Fidelity as a marker of topological phase transitions in 2D Dirac materials

Abstract

Silicene, as other 2D buckled structures, is a gapped Dirac material with intrinsic spin-orbit coupling whose band structure can be controlled by applying a perpendicular electric field. It presents a topological phase transition from a topological insulator to a band insulator at the charge neutrality point. We present in this article a characterization of this phase transition by using fidelity of Loschmidt echoes when a magnetic and two slightly different electric fields are applied by considering the time evolution of two kinds of wave packets, one with a single Gaussian profile and the other with a double Gaussian profile creating a cat state. We also show that Zitterbewegung, classical, and revival Loschmidt periods diverge close to but not exactly at the charge neutrality point and explain this behavior.