Chiral Symmetry Breaking in Superfluid
            <sup>3</sup>
            He-A

Ikegami, Hiroki; Tsutsumi, Yoshio; Kono, Kimitoshi

doi:10.1126/science.1236509

Cited by 67 publications

(71 citation statements)

References 30 publications

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“…Similar asymmetric scattering due to a chiral order parameter was observed by Ikegami et al as the intrinsic Magnus force acting on injected electrons in the surface of 3 He-A. 421) Ishikawa et al 495) proposed an unconventional spin-singlet pairing with broken TRS, which is called the cyclic d-wave pairing. The gap function is obtained from Eq.…”

Section: Topological Crystalline Superconductorssupporting

confidence: 56%

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: Topological Crystalline Superconductorssupporting

confidence: 56%

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

et al. 2016

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“…The common aspects of unconventional superconductivity and superfluid 3 He are currently prime topics of research [29]. While the number of experimental results supporting the chiral nature in other superconductors is growing, Kono and colleagues at RIKEN in Japan garnered indisputable experimental evidence of chiral symmetry in the A-phase using electron bubble transport just below and parallel to the free superfluid surface [30]. In a perpendicular magnetic field this ion transport is subject to a transverse Magnus force from the orbital supercurrent around the bubble, which depends on the sign of the superfluid orbital angular momentum normal to the surface.…”

Section: Symmetry and Multiple Superfluid Phasementioning

confidence: 99%

Recent Progress and New Challenges in Quantum Fluids and Solids

Lee

Halperin²

2017

J Low Temp Phys

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“…Walmsley and Golov [3] were the first to show the existence of a macroscopically aligned orbital angular momentum in a thin slab of 3 He-A by using a torsional oscillator measurement in combination with a rotating ultralow temperature cryostat. Later, Ikegami et al [4,5] obtained direct evidence of a bistability in the effect of the intrinsic Magnus force on electron transport in the vicinity of the free surface of a 3 He-A film. They also observed metastable intermediate states, which suggest the existence of a multidomain structure of macroscopically aligned orbital angular momentum.…”

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confidence: 99%

Chiral Domain Structure in SuperfluidHe3−AStudied by Magnetic Resonance Imaging

et al. 2018

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The existence of a spatially varying texture in superfluid 3He is a direct manifestation of the complex macroscopic wave function. The real space shape of the texture, namely, a macroscopic wave function, has been studied extensively with the help of theoretical modeling but has never been directly observed experimentally with spatial resolution. We have succeeded in visualizing the texture by a specialized magnetic resonance imaging. With this new technology, we have discovered that the macroscopic chiral domains, of which sizes are as large as 1 mm, and corresponding chiral domain walls exist rather stably in 3 He-A film at temperatures far below the transition temperature. DOI: 10.1103/PhysRevLett.120.205301 Modern interest in topological superfluids and superconductors has revived the significance of superfluid 3 He because of the most precisely understood macroscopic wave function of triplet p wave BCS superfluids. The topological nature of these quantum materials appears in connection to the boundary condition at the border and interface of the material. For a precise study on the topological properties, it is important to control the boundary conditions of the materials. The extremely precise understanding of the macroscopic wave function and its controllability of boundary conditions in real experimental situations makes superfluid 3 He an outstandingly suitable system for studying topological superfluids and superconductors. Specifically, the A phase of superfluid 3 He is regarded as a chiral superfluid because of the macroscopically aligned orbital angular momentum of its Cooper pairs [1,2]. Walmsley and Golov [3] were the first to show the existence of a macroscopically aligned orbital angular momentum in a thin slab of 3 He-A by using a torsional oscillator measurement in combination with a rotating ultralow temperature cryostat. Later, Ikegami et al. [4,5] obtained direct evidence of a bistability in the effect of the intrinsic Magnus force on electron transport in the vicinity of the free surface of a 3 He-A film. They also observed metastable intermediate states, which suggest the existence of a multidomain structure of macroscopically aligned orbital angular momentum. The proposed multidomain structure is nothing other than a chiral domain structure, consisting of macroscopic domains of monochirality and chiral domain walls between domains of opposite chirality. Naive consideration suggests the stability of a monochirality single domain structure because of the extra energy cost due to domain walls. As is discussed for the case of a p wave superconductor [6], a mesoscopic sample might have a multichiral domain structure. Some of the experimental studies on the possible chiral superconductor Sr 2 RuO 4 [7,8] have suggested the existence of a multichiral domain structure. The results indicated the existence of a chiral domain wall that separates the domains with opposite chirality. Walmsley et al. [9,10] also suggested the existence of domain walls in their torsional oscillator study to explain...

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Chiral Symmetry Breaking in Superfluid ³ He-A

Cited by 67 publications

References 30 publications

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

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

Recent Progress and New Challenges in Quantum Fluids and Solids

Chiral Domain Structure in SuperfluidHe3−AStudied by Magnetic Resonance Imaging

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Chiral Symmetry Breaking in Superfluid 3 He-A

Cited by 67 publications

References 30 publications

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

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

Recent Progress and New Challenges in Quantum Fluids and Solids

Chiral Domain Structure in SuperfluidHe3−AStudied by Magnetic Resonance Imaging

Contact Info

Product

Resources

About

Chiral Symmetry Breaking in Superfluid ³ He-A

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

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