Effective response theory for zero energy Majorana bound states in three spatial dimensions

Abstract

We propose a gravitational response theory for point defects (hedgehogs) binding Majorana zero modes in (3+1)-dimensional superconductors. Starting in 4+1 dimensions, where the point defect is extended into a line, a coupling of the bulk defect texture with the gravitational field is introduced. Diffeomorphism invariance then leads to an $SU(2{)}_2$ Kac-Moody current running along the defect line. The $SU(2{)}_2$ Kac-Moody algebra accounts for the non-Abelian nature of the zero modes in 3+1 dimensions. It is then shown to also encode the angular momentum density which permeates throughout the bulk between hedgehog-anti-hedgehog pairs.

7 pages, 3 figures

References in corpus (5)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Axion topological field theory of topological superconductors