Superfluid Component Research Articles

Self-Consistent Two-Gap Approach in Studying Multi-Band Superconductivity of NdFeAsO0.65F0.35

High-quality single crystals of NdFeAsO$_{0.65}$F$_{0.35}$ (the transition temperature $T_{\rm c} \simeq 30.6$~K) were studied in zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($\mu$SR) experiments. An upturn in muon-spin depolarization rate at $T\lesssim 3$~K was observed in ZF-$\mu$SR measurements and it was associated with the onset of ordering of Nd electronic moments. Measurements of the magnetic field penetration depth ($\lambda$) were performed in the TF geometry. By applying the external magnetic field $B_{\rm ex}$ parallel to the crystallographic $c$-axis ($B_{\rm ex}\| c$) and parallel to the $ab$-plane ($B_{\rm ex}\| ab$), the temperature dependencies of the in-plane component ($\lambda_{ab}^{-2}$) and the combination of the in-plane and the out of plane components ($\lambda_{ab,c}^{-2}$) of the superfluid density were determined, respectively. The out-of-plane superfluid density component ($\lambda_{c}^{-2}$) was further obtained by combining the results of $B_{\rm ex} \| c$ and $B_{\rm ex} \| {ab}$ set of experiments. The temperature dependencies of $\lambda_{ab}^{-2}$, $\lambda_{ab,c}^{-2}$, and $\lambda_{c}^{-2}$ were analyzed within the framework of a self-consistent two-gap model despite of using the traditional $\alpha$-model. Interband coupling was taken into account, instead of assuming it to be zero as it stated in the $\alpha$-model. A relatively small value of the interband coupling constant $\Lambda_{12} \simeq 0.01$ was obtained, thus indicating that the energy bands in NdFeAsO$_{0.65}$F$_{0.35}$ are only weakly coupled. In spite of their small magnitude, the coupling between the bands leads to the single value of the superconducting transition temperature $T_{\rm c}$.

Condensation and superfluidity of [formula omitted] Bose gas

We perform the comprehensive comparison of properties of the condensate and superfluid densities for the N-component three-dimensional Bose gas with the symmetric inter- and intraspecies short-range interaction between particles. In particular, based on the large-N expansion approach for many-boson systems we obtain general expression for density of the superfluid component that at very low temperatures reproduce the well-know Landau’s formula and non-trivially includes the thermal fluctuations in the finite-temperature region, and compare it to the condensate density calculated previously. The numerically evaluated temperature dependencies are in a qualitatively good agreement with the results of Monte Carlo simulations.

Thermal counterflow and electrical activity of superfluid systems in a magnetic field

The thermal counterflow in superfluid helium placed in a magnetic field is shown to lead to the emergence of an electric field in the surrounding space. This effect is caused by the counterflow nature of thermal conductivity in superfluid systems: heat transfer in such systems is associated with the motion of the normal component, while the average mass flow transported by the normal component is compensated by the mass flow carried by the superfluid component. The local mass flow is nonzero. The effect occurs in case of stationary and non-stationary (second-sound) heat flows. The features of the effect for a number of samples with various geometries are considered. It was established that the magnitude of the arising electric field substantially depends on the shape of the sample containing helium and the direction of the magnetic field.

Thermodynamics of uncharged relativistic multifluids

The internal layers of neutron stars are expected to contain several superfluid components that can significantly affect their dynamics. The description of such objects should rely on hydrodynamic models in which it is possible to unambiguously assign the value of the thermodynamic variables from microscopic calculations of the properties of matter. In this work we consider the phenomenological approach to multifluids modelling championed by Carter and, studying the relaxation of the system towards equilibrium, we assign a precise thermodynamic interpretation to its variables. We show that in thermodynamic equilibrium the equation of state contains less state variables than those needed in the phenomenological model, implying the existence of a gauge freedom of the theory that can be used to simplify the hydrodynamic formulation in the non-dissipative limit. Once this is understood, it becomes easy to translate the different multifluid formalisms that have been proposed in the literature into Carter’s form. Finally, we show that the usual concepts of affinity and reaction coordinates, as they are introduced in chemistry, are not affected by the presence of superfluid currents. In an effort to make the concepts clear, the formalism is developed step-by-step from first principles, providing model examples and several applications of practical relevance for the study of superfluid neutron star interiors.

Hydrodynamical instabilities in the superfluid interior of neutron stars with background flows between the components

The interiors of mature neutron stars are expected to be superfluid. Superfluidity of matter on the microscopic scale can have a number of large scale, potentially observable consequences, as the superfluid component of the star can now flow relative to the `normal' component that is tracked by electromagnetic emission. The most spectacular of such phenomena are pulsar glitches, sudden spin-ups observed in many pulsars. A background flow of a normal-fluid component with respect to the superfluid is also known to lead to a number of instabilities in laboratory superfluids, possibly leading to turbulence and modifying the nature of the mutual friction coupling between the two fluids. In this paper we consider modes of oscillation in the crust and core of a superfluid neutron star, by conducting a plane-wave analysis. We explicitly account for a background flow between the two components (as would be expected in the presence of pinning) and the entrainment, and we consider both standard (Hall-Vinen) and isotropic (Gorter-Mellink) forms of the mutual friction. We find that for standard mutual friction there are families of unstable inertial and sound waves both in the case of a counter-flow along the superfluid vortex axis and for counterflow perpendicular to the vortex axis and find that entrainment leads to a quantitative difference between instabilities in the crust and core of the star. For isotropic mutual friction we find no unstable modes, and speculate that instabilities in a straight vortex array may be linked to glitching behaviour, which then ceases until the turbulence has decayed.

Symmetry-breaking vortex-lattice of a binary superfluid in a rotating bucket

We study spontaneous-symmetry-broken phase-separated vortex lattice in a weakly interacting uniform rapidly rotating binary Bose superfluid contained in a quasi-two-dimensional circular or square bucket. For the inter-species repulsion above a critical value, the two superfluid components separate and form a demixed phase with practically no overlap in the vortex lattices of the two components, which will permit an efficient experimental observation of such vortices and study their properties. In case of a circular bucket with equal intra-species energies of the two components, the two components separate into two non-overlapping semicircular domains for all frequencies of rotation Ω generating distinct demixed vortex lattices. In case of a binary Bose superfluid in both circular and square buckets, (a) the number of vortices increases linearly with Ω in agreement with a suggestion by Feynman, and (b) the rotational energy in the rotating frame decreases quadratically with Ω in agreement with a suggestion by Fetter.

Strong anisotropy of superfluid He4 counterflow turbulence

We report on a combined theoretical and numerical study of counterflow turbulence in superfluid $^{4}$He in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normal-fluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity.

Waves on the He-II Surface, Excited by a Heat Flux in the Bulk

The conditions for the occurrence of an instability generated on the free surface of superfluid He-II by a constant or variable heat flux Q in the He-II bulk have been experimentally studied. This instability is a quantum analog of the Kelvin–Helmholtz instability; it is accompanied by the occurrence of low-frequency oscillations on the surface and develops when the maximum velocity of the counterflow of the normal and superfluid components under the surface reaches the threshold value. It is shown that the large variance in the estimates (differing by a factor of 50–100) of the threshold heat flux Qthr (waves occur on the free He-II surface when the threshold is exceeded) in three series of experiments can be explained by different cross-sectional areas and numbers of channels in the lateral walls, through which the normal He-II component transfers heat from the immobile cell into the external helium bath (i.e., the significant difference in the boundary conditions). It is established that, switching on a heater, one can implement conditions in the liquid bulk that are sufficient for observing simultaneously the parametric Faraday instability and Kelvin–Helmholtz instability on the free He-II surface in a hermetically closed oscillating cell cooled from outside by superfluid He-II at a constant temperature.

Explosive Development of the Kelvin–Helmholtz Quantum Instability on the He-II Free Surface

We analyze nonlinear dynamics of the Kelvin–Helmholtz quantum instability of the He-II free surface, which evolves during counterpropagation of the normal and superfluid components of liquid helium. It is shown that in the vicinity of the linear stability threshold, the evolution of the boundary is described by the |ϕ|4 Klein–Gordon equation for the complex amplitude of the excited wave with cubic nonlinearity. It is important that for any ratio of the densities of the helium component, the nonlinearity plays a destabilizing role, accelerating the linear instability evolution of the boundary. The conditions for explosive growth of perturbations of the free surface are formulated using the integral inequality approach. Analogy between the Kelvin–Helmholtz quantum instability and electrohydrodynamic instability of the free surface of liquid helium charged by electrons is considered.

Leading order corrections to the free energy and phase separation in two-component Fermion systems

We study phase separation in a dilute two-component Fermi system with attractive interactions as a function of the coupling strength and the polarization or number density asymmetry between the two components. In weak and strong couplings with a finite number density asymmetry, phase separation is energetically more favorable. A heterogeneous phase containing a symmetric superfluid component and an asymmetric normal phase has lower energy than a homogeneous normal phase. We show that for a small number density asymmetry, taking into consideration the leading order corrections at order of the interaction parameter, phase separation is stable against the normal phase in the whole BCS range. We investigate the consequences of the consideration of the leading order corrections to the thermodynamic potentials of the normal and BCS phase on the Chandrasekhar–Clogston limit. We have also investigated the stability of a Bose–Fermi mixture in the far-BEC limit. We find that the molecular BEC is locally stable against an external magnetic field h, provided is smaller than the pairing gap .

Glitch time series and size distributions in eight prolific pulsars

Context. Glitches are rare spin-up events that punctuate the smooth slow-down of the rotation of pulsars. For the Vela pulsar and PSR J0537−6910, their large glitch sizes and the times between consecutive events have clear preferred scales (Gaussian distributions), contrary to the handful of other pulsars with enough glitches for such a study. Moreover, PSR J0537−6910 is the only pulsar that shows a strong positive correlation between the size of each glitch and the waiting time until the following one. Aims. We attempt to understand this behaviour through a detailed study of the distributions and correlations of glitch properties for the eight pulsars with at least ten detected glitches. Methods. We modelled the distributions of glitch sizes and of the times between consecutive glitches for the eight pulsars with at least ten detected events. We also looked for possible correlations between these parameters and used Monte Carlo simulations to explore two hypotheses that could explain why the correlation so clearly seen in PSR J0537−6910 is absent in other pulsars. Results. We confirm the above results for Vela and PSR J0537−6910, and verify that the latter is the only pulsar with a strong correlation between glitch size and waiting time to the following glitch. For the remaining six pulsars, the waiting time distributions are best fitted by exponentials, and the size distributions are best fitted by either power laws, exponentials, or log-normal functions. Some pulsars in the sample yield significant Pearson and Spearman coefficients (rp and rs) for the aforementioned correlation, confirming previous results. Moreover, for all except the Crab pulsar, both coefficients are positive. For each coefficient taken separately, the probability of this happening is 1/16. Our simulations show that the weaker correlations in pulsars other than PSR J0537−6910 cannot be due to missing glitches that are too small to be detected. We also tested the hypothesis that each pulsar may have two kinds of glitches, namely large, correlated ones and small, uncorrelated ones. The best results are obtained for the Vela pulsar, which exhibits a correlation with rp = 0.68 (p-value = 0.003) if its two smallest glitches are removed. The other pulsars are harder to accommodate under this hypothesis, but their glitches are not consistent with a pure uncorrelated population either. We also find that all pulsars in our sample, except the Crab pulsar, are consistent with the previously found constant ratio between glitch activity and spin-down rate, ν̇g/|ν̇| = 0.010±0.001, even though some of them have not shown any large glitches. Conclusions. To explain these results, we speculate except in the case of the Crab pulsar, that all glitches draw their angular momentum from a common reservoir (presumably a neutron superfluid component containing ≈1% of the star’s moment of inertia). However, two different trigger mechanisms could be active, a more deterministic one for larger glitches and a more random one for smaller ones.

Heat Transfer under Pulsed Heating in Superfluid Helium

An experimental study of the propagation of long (up to 1000 μs) heat pulses showed that for heat transfer, the formation of a vortex field near the heating medium on characteristic dimensions of the order of several millimetres is crucial, which blocks further backflow of the normal and superfluid components and development of turbulence in the entire waveguide volume.

Particle tracking velocimetry applied to thermal counterflow in superfluid He4 : Motion of the normal fluid at small heat fluxes

Thermal counterflow of normal and superfluid components in superfluid helium leads to a form of turbulence confined to the superfluid component. Contrary to usual assumptions, these vortex filaments are shown to induce a strongly nonuniform flow in the normal fluid, even at small flow velocities.

Formation of vortex turbulence by a heat current in superfluid helium in a long capillary

The propagation of long pulses of the second sound in superfluid helium was experimentally studied. The results of the experiments showed that at the propagation of heat currents of sufficiently high power the process of formation a vortex tangle begins near the heater. It leads to significantly reducing the counterflow of the normal and the superfluid components in helium and, consequently, thermal conductivity of superfluid helium.

Anti-glitches in the Ultraluminous Accreting Pulsar NGC 300 ULX-1 Observed with NICER

Abstract We present evidence for three spin-down glitches (or “anti-glitches”) in the ultraluminous accreting X-ray pulsar NGC 300 ULX-1, in timing observations made with the Neutron Star Interior Composition Explorer. Our timing analysis reveals three sudden spin-down events of magnitudes Δν = −23, −30, and −43 μHz (fractional amplitudes Δν/ν = −4.4, −5.5, and −7.7 × 10−4). We determined fully phase-coherent timing solutions through the first two glitches, giving us high confidence in their detection, while the third candidate glitch is somewhat less secure. These are larger in magnitude (and opposite in sign) than any known radio pulsar glitch. This may be caused by the prolonged rapid spin up of the pulsar, causing a sudden transfer of angular momentum between the superfluid and non-superfluid components of the star. We find no evidence for profile or spectral changes at the epochs of the glitches, supporting the conclusion that these are due to the same process as in normal pulsar glitches, but in reverse.

Temperature-driven dynamics of quantum liquids: Logarithmic nonlinearity, phase structure and rising force

We study a large class of strongly interacting condensate-like materials, which can be characterized by a normalizable complex-valued function. A quantum wave equation with logarithmic nonlinearity is known to describe such systems, at least in a leading-order approximation, wherein the nonlinear coupling is related to temperature. This equation can be mapped onto the flow equations of an inviscid barotropic fluid with intrinsic surface tension and capillarity; the fluid is shown to have a nontrivial phase structure controlled by its temperature. It is demonstrated that in the case of a varying nonlinear coupling an additional force occurs, which is parallel to a gradient of the coupling. The model predicts that the temperature difference creates a direction in space in which quantum liquids can flow, even against the force of gravity. We also present arguments explaining why superfluids, be it superfluid components of liquified cold gases or Cooper pairs inside superconductors, can affect closely positioned acceleration-measuring devices.

Thermodynamically equilibrium quantum vortices in superfluid liquids

The thermodynamic equilibrium is studied for a system of quantised vortices in superfluid liquids in the presence of a counterflow of the normal and superfluid components. The partition function is calculated, which takes into account various configurations of the vortex filaments, as well as the distribution of loops in length. The dependence of the density of vortex filaments on the applied counterflow velocity is discussed.

The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system

The inner crust of a mature neutron star is composed of an elastic lattice of neutron-rich nuclei penetrated by free neutrons. These neutrons can flow relative to the crust once the star cools below the superfluid transition temperature. In order to model the dynamics of this system, which is relevant for a range of problems from pulsar glitches to magnetar seismology and continuous gravitational-wave emission from rotating deformed neutron stars, we need to understand general relativistic Lagrangian perturbation theory for elastic matter coupled to a superfluid component. This paper develops the relevant formalism to the level required for astrophysical applications.

Superfluid density reduction and spin-imbalanced pairing in a fermionic superfluid due to dynamical boson exchange

We explore novel features of a nonrelativistic fermionic superfluid in which the pairing interaction includes a contribution from the exchange of a dynamical bosonic mode. We show that the dynamical boson exchange (DBE), which causes a retarded pairing interaction and thus violates the Galilean invariance of the fermion sector, generically leads to a quantum reduction of the superfluid density and hence a nonzero normal fraction even at zero temperature. For spin-singlet pairing, the DBE also leads to a nonvanishing spin susceptibility at zero temperature, providing a mechanism for the coexistence of pairing and magnetization. While these effects are negligible for weak pairing, they become sizable at strong pairing. For the double superfluidity in ultracold Fermi-Bose mixtures, the superfluid density reduction for the fermion sector induced by the DBE just gives rise to the Andreev-Bashkin drag effect, indicating a strong entrainment between the two superfluid components. The DBE may also provide a new source for the superfluid fraction reduction of neutron matter, which is crucial for models of neutron star glitches based on neutron superfluidity.

Spin Hall effect for polaritons in a transition metal dichalcogenide embedded in a microcavity

The spin Hall effect for polaritons (SHEP) in a transition metal dichalcogenides (TMDC) monolayer embedded in a microcavity is predicted. We demonstrate that two counterpropagating laser beams incident on a TMDC monolayer can deflect a superfluid polariton flow due to the generation the effective gauge vector and scalar potentials. The components of polariton conductivity tensor for both non-interacting polaritons without Bose-Einstein condensation (BEC)and for weakly-interacting Bose gas of polaritons in the presence of BEC and superfluidity are obtained. It is shown that the polariton flows in the same valley are splitting: the superfluid components of the \textit{A} and \textit{B} polariton flows propagate in opposite directions along the counterpropagating beams, while the normal components of the flows slightly deflect in opposite directions and propagate almost perpendicularly to the beams. The possible experimental observation of SHEP in a microcavity is proposed.