Tunable second-order topological insulators in Chern insulators 2H-Fe X 2 ( X   =  Cl and Br)

Engineering topological states in two-dimensional (2D) magnets is of pivotal importance to provide significantly rich physics and application potential. Here, we theoretically demonstrate that the second-order topological insulators (SOTIs) with robust nontrivial corner states can be realized in Chern insulators via the widely used strain engineering. The quantum anomalous Hall effect in Chern insulators of honeycomb 2H-FeX2 (X = Cl and Br) is revealed with a nonzero Chern number C=1 and the emergence of metallic chiral edge states. Remarkably, under compressive or tensile strains, topological phase transitions are proposed with the gap-closing in different valleys, giving birth to the 2D SOTIs or trivial insulating 2D magnets. Moreover, large valley polarizations are clearly shown. Our findings open up a promising way for exploring the first- and higher-order topology with intriguing effects.