Majorana excitations, spin and mass currents on the surface of topological superfluid 3He-B

Hao Wu*, J. A. Sauls

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The B-phase of superfluid 3He is a 3D time-reversal-invariant topological superfluid with an isotropic energy gap, Δ, separating the ground state and bulk continuum states. We report calculations of surface spectrum and spin and mass current densities originating from the Andreev surface states for confined 3He-B. The surface states are Majorana Fermions with their spins polarized transverse to their direction of propagation along the surface, p∥. The negative-energy states give rise to a ground-state helical spin current confined on the surface. The spectral functions reveal the subtle role of the spin-polarized surface states in relation to the ground-state spin current. By contrast, these states do not contribute to the T=0 mass current. Superfluid flow through a channel of confined 3He-B is characterized by the flow field, ps=h/2∇φ. The flow field breaks SO( 2Lz+Sz rotational symmetry and time reversal (T). However, the Bogoliubov-Nambu Hamiltonian remains invariant under the combined symmetry, Uz(π)×T, where Uz(π) is a π rotation about the surface normal. As a result the B phase in the presence of a superflow remains a topological phase with a gapless spectrum of Majorana modes on the surface. Thermal excitation of the Doppler-shifted Majorana branches leads to a power-law suppression of the superfluid mass current for 0<T≲0.5Tc, providing a direct signature of the Majorana branches of surface excitations in the fully gapped 3D topological superfluid, 3He-B. Results are reported for the superfluid fraction (mass current) and helical spin current for confined 3He-B, including the temperature dependencies, as well as dependencies on confinement, pressure and interactions between quasiparticles.

Original languageEnglish (US)
Article number184506
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number18
StatePublished - Nov 12 2013

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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