V. V. Zavjalov

Observation of Half-Quantum Vortices in Topological Superfluid 3He

One of the most sought-after objects in topological quantum-matter systems is a vortex carrying half a quantum of circulation. They were originally predicted to exist in superfluid ^{3}He-A but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid ^{3}He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery provides a pathway for studies of unpaired Majorana modes bound to the HQV cores in the polar-distorted A phase.

Nonlinear NMR in a superfluid B phase of 3He in aerogel

The properties of liquid 3He in a low-density aerogel preliminarily covered with a few monolayers of 4He were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104°. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid 3He phase in the aerogel is analogous to the B-phase in bulk 3He and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid 3He in aerogel.

Experiments on A-like to B phase transitions of 3He confined to aerogel

Abstract We have done pulsed and CW NMR studies of A-like to B phase transition in superfluid 3 He confined within aerogel with 98% porosity. The experiments were performed at pressure of 25.5 bar and in magnetic field of 284 Oe and 1 kOe . A kinetics of the transition is found to be different for pure 3 He in aerogel and for the cell preplated with 4 He .

Transverse and longitudinal nuclear magnetic resonance in superfluid 3He in anisotropic aerogel

Introduction. The system “liquid He + high porosity silica aerogel” allows to investigate the influence of disorder on p-wave superfluidity. The disorder is introduced by the aerogel strands. The diameter of the strands (∼30 Å) is much less than the correlation length of the bulk superfluid He and a characteristic distance between them is large enough, so the superfluidity of He is not fully suppressed [1, 2]. In a weak magnetic field there exist two superfluid phases of He in aerogel called A-like and B-like [3]. The A-like phase appears on cooling from the normal phase at pressures above ≈ 20 bar and exists in rather large temperature range in a metastable (supercooled) state. It is established [3, 4] that the B-like phase is analogous to the B phase of “usual” bulk He, i.e. it is described by the same Balian-Werthamer (BW) order parameter as the bulk B phase. It is also known [3] that the A-like phase belongs to the family of Equal Spin Pairing (ESP) phases, but the exact structure of its order parameter is still unclear. G. E. Volovik suggested that the A-like phase in aerogel is described by the Larkin-Imry-Ma (LIM) model with spatially random orientation of AndersonBrinkman-Morel (ABM) order parameter[5, 6]. In the bulk A phase the order parameter is also described by the ABM model, but it is spatially homogeneous. I.A. Fomin has proposed the so called “robust” ESP phase – the phase in which the orientation of the order parameter is not influenced by the presence of aerogel – as a possible candidate for the A-like phase [7, 8]. In previous experiments in aerogel with porosity of about 98% [3, 9, 10, 11] (and with 97.5% and 99.3% porosity samples [12, 13, 14]) it was found that the NMR properties of the A-like phase are different from the properties of the A phase of bulk He. In the same time the observed 1)e-mail: dmitriev@kapitza.ras.ru NMR properties also do not correspond well to both LIM and “robust” phase models [11]. Recent experiments with 98% aerogel [15] have clarified the problem: it was found that in squeezed by 1-2% aerogel sample the A-like phase behaves as the A phase of the bulk He with vector l̂ fixed along the axis of deformation (i.e. along the axis of anisotropy). This observation agrees with recent theoretical studies, where it was shown that even for small anisotropy (∼1%) spatially homogeneous A phase order parameter is more favorable than LIM or “robust” state [16, 17]. Consequently, if the sample is inside a glass tube as probably was in [3, 14] (or there is no large enough gap between the sample and epoxy walls of the cell or spacers fixing the sample as it was in [9, 10, 11]) then a difference in thermal contraction coefficients of aerogel and the walls could result in uncontrolled deformation and complicate interpretation of the results. Here we present and compare the results of our recent NMR studies of the A-like and the B-like phases in 3 aerogel samples. As it is shown below two of them were anisotropic, while the third one had isotropic NMR properties. Experimental details. Experiments were done at pressures of 26.0 bar and 28.6 bar in the magnetic fields range of 40-528Oe (corresponding to NMR frequencies from 132 to 1714kHz). We used 98.2% porosity aerogel in which silica strands occupy only about 1.8% of the whole volume. Three experimental cells (similar to that described in [4, 10]) with three different aerogel samples were used. The samples had a cylindrical form (sample 1: diameter=4mm, height=3.5mm; samples 2 and 3: diameter=5mm, height=1.5mm) with the axis oriented along z. Samples 1 and 2 were laying freely inside the epoxy cells, so that there were large enough gapsIt is found that the properties of nuclear magnetic resonance of both superfluid phases of 3He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties.

Pulsed NMR experiments in superfluid 3He confined in aerogel

Abstract Pulsed NMR experiments have been performed in both B and supercooled A phases of superfluid 3 He in aerogel. Dependencies of spin precession frequency on tipping angle in B-phase of superfluid 3 He in aerogel are found to be different for pure 3 He and for the cell preplated with 4 He . A sharp increase of the frequency for tipping angles greater than 104° was observed in low temperature superfluid phase of 3 He in 4 He preplated aerogel as it is expected for the B-phase structure of the order parameter. Dependencies of the frequency on the tipping angle in supercooled A-phase are similar for both pure 3 He and 4 He preplated aerogel.

CW NMR Measurements of the Leggett Frequency in 3He‐B in Aerogel

The Leggett frequency in the B‐like phase of 3He in 98% silica aerogel has been measured in a wide range of temperatures and pressures by means ofCW NMR.

NMR Studies of Texture in the B-like Phase of 3He in Aerogel

Continuous wave NMR experiments have been performed in the B‐like phase of 3He in a 98% open aerogel. The results allow us to get information about the texture of the 3He order parameter inside the aerogel. We conclude that in the B‐like phase the boundary between the bulk 3He and the aerogel orients the vector of orbital anisotropy (L) parallel to it. Two stable textures and textural transition between them were observed in our sample.

Measurement of the Leggett frequency in 3He-B in aerogel

The method of measuring the Leggett frequency of 3He-B using spatially homogeneous oscillations of a homogeneously precessing domain was developed. The temperature dependence of Leggett frequency was measured for bulk 3He-B and 3He-B in aerogel at a pressure of 19.5 bar.

Homogeneous spin precession in superfluid 3He confined to aerogel

Abstract We report on systematic studies of creation and relaxation of a macroscopic region of homogeneous spin precession (homogeneously precessing domain—HPD) in B-like phase of 3 He in aerogel. Long lived free induction decay signal has been observed after filling up the whole cell with the HPD and switching off the CW radiofrequency field. Characteristics of CW NMR and free induction decay signal were found to be similar to those known for bulk 3 He -B.

Measurements of longitudinal and transverse magnetic relaxation in superfluid confined to aerogel

Abstract We present results of pulsed NMR measurements of magnetic relaxation in liquid 3 He in aerogel. It was found that both longitudinal and transverse relaxation starts to change below the temperature of the superfluid transition of 3 He in aerogel. Below Tca the longitudinal relaxation depends on the initial tipping angle.