Abstract:

In fractional quantum Hall systems, it is topological degeneracy is determined by the fractional statistics. I will first discuss the simplest non-Abelian statistics through the physics of spinless p+ip superconductor. Then I will show how the topological degeneracy is determined by the non-Abelian statistics and is thus a signature of it. I will also proved an explanation through the physics of spinless BCS superconductor.
Lastly, I will discuss topological degeneracy in the Moore-Read quantum Hall state which has the same class of non-Abelian statistics. I will point out both similarities and differences in comparison with the spinless p+ip superconductor.