Majorana Fermions and Non-Abelian Statistics in Three Dimensions

Understand

We show that three dimensional superconductors, described within a Bogoliubov de Gennes framework can have zero energy bound states associated with pointlike topological defects.

• The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions.
• This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations.
• A new feature of three dimensional systems is that there are "braidless" operations in which it is possible to manipulate the groundstate associated with a set of defects without moving or measuring them.