Abstract We explore the topological phase, which involves Majorana type topological zero mode fermions (MTZFs) at the edge, using d–wave superfluid with Rashba spin-orbit coupling (SOC) interactions. The self-Hermitian of this MTZF(
γ†(k)=γ(k) γ † ( k ) = γ ( k ) ) is similar to that of the Majorana fermions (MFs) (
γ†=γ γ † = γ ). We show that, to realize a single MTZF at each edge in superfluid with d–wave pairing in a Majorana type Kramers Doublet (MTKD) state, it is important to lift both the spin and the Dirac Cones degeneracies. These non-Abelian anyons obey the non-Abelian statistics which may be useful to realize topological quantum computation. We suggest that the topological feature could be tested experimentally in superfluids of cold fermionic atoms with laser field induced spin orbit interactions. These studies give a new possible way to investigate the MTZFs in a two-dimensional (2D) system as compared to MFs in the one-dimensional (1D) nano-wire and 2D system, and enrich the theoretical research on finding non-Abelian anyons in topological system.
Recently, topological excitations obeying non-Abelian statistics attracted intensive attention because of their exotic statistics and possible applications in topological quantum computation. In this paper, based on a topological s -wave superfluid on a Peierls lattice, we find fractionalized flux and non-Abelian anyons, and then give a realistic proposal to realize the universal topological quantum computation, and especially show how to perform the single-qubit gate–phase-shift gate. Finally, we discuss the experimental realization on optical lattices.