Topological superfluid $^3$He-B: fermion zero modes on interfaces and in the vortex core

Details Topological superfluid $^3$He-B: fermion zero modes on interfaces and in the vortex core Topological superfluid $^3$He-B: fermion zero modes on interfaces and in the vortex core

2010-05-25

arxiv.org/abs/1005.4672v2

J.Low.Temp.Phys.161:460,2010

Physics

Condensed Matter

Other Condensed Matter

paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April

Scientific paper

10.1007/s10909-010-0226-z

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 $^3$He-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.

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