Andreev-Majorana bound states in superfluids

Abstract

We consider Andreev-Majorana (AM) bound states with zero energy on surfaces, interfaces and vortices in different phases of the $p$-wave superfluids. We discuss the chiral superfluid ${}^3$He-A, and time reversal invariant phases: superfluid ${}^3$He-B, planar and polar phases. The AM zero modes are determined by topology in bulk, and they disappear at the quantum phase transition from the topological to non-topological state of the superfluid. The topology demonstrates the interplay of dimensions. In particular, the zero-dimensional Weyl points in chiral superfluids (the Berry phase monopoles in momentum space) give rise to the one-dimensional Fermi arc of AM bound states on the surface and to the one-dimensional flat band of AM modes in the vortex core. The one-dimensional nodal line in the polar phase produces the two-dimensional flat band of AM modes on the surface. The interplay of dimensions also connects the AM states in superfluids with different dimensions. For example, the topological properties of the spectrum of bound states in the three-dimensional ${}^3$He-B is connected to the properties of the spectrum in the two-dimensional planar phase (thin film).

paper accepted to the special issue of JETP devoted to 75-th anniversary of A.F. Andreev, 16 pages, 16 figures, references added

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Cited by in corpus (25)

• Topological waves in fluids with odd viscosity
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Topological Lifshitz transitions
• From Standard Model of particle physics to room-temperature superconductivity
• Disorder-induced exceptional points and nodal lines in Dirac superconductors
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Superconducting doped topological materials
• Lifshitz transition in the double-core vortex in 3He-B
• X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot
• Flat bands as a route to high-temperature superconductivity in graphite
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Multiple topological transitions driven by the interplay of normal scattering and Andreev scattering
• Andreev Bound States in Superconducting Films and Confined Superfluid He-3
• Antichiral and nematicity-wave superconductivity
• Non-Abelian Half-Quantum Vortices in ${}^3{P}_2$ Topological Superfluids
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Transport of bound quasiparticle states in a two-dimensional boundary superfluid
• Transient effects in quantum dots contacted via topological superconductor
• Nonlocality and dynamic response of Majorana states in fermionic superfluids
• Quasiparticles near domain walls in hexagonal superconductors
• NMR-like effect on Anisotropic Magnetic Moment of Surface Bound States in Topological Superfluid ${}^3$He-B
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Quasiclassical theory of spin dynamics in superfluid ${}^3$He: kinetic equations in the bulk and spin response of surface Majorana states
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors
• Local energy density functional for superfluid Fermi gases from effective field theory