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Based on the full Hamiltonian of bilayer graphene, phase transitions arerealized by the change of the in-plane magnetic field and the electrical biasin bilayer graphene. We show that the engineering of Chern numbers of fourbands is possible by an applied in-plane magnetic field and an electrical biasin bilayer graphene. Our results are promising for the exploration of newtopological phenomena in 2D materials.

Engineering of Chern number of topological bands in bilayer graphene by in-plane magnetic field and electrical bias