Fidelity in topological superconductors with end Majorana fermions

Abstract

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. It is shown that the fidelity susceptibility manifest itself as a peak at the topological quantum phase transition point for homogeneous Kitaev wire, thus serves as a valid indicator for the topological quantum phase transition which signals the appearance of Majorana fermions. The effect of disorders is investigated within this formalism. We consider three disordered systems and observe fidelity susceptibility peak in all of them. By analyzing the susceptibility peak, we notice that the local potential disorders and the hopping disorders can shift the phase transition point, while off-diagonal disorders have no obvious influence. Our results confirm that the existence of topological quantum phase transition is robust to these disorders, while the behavior of the phase transition might be influenced by disorders.

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Cited by in corpus (6)

• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Entanglement modes and topological phase transitions in superconductors
• Holographic Complexity and Fidelity Susceptibility as Holographic Information Dual to Different Volumes in AdS
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Exact scaling of geometric phase and fidelity susceptibility and their breakdown across the critical points