Interplay of Kekul\'{e} bond order and lattice instability in $\mathrm{C}_6\mathrm{Li}$

TL;DR

This paper explores how charge order and lattice instability interact in the novel material C6Li, revealing mechanisms behind Kekulé bond order and lattice distortion driven by electronic interactions and electron-phonon coupling.

Contribution

It introduces C6Li as a new platform to study charge order mechanisms and their relationship with lattice distortions in quantum materials.

Findings

Kekulé bond order is driven by hybridization between carbon and lithium orbitals.

Lattice distortion is induced via electron-phonon coupling.

Fermi surface nesting stabilizes Kekulé bond order in certain limits.

Abstract

Understanding the interplay between charge order and lattice instability in quantum materials remains a central challenge, as their coexistence often obscures causal relationships. This work introduces $\mathrm{C}_6\mathrm{Li}$ as a novel platform to investigate charge order mediated by two distinct mechanisms. We show that the hybridization between carbon $\pi$ and lithium $s$ orbitals generates an effective long-range hopping within Li-centered hexagons. This hopping drives a Kekul\'{e} bond order, whose structure varies with charge density and the sign of the hopping. This bond order induces a Kekul\'{e} lattice distortion via electron-phonon coupling. In the limit where lithium atoms are distant from the graphene layer, a Fermi surface nesting-driven Kekul\'{e} bond order emerges, stabilized by the electron-phonon interaction. Our results establish $\mathrm{C}_6\mathrm{Li}$ as a tunable platform for elucidating the causal hierarchy between electronic and structural orders in quantum materials.