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({{boldsymbol{gamma }}}^{{boldsymbol{dagger }}}{boldsymbol{(}}{bf{k}}{boldsymbol{)}}{boldsymbol{=}}{boldsymbol{gamma }}{boldsymbol{(}}{bf{k}}{boldsymbol{)}}) is similar to that of the Majorana fermions (MFs) ({{boldsymbol{gamma }}}^{{boldsymbol{dagger }}}={boldsymbol{gamma }}). 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.
Highlights
Some experiments demonstrating the synthetic spin-orbit coupling (SOC) interaction in ultracold Fermi gases have stimulate a lot of interest in researching topological properties of ultracold atoms[30,31]
By increasing the SOC interaction strength, we find that the Majorana type Kramers Doublet (MTKD) or a single MTZF appears at each edge in the superfluid when the system is under the open edge condition
We show that a MTKD appears at each edge of the topological superfluid (TS)
Summary
Some experiments demonstrating the synthetic SOC interaction in ultracold Fermi gases have stimulate a lot of interest in researching topological properties of ultracold atoms[30,31]. Only lifting the spin degeneracy cannot realize MTKD or a single MTZF at each edge in the d–wave superfluid (Fig. 2(c)). Inspired by this result, we consider to lift the Dirac Cones degeneracy with the nearest neighbor hopping matrix. We map our d–wave superfluid Hamiltonian into the widely known spin-triplet chiral p–wave superconductor model This mapping is helpful to intuitively understand the origin of the topological order presented above.
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