Instabilities on graphene's honeycomb lattice with electron-phonon interactions

TL;DR

This paper investigates how electron-phonon interactions influence electronic instabilities and competing orders in graphene's honeycomb lattice using a functional renormalization group approach, revealing favored bond orderings and effects on density wave phases.

Contribution

It introduces a momentum-resolved functional renormalization group analysis of phonon-mediated interactions on graphene, highlighting their role in stabilizing certain bond orderings and modifying electronic phase boundaries.

Findings

Kekulé and nematic bond orderings are favored over s-wave superconductivity.

Phonon interactions suppress competing orders and extend spin density wave regimes.

Repulsive interactions between phonons at different wavevectors influence ordering tendencies.

Abstract

We study the impact of electron-phonon interactions on the many-body instabilities of electrons on the honeycomb lattice and their interplay with repulsive local and non-local Coulomb interactions at charge neutrality. To that end, we consider in-plane optical phonon modes with wavevectors close to the $\Gamma$ point as well as to the $K, -K$ points and calculate the effective phonon-mediated electron-electron interaction by integrating out the phonon modes. Ordering tendencies are studied by means of a momentum-resolved functional renormalization group approach allowing for an unbiased investigation of the appearing instabilities. In the case of an exclusive and supercritical phonon-mediated interaction, we find a Kekul\'e and a nematic bond ordering tendency being favored over the $s$-wave superconducting state. The competition between the different phonon-induced orderings clearly shows a repulsive interaction between phonons at small and large wavevector transfers. We further discuss the influence of phonon-mediated interactions on electronically-driven instabilities induced by onsite, nearest neighbor and next-to-nearest neighbor density-density interactions. We find an extension of the parameter regime of the spin density wave order going along with an increase of the critical scales where ordering occurs, and a suppression of competing orders.