Tight-Binding Model Study of Anti-ferromagnetic Order in AA-Stacked Bi-layer Graphene

Abstract

We address here the anti-ferromagnetic order present in AA-stacked bi-layer graphene in a transversely applied electric field. The system is described by kinetic energy with nearest-neighbor electron hopping with same hopping integral t 1 for both the layers. Besides this, Coulomb interaction exists at A and B sub-lattices with same Coulomb correlation energy. The electron Green’s functions are calculated by Zubarev’s Green’s technique. The temperature-dependent anti-ferromagnetic magnetization is calculated from the Green’s function and is computed numerically and self-consistently. The strong on-site Coulomb interaction stabilizes the anti-ferromagnetic order in graphene. We assume that the electron spin at A site in the first layer is directed in the opposite direction to that of A site electron in the second layer. Similar spin order is observed for electrons in B site atom in reversed order. It is observed that anti-ferromagnetic (AFM) magnetization in the first layer nearly remains constant up to certain temperature and then increases with temperature, while the AFM magnetization in the second layer remains nearly constant and then rapidly decreases with temperature. The net AFM magnetization in bi-layer graphene remains constant and then rapidly increases with temperature. The evolution of the AFM magnetization is studied by varying transverse electric field, Coulomb energy, and temperature.