Journal of Low Temperature Physics

, Volume 161, Issue 5–6, pp 460–473 | Cite as

Topological Superfluid 3He–B: Fermion Zero Modes on Interfaces and in the Vortex Core

  • M. A. SilaevEmail author
  • G. E. Volovik


Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which are robust to perturbation and interaction. We discuss the nodeless 3D system, such as superfluid 3He–B, vacuum of Dirac fermions, and relativistic singlet and triplet supercondutors which may arise in quark matter. The systems, which have nonzero value of topological invariant, have gapless fermions on the boundary and in the core of quantized vortices. We discuss the index theorem which relates fermion zero modes on vortices with the topological invariants in combined momentum and coordinate space.


Topological superfluid 3He–B Relativistic superconductor Index theorem 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute for Physics of Microstructures RASNizhny NovgorodRussia
  2. 2.Low Temperature LaboratoryAalto UniversityAaltoFinland
  3. 3.L.D. Landau Institute for Theoretical PhysicsMoscowRussia

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