Magnetically controlled topological braiding with Majorana corner states in second-order topological superconductors

We theoretically investigate the electronic properties of finite-sized (e.g., triangular and diamond-shaped) Kane-Mele-type topological insulator nanoflakes on top of an s-wave superconductor. We find that the second-order topological superconductor can be generated when the magnetism is only applied on the system boundaries, which host two Majorana corner states located at the corners of two neighboring boundaries. By tuning the applied boundary magnetism, we observe that two isolated Majorana corner states can be adiabatically moved along the system boundaries. Furthermore, we show the possibility of performing topological quantum braiding of the Majorana corner states towards the far-reaching implications of quantum information and quantum computation.