Study of Superfluid $$^3$$ 3 He Under Nanoscale Confinement

Levitin, L. V.; Bennett, Robert; Casey, A.; Cowan, Brian; Saunders, J.; Drung, D.; Schurig, T.; Parpia, J. M.; Ilić, B.; Zhelev, Nikolay

doi:10.1007/s10909-014-1145-1

Cited by 17 publications

(17 citation statements)

References 61 publications

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“…Indeed, such a restricted geometry with D ≲ d has been accomplished by several experimental groups. [40][41][42][43]332,388,[393][394][395][396][397][398][399] In this situation, the gapless edge states exist, whose dispersion at the edge x ¼ 0 of Fig. 16(a) is given as 73)…”

Section: Weyl Superfluidity and Mirror Chern Number In 3 He-amentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid 3 He, which serves as a rich repository of novel topological quantum phenomena originating from the intertwining of symmetries and topologies. In particular, it is emphasized that the quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase, the A-phase as a Weyl superfluid, the nodal planar and polar phases, and the crystalline ordered stripe phase. All these phases generate noteworthy topological phenomena, including topological phase transitions concomitant with spontaneous symmetry breaking, Majorana fermions, Weyl superfluidity, emergent supersymmetry, spontaneous edge mass and spin currents, topological Fermi arcs, and exotic quasiparticles bound to topological defects. In relation to the mass current carried by gapless edge states, we also briefly review a longstanding issue on the intrinsic angular momentum paradox in 3 He-A. Moreover, we share the current status of our knowledge on the topological aspects of unconventional superconductors, such as the heavy-fermion superconductor UPt 3 and superconducting doped topological insulators, in connection with the superfluid 3 He.In Sect. 3, we will share the topological aspect of a spinpolarized chiral p-wave superconducting state as a specific model having nontrivial w 2d ¼ Ch 1 . Topology subject to discrete symmetriesNaively, any one-dimensional closed loop S 1 cannot cover the target space S 2 . Thus, a generic 2 Â 2 Hamiltonian in one dimension cannot provide a stable topological structure. However, discrete symmetries of H in Eq. (3) impose strong constraints on the spinorm, and thus nontrivial topological numbers can be introduced even in one dimension, as illustrated below.Particle-hole symmetry C 2 ¼ þ1 (class D)-Let us first suppose that the minimal Hamiltonian (13) holds the PHS C ¼ x K (C 2 ¼ þ1). The operation of PHS changes the spinor mðkÞ to ½Àm x ðÀkÞ; Àm y ðÀkÞ;m z ðÀkÞ. For the momentum space characterized by S 2 , there are two particle-hole invariant momenta, k ¼ 0 and jkj ¼ 1, where the infinite points are identical to a single point. At the particle-hole invariant momenta, the spinorm must point to the north or south pole on S 2 . Therefore, we have two different situations: One is that the spinorsm at k ¼ 0 and jkj ¼ 1 point in the same direction,m z ð0Þ ¼m z ð1Þ; ð26Þ Fig. 3. (Color online) Target spaces M subject to discrete symmetries T and C. Possible trajectories ofm on M with C 2 ¼ þ1 are also depicted.Fig. 24. (Color online) Low-lying quasiparticle spectra for the axisymmetric w-vortex (a) and v-vortex (b) with k z ¼ 0 and ...

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Section: Weyl Superfluidity and Mirror Chern Number In 3 He-amentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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“…Nevertheless, in two dimensions (2D), this system is gapful ("insulating"). While this phase has not been identified experimentally yet, in recent experiments [5][6][7][8][9] strong suppression of the transverse gap has been observed.…”

Section: Introductionmentioning

confidence: 88%

“…In recent experiments [5][6][7][8][9], indications of the strongly distorted B phase were found, and the planar phase may become observable too. As estimated in Ref.…”

Section: Planar Phasementioning

confidence: 97%

Topology of the planar phase of superfluidHe3and bulk-boundary correspondence for three-dimensional topological superconductors

2014

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We provide topological classification of possible phases with the symmetry of the planar phase of superfluid 3 He. Compared to the B phase [class DIII in classification of A. Altland and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)], it has an additional symmetry, which modifies the topology. We analyze the topology in terms of explicit mappings from the momentum space and also discuss explicitly topological invariants for the B phase. We further show how the bulk-boundary correspondence for the three-dimensional (3D) B phase can be inferred from that for the 2D planar phase. A general condition is derived for the existence of topologically stable zero modes at the surfaces of 3D superconductors with class-DIII symmetries.

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“…Studies range from the physics of topological excitations -Majorana and Weyl Fermions confined on boundaries, interfaces and topological defects, 15,[44][45][46][47][48][49][50][51][52] to the nucleation of topological defects in broken symmetry phases during nonequilibrium phase transitions. 17,53 The knowledge obtained from research on superfluid 3 He confined in aerogels, combined with theoretical developments in topological quantum matter, has led to new directions in the study of quantum fluids confined in engineered nano-scale structures, 16,54 from high-Q fluid-mechanical resonantors, to nano-fluidic devices 55 and ultrasonic cavities for quantum transport and dynamics of quantum fluids. [56][57][58][59] This marriage of quantum fluids, nano-scale materials and nano-fabrication is part of a new frontier in the field of hybrid quantum materials.…”

Section: Topological Superfluid 3 Hementioning

confidence: 99%

Superfluid helium-3 in confined quarters

Halperin¹,

Parpia²,

Sauls³

2018

Physics Today

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Study of Superfluid $$^3$$ 3 He Under Nanoscale Confinement

Cited by 17 publications

References 61 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Topology of the planar phase of superfluidHe3and bulk-boundary correspondence for three-dimensional topological superconductors

Superfluid helium-3 in confined quarters

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Study of Superfluid $$^3$$ 3 He Under Nanoscale Confinement

Cited by 17 publications

References 61 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

Topology of the planar phase of superfluidHe3and bulk-boundary correspondence for three-dimensional topological superconductors

Superfluid helium-3 in confined quarters

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Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—