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

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 Kekulé 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.

9 pages, 5 figures

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Cited by in corpus (15)

• Ising and Gross-Neveu model in next-to-leading order
• Gauge-field-assisted Kekulé quantum criticality
• Triggering a global density wave instability in graphene via local symmetry-breaking
• Reference results for the momentum space functional renormalization group
• Magnetism and charge order in the honeycomb lattice
• Momentum dependence of quantum critical Dirac systems
• divERGe implements various Exact Renormalization Group examples
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
• Optoelectronic Fingerprints of Interference between Different Charge Carriers in Graphene Superlattices and Analogies to Twisted Graphene Bilayers
• Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger Model and its relevance to Graphene
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Kohn-Luttinger-like mechanism for unconventional charge density waves
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials