Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions

摘要

We report on Hybrid-Monte-Carlo simulations of the tight-binding model withlong-range Coulomb interactions for the electronic properties of graphene. Weinvestigate the spontaneous breaking of sublattice symmetry corresponding to atransition from the semimetal to an antiferromagnetic insulating phase. Ourshort-range interactions thereby include the partial screening due to electronsin higher energy states from ab initio calculations based on the constrainedrandom phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106},236805 (2011)]. In contrast to a similar previous Monte-Carlo study[M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we alsoinclude a phenomenological model which describes the transition to theunscreened bare Coulomb interactions of graphene at half filling in thelong-wavelength limit. Our results show, however, that the critical couplingfor the antiferromagnetic Mott transition is largely insensitive to thestrength of these long-range Coulomb tails. They hence confirm the predictionthat suspended graphene remains in the semimetal phase when a realistic staticscreening of the Coulomb interactions is included.