Guo-Qiao Zha, Lucian Covaci, F. M. Peeters, and Shi-Ping Zhou, Phys. Rev. B 90, 014522 (2014)
We found that the energy spectrum splits when the SO interaction is involved and the Majorana zero mode can be realized in the  edges of square systems for an appropriate SO coupling strength. Superconducting phase transitions appear when the energy gap closes, accompanied by energy jumps between different energy parabolas in the ground state, which provides a possible mechanism to support fractional flux periodicity of supercurrent..