Generalized dynamical mean-field theory of two-sublattice systems with long-range interactions and its application to study charge and spin correlations in graphene

Abstract

We investigate magnetic and charge correlations in graphene by using the formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. First, we map the average non-local interaction onto the effective static interaction between different sublattices, which is treated together with the local interaction within an effective "two-orbital" local model. The remaining part of the non-local interaction is considered by introducing an effective retarded interaction within the E-DMFT approach. The non-local susceptibilities in charge and spin channel are further evaluated in the ladder approximation. We verify the applicability of the proposed method to describe the effect of uniformly screened long-range Coulomb potential $\propto 1/r$, as well as screened realistic long-range electron interaction [T. O. Wehling et al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the developed approach describes a competition of semimetal, spin density wave (SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram is in a good agreement with recent results of functional renormalization group (fRG) for finite large graphene nanoflakes and scaling analysis of quantum Monte Carlo data on finite clusters. Similarly to the previously obtained results within the fRG approach, the realistic screening of Coulomb interaction by $\sigma$ bands causes moderate (strong) enhancement of critical long-range interaction strength, needed for the SDW (CDW) instability, compared to the results for the uniformly screened Coulomb potential.