ABSTRACT - DRUM - University of Maryland

This conclusion can be generalized to the case where multiple vortices are present.
In that case the right hand side is basically the sum of vorticities of all vortices.
The index theorem (3.37) requires chiral symmetry which is broken by presence
of a finite chemical potential µ ≠ 0. Now we argue that when chiral symmetry is
broken the Majorana zero modes admit a Z 2 classification corresponding to evenodd
number of zero energy solutions. Generally speaking, a small chiral symmetry
breaking term cause coupling between zero modes and split them away from zero
energy. However, due to particle-hole symmetry, the number of zero modes that are
split by chiral symmetry breaking term must be even. So the parity of the topological
index is preserved in the generic case. This is consistent with an explicit solutions
of zero mode in TI/SC heterostruture with finite chemical potential.
Thus, we
conclude that without chiral symmetry the Majorana zero modes bound to vortices
are classified by Z 2 corresponding to even or odd number of zero modes.
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