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 (13)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Periodic table for topological insulators and superconductors
• Resonantly-paired fermionic superfluids
• Stability of Fermi Surfaces and K-Theory
• Quantum phase transitions from topology in momentum space
• Detecting the Majorana fermion surface state of ${}^3$He-B through spin relaxation
• Topologically stable gapless phases of time-reversal invariant superconductors
• Fermion zero modes at the boundary of superfluid 3He-B
• Topological invariant for superfluid 3He-B and quantum phase transitions
• Topological invariants for Standard Model: from semi-metal to topological insulator
• Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases
• Is a color superconductor topological?
• BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation

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