Majorana zero modes in the ferromagnet-superconductor-ferromagnet and superconductor-ferromagnet-superconductor heterostructures
Chien-Te Wu1*, Shao-Hung Huang1
1Electrophysics, National Chiao Tung University, Hsinchu, Taiwan
* Presenter:Chien-Te Wu,
In this work, we focus on the emergence of Majorana zero modes in heterostructures composed of superconducting and ferromagnetic materials. In previous studies, scientists have found that Majorana zero modes emerge with the following ingredients: a conventional s-wave superconductor coupled with non-superconducting materials via superconducting proximity effects, spin polarization, and appropriate spin-orbit coupling in the heterostructure. Furthermore, the emergence of Majorana zero modes is associated with a topological phase which may exhibits a 4π periodic Josephson effect when the heterostructure is of a Josephson junction type. In the work, we numerically calculate Bogoliubov-de Gennes equation suitable for our system. For the first part, we construct a target model by combining two ferromagnetic materials with a conventional superconductor. The ferromagnetic regions we consider here is described by a conical exchange interaction which can be shown to be equivalent to the combination of a constant Zeeman field and one-dimensional spin-orbit coupling. We vary the direction of the conical axes and the strength of Zeeman field for both ferromagnetic regions to study the stability of the topological properties of our system. For the second part, we turn our attention to a trilayer consisting of two superconductors and a conical ferromagnet in the geometry of a conventional Josephson junction. By choosing appropriate parameters, the Josephson junction can host Majorana zero modes. We change the relative phase of the order parameter between two superconductors. As the relative phase is tuned to π, the Majorana zero modes is suppressed. Therefore, when we tuned the relative phase from 0 to π, the system undergoes a single topological phase transition. As a result, this system displays 2π periodic physical phenomena.

Keywords: proximity effects, Majorana zero modes, spin-orbit interaction, Josephson junctions