Dimensional tuning of Majorana fermions and real space counting of the Chern number

Abstract

We demonstrate that it is possible to use atomic manipulation techniques to adiabatically tune between one-dimensional and two-dimensional topological superconductors in magnet-superconductor hybrid (MSH) structures. This allows one to change the nature of the associated Majorana fermions between localized bound states and chiral Majorana edge modes, and provides a new approach for counting the topological invariant of the system-the Chern number-in real space. Moreover, we show that the topological nature of finite-size MSH structures can be characterized using the Chern number density which adiabatically connects MSH structures to macroscopic, translationally invariant topological supercon..