Singular and Half-Quantum Vortices and Associated Majorana Particles in Superfluid 3He-A between Parallel Plates

Abstract

Motivated by a recent experiment on superfluid 3He-A confined in narrow parallel plates using a rotating cryostat, we explore possible vortices stable under magnetic field applied to arbitrary angle relative to the plates in order to seek vortices which can accommodate the Majorana zero mode in the core. After proving that the singular vortex with the unit winding number provides the Majorana mode in the spinful situation, we establish the phase diagram in the plane; the rotation frequency $\Omega$ vs system size R by finding possible order parameter textures within the Ginzburg-Landau framework. We also analyze the stability for a single and a pair of half-quantum vortices, which possesses the Majorana mode in its core. It is concluded from the above mention that the Majorana zero mode can be found in the present on-going experimental setting at ISSP, Univ. Tokyo.

9 pages, 15 figures

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Cited by in corpus (9)

• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Majorana edge modes of superfluid 3He A-phase in a slab
• Zero Energy Modes and Statistics of Vortices in Spinful Chiral p-Wave Superfluids
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Half-Quantum Vortices in Thin Film of Superfluid ${}^3$He