An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors

Details An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors

2006-09-21

arxiv.org/abs/cond-mat/0609556v1

Phys. Rev. Lett. 99, 037001 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevLett.99.037001

We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D $p_x+ip_y$-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion theory where the first and second components are related by parity reversal and hermitian conjugation.

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