Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional Renormalization Group calculation with high wavevector resolution

TL;DR

This paper uses a high-resolution functional Renormalization Group approach to study competing electronic instabilities in extended Hubbard models on the honeycomb lattice, revealing various charge and spin orderings and their dependence on interaction range.

Contribution

It introduces a highly resolved fRG scheme to analyze wavevector-dependent interactions, uncovering new incommensurate charge density waves and stability conditions in honeycomb lattice models.

Findings

Anti-ferromagnetic spin density wave for dominant on-site repulsion

Charge order with different modulations for extended interactions

Suppression of charge order and stabilization of semi-metallic state with realistic Coulomb potentials

Abstract

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution.