Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $Z_2$ index for gapless fermionic modes in the vortex core of three
  dimensional paired Dirac fermions   We consider the gapless modes along the vortex line of the fully gapped,
momentum independent paired states of three-dimensional Dirac fermions. For
this, we require the solution of fermion zero modes of the corresponding
two-dimensional problem in the presence of a point vortex, in the plane
perpendicular to the vortex line. Based on the spectral symmetry requirement
for the existence of the zero mode, we identify the appropriate generalized
Jackiw-Rossi Hamiltonians for different paired states. A four-dimensional
generalized Jackiw-Rossi Hamiltonian possesses spectral symmetry with respect
to an antiunitary operator, and gives rise to a single zero mode only for the
{\em odd vorticity}, which is formally described by a $Z_2$ index. In the
presence of generic perturbations such as chemical potential, Dirac mass, and
Zeeman couplings, the associated two-dimensional problem for the odd parity
topological superconducting state maps onto {\em two} copies of generalized
Jackiw-Rossi Hamiltonian, and consequently an odd vortex binds two Majorana
fermions. In contrast, there are no zero energy states for the topologically
trivial $s$-wave superconductor in the presence of any chiral symmetry breaking
perturbation in the particle-hole channel, such as regular Dirac mass. We show
that the number of one-dimensional dispersive modes along the vortex line is
also determined by the index of the associated two-dimensional problem. For an
axial superfluid state in the presence of various perturbations, we discuss the
consequences of the $Z_2$ index on the anomaly equations.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th