Topological Majorana and Dirac zero modes in superconducting vortex cores

Abstract

We provide an argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem and applies to disordered systems as well. It also provides a new way of understanding the zero modes in the vortex cores of a spinless $p_x+i{p}_y$ superconductor. Applying this approach to superconductors with and without time reversal and spin rotational symmetry, we predict the necessary and sufficient conditions for protected zero modes to exist in their vortices.

5 pages, 1 figure

References in corpus (4)

• Non-Abelian Anyons and Topological Quantum Computation
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors

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