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Topological quantum phase transitions in topological insulator thin film

Topological quantum phase transition in electron gas systems is an enthralling phenomena. This phase transition has a unique property in that it is associated with a quantum phase transition point, which separates different regions with gapped phases, characterized by an immutable topological quantity called the Chern number. In this paper, we study a tight binding model for a three-dimensional topological insulator $(TI)$ thin film that captures different topological quantum phase transitions in the entire Brillouin zone. We investigate the effects of a staggered magnetic field, an off-diagonal coupling term, and a Rashba spin-orbit coupling $(SOC)$ on the topological insulator thin film model. We give a lucid exposition of the topological phases by exploring all the topological properties of this system in the entire Brillouin zone, as a function of the competing interactions. We find that the system exhibits quantum spin Hall $(QSH)$ phase, quantum anomalous Hall $(QAH)$, semi-metallic phase, and an ordinary insulator phase. The transition from one phase to another is invariably associated with a gap closing point. We further corroborate our results by solving for the edge states modes of the system.