Topological phases and tunable Majorana zero modes in Rashba superconducting systems in the presence of Zeeman field

Abstract

In the framework of the extended Bogoliubov-de Gennes theory, topological phase transitions and Majorana zero modes are investigated by diagonalizing the tight-binding model Hamiltonian for two-dimensional superconducting systems with Rashba spin-orbit coupling and spin correlations when the effect of Zeeman field is involved. With increasing the Zeeman-field strength, the first-order topological superconductivity and chiral Majorana edge modes may develop for the long Rashba superconducting stripe under appropriate chemical potential. Moreover, the second-order topological phase can be found for the Rashba loop-frame geometry. Relying on the chosen chemical potential near half filling, Majorana zero-energy states located at corners of the square loop are more feasible in the weak exchange-field regime. Particularly, the transitions between Majorana edge and corner modes can take place in the loop system when the field strength is varied. In addition, the number and location of robust Majorana corner modes are highly sensitive to the introduced surface defects. Our theoretical predictions may provide useful guidance for observing and tuning Majorana zero modes in future experiments and applications.