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arXiv · 1404.6379

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

Laura Classen·Michael M. Scherer·Carsten Honerkamp
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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 $Γ$ 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.

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Laura Classen, Michael M. Scherer, Carsten Honerkamp. 2014-04-25. Instabilities on graphene's honeycomb lattice with electron-phonon interactions. https://doi.org/10.1103/physrevb.90.035122

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