Zero Energy Modes and Statistics of Vortices in Spinful Chiral p-Wave Superfluids

Abstract

The possible stable singular vortex (SV) and half-quantum vortex (HQV) of the superfluid ${}^3$He-A phase confined in restricted geometries are investigated. The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics. The energetics between those vortices is carefully examined using the standard Ginzburg-Landau (GL) functional with a strong-coupling correction. The Fermi liquid effect, which is not included in the GL functional, is considered approximately within the London approach. This allows us to determine the stability regions in pressure, temperature, and applied field for SV and HQV. The existence of the Majorana zero mode and its statistics, either Abelian or non-Abelian under braiding of SVs, is studied by solving the Bogoliubov-de Gennes equation for spinful chiral p-wave superfluids at sufficiently low temperatures. We determined several conditions controllable external parameters for realizing the non-Abelian statistics of Majorana zero modes e.g., pressure, field direction, and strength.

12 pages, 8 figures

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Cited by in corpus (16)

• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Odd-frequency Cooper pair amplitude around a vortex core in a chiral p-wave superconductor in the quantum limit
• Symmetry protected vortex bound state in superfluid ${}^3$He B-phase
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Scattering theory on surface Majorana fermions by an impurity in 3He-B
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• Topological superconductivity induced by a Kitaev spin liquid
• Coherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors