Fidelity in topological superconductors with end Majorana fermions

Fidelity and fidelity susceptibility are introduced to investigate the topological superconductors with end Majorana fermions. A general formalism is established to calculate the fidelity and fidelity susceptibility by solving Bogoliubov-de Gennes equations. Both clean and disordered systems are studied within this formalism, and the results show that the fidelity susceptibility serves as a valid indicator for the topological quantum phase transition which signals the appearance of Majorana fermions. Our study provides a useful tool to investigate the topological quantum phase transition in superconductors, which is helpful to find topological phases in various systems.