Ground state phase diagram of bilayer graphene within mean-field theory

Abstract

In uniform electron gas, correlation effects become dominant when electron-electron interaction dominates over the kinetic energy at low electron densities. Similar phenomenon could be seen in other systems. In this project, an algorithm is proposed to apply the Hartree-Fock method to the four-band description of bilayer graphene, focusing on how the spin and valley degrees of freedom are occupied in the ground state. A polarization map is used to visualize the occupation of different flavors. Then by establishing the relation between total carrier density and Fermi energy, we can inversely determine the occupation of each flavor at a given carrier density. After that, a self-consistent calculation is applied. The complete procedure will continue until they converge. At last, the ground state energy can be calculated and extracted from the (V , S) polarization map. Our work reveals that there is a phase transition from a polarized ground state at low densities to a spin-valley unpolarized ground state at high densities.