Majorana edge states and topological properties in 1D/2D Rashba semiconductor proximity coupled to iron-based superconductor

We study Majorana edge states and their topological properties of one-dimensional(1D) and two-dimensional(2D) Rashba semiconductor deposited on iron-based superconductor under the applied Zeeman field for various directions. Using the recursive Green's function method, we calculate the local density of states(LDOS) both for $s_{\pm}$ and $s_{++}$-wave pairings. We elucidate that it shows anisotropic response to the applied Zeeman field specific to Majorana edge states. This anisotropy can be understood by the winding number, which shows whether the present system is topological or not. The resulting LDOS and winding numbers for $s_{\pm}$ and $s_{++}$-wave pairings are significantly different at the lower Zeeman field. These results serve as a guide to determine the pairing symmetry of iron-pnictide.

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