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

Abstract

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.

paper is prepared for Proceedings of the Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence held on 11-16 April 2010, Lammi, Finland

References in corpus (2)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Resonantly-paired fermionic superfluids

Cited by in corpus (5)

• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Search for Majorana fermions in multiband semiconducting nanowires
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points
• Structure and consequences of vortex-core states in p-wave superfluids