Tight-Binding Model Study of the Tunable Anti-ferromagnetism and Electron specific heat of AA-Staked bi-layer Graphene in a Transverse Electric Field

Abstract

We communicate a microscopic theoretical model study of electronic and thermal properties of AA-stacked bi-layer graphene in a transverse electric field. In order to describe the system, we have considered a Hamiltonian consisting of nearest-neighbor electron hopping in both the layers in presence of a transverse electric field between the two layers created by a gate electrode. The inter-layer electron hopping from A1 atom of the first layer to A2 atom of the second layer is considered with a hopping energy εk,⊥=t⊥γ⊥(k). Due to strong on-site Coulomb correlation between the electrons of sub-lattices of both the layers, anti-ferromagnetic order is developed in the system. The electron Green's functions of both sub-lattices in the two layers are solved by Zubarev’s Green's function technique. The anti-ferromagnetic (AFM) gap equation is found from the electron correlations of the corresponding Green’s functions. It is assumed that the A-site magnetization dominates over the B-site magnetization giving rise to the anti-ferromagnetic order. The temperature dependent AFM gap exhibits high Neel’s temperature where electronic specific heat shows a sharp jump. Besides this, the specific heat exhibits another flat peak arising due to the onset of AFM order in A and B sub-lattices of the layer. The evolution of the gap equation and specific heat are reported by varying the model parameters like Coulomb energy, electric field, transverse electron hopping integral and chemical potential.