B-like Phase Research Articles

Coherent reaction of Fermi superfluid on correlated disorder

Motivated by the disparity between the experimentally observed properties of superfluid ${}^{3}$He in aerogel and predictions of the Abrikosov and Gor'kov theory of superconducting alloys, we consider the effect of correlated pair-breaking impurities on the temperature dependence of the square of magnitude of the average order parameter and related thermodynamic properties of a Fermi superfluid. We show that by increasing the spectral density of the fluctuations with small wave vectors, the correlations increase the transition temperature and enhance a temperature region below ${T}_{c}$ where fluctuations of the order parameter dominate. Outside of this region, we treat the effect of impurities as a perturbation and express corrections to thermodynamic properties in terms of the structure factor of impurities. Assuming a simple model expression for the correlation function of aerogel, we find corrections to the temperature dependence of the NMR frequency shifts for A-like and B-like phases of ${}^{3}$He, and we compare these with experimental data.

Vortex core transitions in superfluidH3ein globally anisotropic aerogels

Core structures of a single vortex in A-like and B-like phases of superfluid $^{3}\text{H}\text{e}$ in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like phase while no strange vortex core is expected in the corresponding A-like phase. By contrast, in a stretched aerogel, the VCT in the B-like phase is lost while another VCT is expected to occur between a nonunitary core and a polar one in the A-like phase. Experimental search for these results is hoped to understand correlation between superfluid $^{3}\text{H}\text{e}$ and aerogel structure.

Magnetic Field Dependence of the A-like to B-like Transition of Superfluid 3He in Aerogel

Longitudinal ultrasound attenuation of superfluid 3He in 98% aerogel has been measured at 33 bar and 6.22 MHz in the presence of magnetic fields up to 4.44 kG. The A-like to B-like (A-B like) phase transition in aerogel was identified by a rounded jump in attenuation while sweeping the temperature at a fixed magnetic field perpendicular to the direction of sound propagation. The suppression of the B-like phase was monitored as the magnetic field increased until the A-like phase region extended below our lowest attainable temperature (0.2 mK) at the highest field. In addition, the attenuation in the metastable A-like phase that appears when cooling in zero magnetic field was almost identical to the values observed in the A-like phase in high magnetic field.

Ultrasound attenuation measurements in the A-like phase of superfluid 3He in aerogel

Liquid 3He impregnated in high porosity aerogel shows many interesting features: significant suppression of superfluid transition and substantial modification of the the A-like to B-like transition. Ultrasound has been found to be a sensitive tool to measure these changes. Recently, the ultrasound attenuation measurements done in the B-like phase provided strong evidence for gapless superfluidity in liquid 3He in aerogel. We conducted high frequency sound propagation measurements at 6.22 MHz in the A-like phase of superfluid 3He induced by magnetic fields up to 4.44 kG. The magnetic field is applied perpendicular to the direction of sound propagation to see the noticeable change in attenuation between the A-like and the B-like phases. We measured the sound attenuation in the A-like phase to be larger than in the B-like phase, and this observation enabled us to identify the A-like to B-like phase transition as a function of magnetic field and pressure.

In globally isotropic aerogel, A-B phase separation of superfluid 3He in radial direction

It is observed that the A-like phase and the B-like phase, which are superfluid phases of 3He in high porosity silica aerogel as an impurity, coexist stably [1]. In this coexisting state, we showed by NMR experiments with radial gradient magnetic field that the A-like phase is in the edge part of a cylindrical aerogel and the B-like phase is in the central part of that [2]. It is proposed that the A-like phase might be more stabilized in globally anisotropic aerogel. According to this proportion, the aerogel might be globally anisotropic in edge part. In order to study whether the aerogel is globally anisotropic, we have performed optical birefringence experiment on aerogel samples in the same batch. This optical method is a useful tool to characterize a global anisotropy of aerogel [3]. Then, we found that aerogel samples are not globally anisotropic. Therefore, there are another mechanism for the A-B phase separation in radial direction.

Structure of vortices in superfluid 3He A-like phase in uniaxially stretched aerogel

Possible vortex-core transitions in A-like phase of superfluid 3He in uniaxially stretched aerogel are investigated. Since the global anisotropy in this system induces the polar pairing state in a narrow range close to the superfluid transition in addition to the A-like and B-like phases, the polar state may occur in the core of a vortex in the A-like phase identified with the ABM pairing state, like in the case of the bulk B phase where a core including the ABM state is realized at higher pressures. We examine the core structure of a single vortex under the boundary condition compatible with the Mermin-Ho vortex in the presence of the dipole interaction. Following Salomaa and Volovik's approach, we numerically solve the Ginzburg-Landau equation for an axially symmetric vortex and, by examining its stability against nonaxisymmetric perturbations, discuss possible vortex core states. It is found that a first order transition on core states may occur on warming from an axisymmetric vortex with a nonunitary core to a singular vortex with the polar core.

Superfluid phase stability of 3He in axially anisotropic aerogel

Measurements of superfluid 3He in 98% aerogel demonstrate the existence of a metastable A-like phase and a stable B-like phase. It has been suggested that the relative stability of these two phases is controlled by anisotropic quasiparticle scattering in the aerogel. Anisotropic scattering produced by axial compression of the aerogel has been predicted to stabilize the axial state of superfluid 3He. To explore this possiblity, we used transverse acoustic impedance to map out the phase diagram of superfluid 3He in a ∼ 98% porous silica aerogel subjected to 17% axial compression. We have previously shown that axial anisotropy in aerogel leads to optical birefringence and that optical cross-polarization studies can be used to characterize such anisotropy. Consequently, we have performed optical cross-polarization experiments to verify the presence and uniformity of the axial anisotropy in our aerogel sample. We find that uniform axial anisotropy introduced by 17% compression does not stabilize the A-like phase. We also find an increase in the supercooling of the A-like phase at lower pressure, indicating a modification to B-like phase nucleation in globally anisotropic aerogels.

Observation of vortex-creep in superfluid 3He B-like phase in aerogel by the HPD

Superfluid 3He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2πrad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29mT and 3.0MPa. We studied the dissipation of the HPD in aerogel and found that the HPD-mode was destroyed by onset of the thermal runaway for sufficient large sample under a large field gradient. From the field dependence of the onset of thermal runaway, we estimated dissipation of the HPD in aerogel and compared with that of the bulk B-phase. When angular velocity of rotation goes beyond Ωc, vortices are introduced and pinned. We estimate roughly the excess dissipation due to vortices and compare it with that of vortices in bulk B-phase.

Quantum Fluid Dynamics of Rotating Superfluid 3He in Aerogel

Superfluid 3He A-like and B-like phases in 98% aerogel have been studied under rotation up to 2π rad/s by using cw-NMR and Homogeneous Pressing Domain (HPD) NMR at 29 mT and 3.0 MPa. Triplet superfluid 3He has continuous symmetries whose degeneracies are lifted by small perturbations of magnetic field, boundary condition of the sample cell, counterflow and global anisotropies of aerogel. We report NMR results of the two typical samples in aerogel under rotation, which are almost identical in the phase diagram, T c and the critical velocity of the multiplication of vortex but are very different in textures and responses to the flow with each other. One samples (S-D) is slightly compressed by squeezing and thermal stress and thus has global anisotropic deformation along the sample axis. The other cell (S-H) has randomly(not uniaxially)-oriented global anisotropy. In the S-D, we observed a large negative shift in cw-NMR and spin wave and HPD in the B-like phase. Comparing textures determined by NMR and its response to the counterflows between two samples, we discuss how the long-range order of the continuous symmetry and textures are controlled by orientation effects due to global anisotropy in aerogel.

Magnetic Distortion of the B-like Phase of Superfluid 3He Confined in Aerogel

We present measurements of the response of the B-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.

A-B Phase Conversion and Coexistence of Superfluid 3He in Aerogel

We have studied phase transition of superfluid 3He at 2.4 MPa in cylindrical aerogel by NMR method. When the liquid is cooled down from the normal state, the A-like phase appears below superfluid transition temperature T which is suppressed in comparison with the transition temperature of the bulk liquid. With further cooling below the certain temperature T , , the A-like phase is converted into the B-like phase gradually. Both phases stably coexist within about 90 μK. When you keep the temperature constant in which both phases coexist, the A-B phase conversion stops. With furthermore cooling, the whole liquid becomes the B-like phase. The cwNMR spectra at the coexistence state suggest that the B-like phase is not uniformly distributed in the A-like phase like a large number of small bubbles in a liquid, but separated as a whole from the A-like phase. By applying a field gradient which changes as a function of square of radius, we found that the A-like phase is in the edge part with a cylindrical shape and the B-like phase is in the central part with a columnar shape.

Orientation effect on superfluid 3He in anisotropic aerogel

The orientation of the order parameter in the A-like and B-like phases of superfluid 3He immersed in uniaxially compressed aerogel is reported. With the use of NMR methods, it is found that the orbital momentum of the A-and B-like phases is oriented along the deformation. In the A-like phase, a relatively narrow NMR line with an anomalously large negative frequency shift is observed. The Leggett frequency in the A-like phase, which shows the same energy gap suppression as in the B-like phase, is measured.

Textures of Superfluid 3He A-like and B-like Phases in Aerogel under Rotation

Superfluid 3He A-like and B-like phases in 98% aerogel under rotation up to 2π rad/sec have been studied by cw-NMR and Homogeneous Precessing Domain (HPD) NMR at 29 mT and 3.0 MPa. In the A-like phase, a large negative frequency shift was observed in the cw-NMR spectrum and no effect of rotation on the spectrum was found. In the B-like phase, the spin wave spectrum was observed when the sample was cooled through T c under rotation and was affected by the counter flow due to the trapped vortices. The HPD was excited in a part of the aerogel sample but introduction of vortices into the sample by rotation or trapped vortices destroyed the HPD.

Phase Transition of Superfluid 3He in Aerogel

We have studied phase transition of superfluid 3He in 97.5% porosity aerogel by NMR method. Above 1.0 MPa, superfluid phase transition has been observed. The transition temperature Tca is strongly suppressed from its bulk value. The Pressure-Temperature diagram suggests that superfluid phase will not appear below near 0.8 MPa. The A-B phase transition has been observed above 1.3 MPa, below which a state of superfluid phases remains to be identified. The temperature dependence of NMR frequency shifts Δf in the A-like and the B-like phases are almost linear at pressures below 2.4 MPa. We obtained the differential coefficient of NMR frequency shifts ∂(Δf)/∂(T/Tca) at 0.9Tca as a function of pressure, and it suggests that superfluid phase will not appear below near 0.8 MPa which is the same pressure estimated by P-T diagram.

Fourth Sound Measurement of Superfluid 3He in Aerogel

The fourth sound resonance experiment has been done on liquid 3He in 98.5% porosity aerogel. Aerogel was grown inside the pores among the sintered silver powder to avoid the vibration of the aerogel strands by the sound experiment. The measurement was performed at zero magnetic field and 27 bar. We observed the phase transition between the A-like and B-like phases and also their coexistent state. The A-like to B-like phase transition occurs not at a temperature but within a temperature band. In this band, the A-like phase gradually converts to the B-like phase. Possible picture of the coexistent state is discussed.

Crystalline Order in SuperfluidHe3Films

We predict an inhomogeneous phase of superfluid (3)He films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, D(c2)(T) < D < D(c1)(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D(c2) approximately 9 xi (T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at D(c1) approximately 13 xi (T).

Longitudinal NMR and spin states in the A-like phase of 3He in aerogel

It was found that two different spin states of the A-like phase can be obtained in aerogel sample. In one of these states we have observed the signal of the longitudinal NMR, while in another state no trace of such a signal was found. The states also have different properties in transverse NMR experiments. Longitudinal NMR signal was also observed in the B-like phase of 3He in aerogel.

Pinning of Texture and Vortices of the RotatingB-like Phase of SuperfluidHe3Confined in a 98% Aerogel

We have investigated pinning effects on texture and vortices of the B-like phase of superfluid (3)He in a rotating aerogel up to +/-2pi rad/s by cw-NMR. We observed deformation of the NMR spectra in rotation, due to counterflow between the superflow and the normal flow. The average intensity of the counterflow was calculated from the change of NMR spectra. The rotation dependence of the counterflow intensity is similar to the magnetization curve of hard type II superconductors or the counterflow response of (4)He-II in packed powders. This counterflow behavior is in qualitative agreement with a model that vortices are pinned unless the counterflow exceeds a critical velocity v(c). The temperature independence of v(c) suggests that v(c) is associated with the expansion of primordial vortices.

Impurity Scattering Effect on Superfluid Phases of 3He in 97.5% Porous Silica Aerogel

NMR studies of superfluid 3He in 97.5% aerogel have been performed in a magnetic field of 28.4 mT. A small-angle neutron scattering experiment on the structure of the aerogel shows that the average separation distance of silica strands is 54 nm. The aerogel strands were covered with a few layers of solid 3He whose magnetization shows Curie-Weiss behaviour. On cooling process A-like phase appeared at suppressed superfluid transition temperature TCaero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to TCaero on warming process above 2.1 MPa. The superfluid transitions in aerogel always occur below the AB phase transition temperature of bulk liquid at all pressures. An isotropic inhomogeneous scattering model(IISM) proposed by Thuneberg et al. explained well the observed suppressed TCaero in 97.5% with the radius 59 nm of voids in this model. This radius is similar with the average strand separation distance of 54 nm measured in the structural analysis. This similarity of two lengths shows the connection of the suppression of TCaero with the actual average separation distance of the silica strands.

Superfluid Phases of 3He in Aerogel

Formal derivation of criterion for selection of superfluid phases of 3He in aerogel is presented. At the strength of the derived criterion variation of the order parameter of B-like phase in magnetic field differs from that of B-phase of pure 3He. Possible observable consequences of this difference is discussed.