Interaction effects in multilayer graphene

Coulomb repulsion between electrons plays a key role in determining the ground state of multilayer graphene at charge neutrality. In fact, experiments show that the system undergoes a finite-temperature second-order phase transition to a broken symmetry state, which evolves to the ground state at zero temperature. This state is gapped in even multilayers, and ungapped in the odd case. We investigate theoretically the microscopic nature of this phenomenon, adopting a mean-field approach cast in the language of functional integration. We show that this model allows for the broken symmetry state to appear under a critical temperature T_c, reproducing the commonly accepted phenomenological model. This description relies on the appearance at T_c of a mean-field potential that changes sign from one layer to the other, and explains the differences between the even and the odd cases. Due to the poor agreement between the gap estimates from our model and experimental data, we conclude that our theory could be improved by employing a more detailed description of the screening effects, thus leading to a faithful representation of the phenomenon under examinatio