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Pairing symmetry and vortex zero-mode for superconducting Dirac fermions

We study the vortex zero-energy bound states in presence of pairing among the low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the $s$-wave, $p$-wave, and, in particular, the mixed-parity symmetry, which arises in absence of the inversion symmetry on the surface. The zero-mode is analyzed within the generalized Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass-term, and includes the effects of the electromagnetic gauge field and the Zeeman coupling as well. At a finite chemical potential, as long as the spectrum without the vortex is fully gapped, the presence of a single Fermi surface with a definite helicity always leads to one Majorana zero-mode, in which both electron's spin projections participate. In particular, the critical effects of the Zeeman coupling on the zero-mode are discussed.