-fluid model with weak mean-square fluctuations <(d rho_s)^2 > in rho_s and a frequency-independent quasiparticle conductivity, the extra absorption has oscillator strength proportional to the quantity <(d rho_s)^2>/rho_s, as observed in some experiments. Similar behavior is found in a two-fluid model with anticorrelated fluctuations in the superfluid and normal fluid densities. The extra absorption typically occurs as a Lorentzian centered at zero frequency. We present simple model calculations for this extra absorption under conditions of both weak and strong fluctuations. The relation between our results and other model calculations is briefly discussed.

Path integral calculation of superfluid [formula omitted] vortex core structure

A structure of a superfluid 4 He vortex core is studied with a path integral Monte Carlo method. The distribution of superfluid and normal fluid densities around the vortex core is obtained. The total particle density decreases in the vortex core region. The radius of the core is nearly equal to the particle diameter. The vortex core is filled with normal fluid in the temperature region T≃ T λ . In the low temperature region, the normal fluid component of a vortex core decreases remarkably. Consequently the number of particle density of a vortex core region becomes extremely small.

Low-frequency optical conductivity in inhomogeneousd-wave superconductors

Motivated by the recent optical conductivity experiments on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ films, we examine the possible origin of low-frequency dissipation in the superconducting state. In the presence of spatial inhomogeneity of the local phase stiffness ${\ensuremath{\rho}}_{s},$ it is shown that some spectral weight is removed from $\ensuremath{\omega}=0$ to finite frequencies and contribute to dissipation. A case where both ${\ensuremath{\rho}}_{s}$ and the local normal-fluid density are inhomogeneous is also considered. We find an enhanced dissipation at low frequency if the two variations are anticorrelated.

Estimate of the gap parameter for superfluid3Hein aerogel

We infer the magnitude of the superfluid gap for 3 He in aerogel from measurements of the normal fluid density as a function of temperature. We compute the effective Yosida function for two different aerogel samples over a range of pressures. We find that the suppression factor of the zero-temperature superfluid gap, scaled by k B T c , ranges from 0.5 to 0.8 as compared to the pressure-dependent weak-coupling plus gap, with the scaling factor dependent on the suppression of T c relative to the bulk value.

The levels of soluble amyloid beta in different high density lipoprotein subfractions distinguish Alzheimer's and normal aging cerebrospinal fluid: implication for brain cholesterol pathology?

Several previous studies reported the association of the soluble form of amyloid β (sAβ) protein, a major constituent of amyloid deposits in Alzheimer's disease (AD), with normal blood, cerebrospinal fluid (CSF) and central nervous system high density lipoproteins (HDLs). The present report aimed to elucidate the pattern of sAβ and apolipoprotein (apo) distribution in AD CSF-HDL subfractions. We studied AD CSF-HDL subfractions by SDS/PAGE and immunoblot analysis after CSF fractionation via density flotation ultracentrifugation. AD CSF was characterized by (i) increased sAβ and apo content of the HDL 1, and (ii) sAβ association with apoE and apoJ in HDL 2, HDL 3 and very high density lipoproteins. The finding supports our proposed hypothesis that upregulation of brain cholesterol dynamics is a fundamental event in the pathophysiology of AD and that sAβ binding to apo and lipid may have important structure-functional consequences.

Vortex dynamics in the two-fluid model

We have used two-fluid dynamics to study the discrepancy between the work of Thouless, Ao and Niu (TAN) and that of Iordanskii. In TAN no transverse force on a vortex due to normal fluid flow was found, whereas the earlier work found a transverse force proportional to normal fluid velocity u and normal fluid density. We have linearized the time-independent two-fluid equations about the exact solution for a vortex, and find three solutions which are important in the region far from the vortex. Uniform superfluid flow gives rise to the usual superfluid Magnus force. Uniform normal fluid flow gives rise to no forces in the linear region, but does not satisfy reasonable boundary conditions at short distances. A logarithmically increasing normal fluid flow gives a viscous force. As in classical hydrodynamics, and as in the early work of Hall and Vinen, this logarithmic increase must be cut off by nonlinear effects at large distances; this gives a viscous force proportional to u/ln(u), and a transverse contribution which goes like u/(ln u)^2, even in the absence of an explicit Iordanskii force. In the limit u goes to zero the TAN result is obtained, but at nonzero u there are important corrections that were not found in TAN. We argue that the Magnus force in a superfluid at nonzero temperature is an example of a topological relation for which finite-size corrections may be large.

Superfluid and normal-fluid density in the cuprate superconductors

As carriers are introduced into the cuprates (by doping the insulating “parent” compounds) spectral weight appears in the optical spectrum at photon energies below the charge-transfer gap. This spectral weight increases as the doping level increases. Magnetic penetration depth measurements have shown a good correlation between superfluid density and superconducting transition temperature in the underdoped-to-optimally-doped part of the phase diagram. Optical measurements allow independent determination of the total doping-induced spectral weight and the superfluid density. These measurements, made on cuprates with transition temperatures from 40 to 110 K, find that in optimally doped materials only about 20% of the doping-induced spectral weight joins the superfluid. The rest remains in finite-frequency, midinfrared absorption. In underdoped materials, the superfluid fraction is even smaller. This result implies extremely strong coupling for these superconductors.

Formation and decay of vorticity in coupled helium-II flow

The kinematic viscosity of helium II below the transition temperature can be defined with the total density of the liquid or the normal-fluid density alone. These two definitions have very different temperature dependences. In this work we considered the decay of Gaussian distributions of vorticity in helium II using the two fluid Hall-Vinen-Bekharevich-Khalatnikov equations. Our calculation shows that in these two-dimensional axisymmetric flows both fluids decay together with a viscous time scale set by the total fluid density and not by the normal-fluid density alone. We also considered the spin-up of each fluid and observed that for all initial conditions considered both fluids tend towards a matched vorticity state.

Superfluid and normal-fluid densities in the high- Tc superconductors

In clean metallic superconductors, 100% of the mobile carriers participate in the condensate, so that the London penetration depth (which measures the electromagnetic screening by the superconductor) indicates charge densities comparable to those inferred from the free-carrier plasma frequency. In the cuprates, this is not the case, even though penetration depth measurements have shown a good correlation between superfluid density and superconducting transition temperature in the underdoped-to-optimally-doped part of the phase diagram. Optical measurements, which permit independent determination of the total doping-induced spectral weight and the superfluid density, show that in optimally doped materials only about 20% of the doping-induced spectral weight joins the superfluid. The rest remains in finite-frequency, midinfrared absorption. In underdoped materials, the superfluid fraction is even smaller. This result implies extremely strong coupling for these superconductors.

Classical character of turbulence in a quantum liquid

A theoretical discussion is presented of recent experiments in which it has been shown that turbulence in the superfluid phase of liquid ${}^{4}\mathrm{He}$ can be very similar in its characteristics to that in a conventional fluid; particular attention is focused on the work of Stalp, Skrbek, and Donnelly [Phys Rev. Lett. 82, 4831 (1999)]. It is argued that on length scales significantly greater than both the spacing between the quantized vortex lines in the turbulent superfluid component and the scale on which viscous dissipation occurs in the normal fluid, the two fluids are likely to be coupled together and to behave like a conventional fluid. On smaller length scales account must be taken of dissipation, due to viscosity in the normal fluid, frictional interaction between the vortex lines and the normal fluid, and the radiation of sound from the vortex lines; it is shown that the rate of dissipation is likely to be given by an expression that is similar to that in a conventional fluid but with some important differences. Emphasis is placed on the need for experiments at a very low temperature in which the complicating effects of the normal fluid are either absent or easily taken into account, and the paper includes some theoretical discussion of the decay of superfluid turbulence in the absence of normal fluid and when the normal fluid density is very low. This last discussion is inspired by the ideas of Svistunov [Phys. Rev. B 52, 3647 (1995)].

Persistent Coherent Spin Precession in SuperfluidH3e−BDriven by Off-Resonant Excitation

In superfluid ${}^{3}\mathrm{He}\ensuremath{-}B$ under conditions of negligible normal fluid density we are able to trap a domain of coherent spin precession away from the destructive influence of boundaries. After the domain is generated by an NMR pulse, the free spin precession may continue for several minutes. Remarkably, we find that these precessing domains may also be generated by cw excitation but only at a frequency considerably higher than that of the precession. We believe that this behavior may indicate that at our temperatures the precessing spin is able to stimulate the orbital moment into sympathetic precession.

The Observed Properties of Liquid Helium at the Saturated Vapor Pressure

The equilibrium and transport properties of liquid He4 are deduced from experimental observations at the saturated vapor pressure. In each case, the bibliography lists all known measurements. Quantities reported here include density, thermal expansion coefficient, dielectric constant, superfluid and normal fluid densities, first, second, third, and fourth sound velocities, specific heat, enthalpy, entropy, surface tension, ion mobilities, mutual friction, viscosity and kinematic viscosity, dispersion curve, structure factor, thermal conductivity, latent heat, saturated vapor pressure, thermal diffusivity and Prandtl number of helium I, and displacement length and vortex core parameter in helium II.

Superfluid and normal fluid density in high- Tc superconductors

The electronic properties of the cuprate superconductors have been studied by measuring the reflectance over the frequency range from the far-infrared to the near-ultraviolet(roughly, 10 meV-5 eV). There is an interesting behavior in both the normal state and the superconducting state. In the normal state, there is the well-known non-Drude distribution of the doping-induced spectral weight. In the superconducting state, the spectral weight of the superconducting condensate correlates with T c in a variety of materials. Remarkably, in optimally doped superconductors, only about 20% of the doping-induced carriers joins the superfluid; the rest of the spectral weight remains at finite frequencies.

Superfluid bosons and flux liquids: disorder, thermal fluctuations, and finite-size effects

The influence of different types of disorder (both uncorrelated and correlated) on the superfluid properties of a weakly interacting or dilute Bose gas, as well as on the corresponding quantities for flux line liquids in high-temperature superconductors at low magnetic fields are reviewed, investigated and compared. We exploit the formal analogy between superfluid bosons and the statistical mechanics of directed lines, and explore the influence of the different “imaginary time” boundary conditions appropriate for a flux line liquid. For superfluids, we discuss the density and momentum correlations, the condensate fraction, and the normal-fluid density as function of temperature for two- and three-dimensional systems subject to a space- and time-dependent random potential as well as conventional point-, line-, and plane-like defects. In the case of vortex liquids subject to point disorder, twin boundaries, screw dislocations, and various configurations of columnar damage tracks, we calculate the corresponding quantities, namely, density and tilt correlations, the “boson” order parameter, and the tilt modulus. The finite-size corrections due to periodic vs. open “imaginary time” boundary conditions differ in interesting and important ways. Experimental implications for vortex lines are described briefly.