JETP Letters

, Volume 91, Issue 4, pp 201–205 | Cite as

Topological superfluid 3He-B in magnetic field and ising variable

  • G. E. Volovik
Condensed Matter


The topological superfluid 3He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of 3He-B. Magnetic field violates the time reversal symmetry. As a result, the topological invariant supported by this symmetry ceases to exist; and thus the gapless fermions on the surface of 3He-B are not protected any more by topology: they become fully gapped. Nevertheless, if perturbation of symmetry is small, the surface fermions remain relativistic with mass proportional to symmetry violating perturbation—magnetic field. The 3He-B symmetry gives rise to the Ising variable I = ±1, which emerges in magnetic field and which characterizes the states of the surface of 3He-B. This variable also determines the sign of the mass term of surface fermions and the topological invariant describing their effective Hamiltonian. The line on the surface, which separates the surface domains with different I, contains 1 + 1 gapless fermions, which are protected by combined action of symmetry and topology.


Magnetic Field Surface Fermion JETP Letter Spin Orbit Spin Orbit Interaction 
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© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Low Temperature LaboratoryAalto UniversityAaltoFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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