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

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 $π$ and lithium $s$ orbitals generates an effective long-range hopping within Li-centered hexagons. This hopping drives a Kekulé bond order, whose structure varies with charge density and the sign of the hopping. This bond order induces a Kekulé lattice distortion via electron-phonon coupling. In the limit where lithium atoms are distant from the graphene layer, a Fermi surface nesting-driven Kekulé 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.

Figures (4)

• Figure 1: (a) The honeycomb lattice. (b) The nearest-neighbor (NN) charge bond $B_\gamma$ on the honeycomb lattice for $n=2/3$ and $t^\prime=0.3t$. (c) The NN charge bond on the honeycomb lattice for $n=2$ and $t^\prime=0.3t$. (d) The NN charge bond on the honeycomb lattice for $n=2/3$ and $t^\prime=-0.3t$. (e) The NN charge bond on the honeycomb lattice for $n=2$ and $t^\prime=-0.3t$. (f) The Kekulé bond order $\Delta$ as a function of density $n$ at $t^{\prime}=0.3t$. (g) The Kekulé bond order $\Delta$ as a function of density $n$ at $t^{\prime}=-0.3t$.
• Figure 2: (a) The spectral function along the high-symmetry path for $t^\prime=0.05t$. (b) The spectral function along the high-symmetry path for $t^\prime=0.3t$. (c) The spectral function for $t^\prime=0.05t$ along the $M_1$-$\Gamma$-$M_3$ path. (d) The spectral function for $t^\prime=0.05t$ along the $K_5$-$\Gamma$-$K_2$ path. (e) The Fermi surface at $n=2$ and $t^\prime=0.05t$. (f) The Fermi surface at $n=2/3$ and $t^\prime=0.05t$. (g) The phase transition between the metallic and insulating Kekulé bond orders as a function of $t^\prime$ at $n=2/3$.
• Figure 3: Lattice distortion at $n=2$ and $n=2/3$ for $t^\prime=0.2t$. (a),(b) Lattice distortion patterns in the honeycomb lattice, where both A and B sublattices are allowed to move. (c),(d) Lattice distortion patterns in the honeycomb lattice, where only the A sublattice is allowed to move. (e) The projected displacement as a function of density $n$ at $g=1$, $t^\prime=0.2t$, and $\beta=10t$. (f) The Kekulé bond order as a function of density at $t^\prime=0.2t$ and $\beta=10t$. The phonon frequency is set as $\Omega=t$.
• Figure 4: Bond correlation functions $\chi_b(K)$ at the K momentum point for (a) $g=1$ and (b) $g=2$. The correlation length $\xi_b$ of $\chi_b(k)$ for (c) $g=1$ and (d) $g=2$. The phonon frequency is set as $\Omega=t$, and the charge density $n$ is 2/3. The dashed curves are guides to the eye.