Dimensional Tuning of Majorana Fermions and the Real Space Counting of the Chern Number

TL;DR

This paper presents a method to tune between different topological superconductors using atomic manipulation, enabling real-space counting of the Chern number and advancing the study of Majorana fermions.

Contribution

It introduces a novel approach to adiabatically tune topological phases in magnet-superconductor hybrid structures and to measure the Chern number in real space.

Findings

Adiabatic tuning between 1D and 2D topological superconductors is demonstrated.

Real-space counting of the Chern number is achieved through atomic manipulation.

Topological nature of finite-size structures characterized by Chern number density.

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 superconductors characterized by an integer Chern number. These results open new possibilities for studying the nature of topological superconductivity in MSH structures using atomic manipulation techniques.