Chiral Majorana hinge modes on a curved surface with magnetic impurities

Chiral Majorana one-dimensional modes have been proposed as they key component for topological quantum computing. In this study, we explore their potential realization as hinge modes in higher-order topological superconductors. To create such phases, we engineer a sign-changing, time-reversal symmetry-breaking mass term through an ensemble of magnetic impurities on the surface of a sphere. The magnetization of this ensemble arises from the competition between the external magnetic field and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction among the impurities, mediated by the surface Majorana modes. We determine the magnetic phase diagram and identify the optimal magnetic field to minimize orbital effects and induce a sign changing mass term. This term opens a gap in the surface spectrum, resulting in a gapless one-dimensional chiral Majorana mode along the nodal line of the mass term, thereby implementing a second-order topological superconductor.