Influence of disorder on the magnetism of graphene bilayers

We numerically calculate the impact of site-energy disorder on the magnetism of biased bilayer graphene formed with the Bernal stacking. By using the mean-field method, we approximately solve the Hubbard Hamiltonian and calculate the average magnetization of the two layers, which indicates that the disorder does not change the nature of the first-order phase transition between paramagnetism and ferromagnetism, but may increase the critical interaction strength U_c of the Hubbard Hamiltonian for the system to become the ferromagnetic phase. We also calculate the dependencies of relevant physical quantities on temperature. The implications of the results are discussed.