Size effects in superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>films

Freeman, M. R.; Richardson, Robert C.

doi:10.1103/physrevb.41.11011

Cited by 74 publications

(106 citation statements)

References 54 publications

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“…The surface roughness drastically changes the surface structure of order parameters and low-lying surface states in the superfluid 3 He-B [106,108,152,154]. The pair-breaking effect and the enhancement of the surface density of states due to the existence of the surface Andreev bound states have been observed in several experiments [109,110,271,112,113,114,115,116,117,118,155,156,157,158,159]. The contributions of surface Andreev bound states have also been detected through the deviation of the heat capacity from that in the bulk 3 He-B [160] as well as the anomalous attenuation of transverse sound wave [161].…”

Section: 3mentioning

confidence: 93%

“…This indicates that the topological phase transition from the time-reversal invariant B-phase to time-reversal breaking Aphase occurs at the critical value of the "thickness" even at zero pressures. Several experiments have observed the confinement-induced A-B phase transition in a slab geometry with a thickness comparable to the superfluid coherence length [109,110,271,112,113,114,115,116,117,118]. We introduce in Sec.…”

mentioning

confidence: 99%

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Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

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Section: 3mentioning

confidence: 93%

mentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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“…At temperatures T ∼ 1 mK, where 3 He is superfluid, the scattering occurs only on aerogel strands and boundary conditions may be varied by a small amount of 4 He which covers the strands by a few atomic layers. In pure 3 He the strands are covered by ∼ 2 atomic layers of paramagnetic solid 3 He [2] and the scattering is diffusive but in presence of more than ≈ 2.5 layers of 4 He it is nearly specular at low pressures and becomes purely diffusive above ≈ 25 bar [3][4][5][6][7]. The 4 He coverage also removes the solid 3 He, and spin is conserved during the scattering.…”

mentioning

confidence: 99%

Effect of Magnetic Boundary Conditions on SuperfluidHe3in Nematic Aerogel

2018

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We report results of experiments with superfluid 3 He confined in aerogels with parallel strands which lead to anisotropic scattering of 3 He quasiparticles. We vary boundary conditions for the scattering by covering the strands by different numbers of atomic 4 He layers and observe that the superfluid phase diagram and the nature of superfluid phases strongly depend on the coverage. We assume that the main reason of these phenomena is a magnetic channel of the scattering which becomes important at low coverages. Our results show that the magnetic channel also may be important in other Fermi systems with the triplet pairing.Introduction.-In many Fermi systems, e.g. in liquid 3 He, in some cold atomic gases, and unconventional superconductors, a triplet Cooper pairing occurs that results in superfluid (superconducting) states. An ideal object to study an effect of impurities on such states is 3 He: it has a spherical Fermi surface, its superfluid phases (A, B and A 1 ) are well understood, and its superfluid coherence length can be varied by pressure in range of 20-80 nm [1]. Although superfluid 3 He is originally pure, a well defined system of impurities can be introduced by a high porosity aerogel. In such experiments silica aerogels are typically used. The main effect of the aerogel is to scatter 3 He quasiparticles. At temperatures T ∼ 1 mK, where 3 He is superfluid, the scattering occurs only on aerogel strands and boundary conditions may be varied by a small amount of 4 He which covers the strands by a few atomic layers. In pure 3 He the strands are covered by ∼ 2 atomic layers of paramagnetic solid 3 He [2] and the scattering is diffusive but in presence of more than ≈ 2.5 layers of 4 He it is nearly specular at low pressures and becomes purely diffusive above ≈ 25 bar [3][4][5][6][7]. The 4 He coverage also removes the solid 3 He, and spin is conserved during the scattering. In contrast, in pure 3 He spin is not conserved due to a fast exchange between atoms of liquid and solid 3 He that should result in an additional spin-exchange (magnetic) scattering channel. However, experiments with silica aerogels do not show a clear evidence of the magnetic channel. In particular, the observed A-like and B-like phases correspond to A and B phases of bulk 3 He, regardless of presence or absence of 4 He [8][9][10][11][12][13][14]. Moreover, the superfluid transition temperature of 3 He in aerogel (T ca ) is independent on the coverage at high pressures [8,12] but slightly higher in presence of the coverage at lower pressures [15,16] probably due to the change of the scattering specularity. In most of theoretical models of 3 He in aerogel the magnetic channel is neglected except only a few papers where it was shown that the magnetic scattering may affect A-A 1 transition in high magnetic fields [17][18][19] and a heat transport in the normal phase [20].Presumably, the magnetic scattering in 3 He in silica aerogels is masked due to their small global anisotropy.

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“…This self-purification of 3 He has made it impossible to introduce disorder or impurities into the system. Experiments show that 3 He superfluids in aerogel display behavior [1][2][3] very different from earlier studies in confined geometries where diffuse surface scattering that suppresses T c dominates [4] and the size distribution smears out the sharp magnetic and mechanical responses of the bulk [5,6,7]. It was generally believed that p-wave superfluids are easily damaged by disorder [8], but the newest experiments [1][2][3] show that notwithstanding the T c suppression, superfluid coherence remains robust in aerogel.…”

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confidence: 51%

Quantum Phase Transition of3Hein Aerogel at a Nonzero Pressure

et al. 1997

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We present evidence for a nonzero pressure, T 0 superfluid phase transition of 3 He in 98.2% open aerogel. Unlike bulk 3 He which is a superfluid at T 0 at all pressures (densities) between zero and the melting pressure, 3 He in aerogel is not superfluid unless the 3 He density exceeds a critical value r c . About 90% of the 3 He added above r c contributes to the superfluid density. [S0031-9007(97) PACS numbers: 67.57. -zThe only known substance naturally free of impurities is the low temperature liquid phase of 3 He which allows the study of Fermi superfluids in their purest forms. This self-purification of 3 He has made it impossible to introduce disorder or impurities into the system. Experiments show that 3 He superfluids in aerogel display behavior [1][2][3] very different from earlier studies in confined geometries where diffuse surface scattering that suppresses T c dominates [4] and the size distribution smears out the sharp magnetic and mechanical responses of the bulk [5,6,7]. It was generally believed that p-wave superfluids are easily damaged by disorder [8], but the newest experiments [1][2][3] show that notwithstanding the T c suppression, superfluid coherence remains robust in aerogel. However, the phase diagram is completely modified despite the small volume fraction occupied by the aerogel.Aerogel is a tenuous random solid network of SiO 2 particles ͑ഠ25 Å radii͒ with fractal correlations between 30 and 1000 Å [9]. Aerogels have very large surface areas and very low densities (22.9 m 2 ͞cm 3 and 39.4 g͞l, respectively, for our samples), and very dilute aerogels occupy less than a few percent of the volume. Despite the tenuous fractal structure, the mean distance from a point in the open volume to a silica strand can be 100 Å. Since the silica diameter is smaller than the superfluid coherence length ͑j 0 150 800 Å͒, the aerogel will not behave like a surface. Instead it acts more like a collection of impurities, thus allowing the study of impurity effects on strongly interacting Fermi liquids. This "impurity" view is supported by the fact that superfluid 3 He in aerogel is coherent and homogeneous [2]. In many ways, the depairing effect of aerogel on the p-wave superfluid is similar to that of magnetic impurities on s-wave superconductors [10]. An aerogel concentration of ϳ2% strongly suppresses T c [1,2]. The possibility that this strong suppression can result in a T 0 phase transition and the very low temperature behavior of this system are the subject of this investigation.To put our results which we present later in perspective, we first summarize recent experimental findings: (i) The superfluid behaves as a homogeneous fluid with sharp magnetic [2,3,11] and mechanical [1,11] responses. (ii) In magnetic fields of the order of 1 kG, the superfluid phase appears to be A-like [2]. Recent experiments [3] show that the superfluid behaves like the B-phase if the 3 He on the surface of the aerogel is replaced with 4 He. Experiments in Manchester [11] in much lower fields (50 G) show that the mag...

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Size effects in superfluidHe3films

Cited by 74 publications

References 54 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Effect of Magnetic Boundary Conditions on SuperfluidHe3in Nematic Aerogel

Quantum Phase Transition of3Hein Aerogel at a Nonzero Pressure

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Size effects in superfluidHe3films

Cited by 74 publications

References 54 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Effect of Magnetic Boundary Conditions on SuperfluidHe3in Nematic Aerogel

Quantum Phase Transition of3Hein Aerogel at a Nonzero Pressure

Contact Info

Product

Resources

About

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B