Electron-phonon coupling in graphene antidot lattices: An indication of polaronic behavior

We study graphene antidot lattices—superlattices of perforations (antidots) in a graphene sheet—using a model that accounts for the phonon modulation of the $\pi$-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semiempirical methods. Based on the adopted model, we quantify the nature of charge carriers in the system by computing the quasiparticle weight due to the electron-phonon interaction for an excess electron in the conduction band. We find a very strong phonon-induced renormalization, with the effective electron masses exhibiting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of transport in graphene antidot lattices.

Figure 1

(a) A segment of a triangular graphene antidot lattice with circular antidots and basis vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$. The lattice period is $\left|{\mathbf{a}}_1\right|=\left|{\mathbf{a}}_2\right|=La\sqrt{3}$. (b) unit cell of an antidot lattice, with vectors ${\mathit{\delta }}_1$, ${\mathit{\delta }}_2$, and ${\mathit{\delta }}_3$ specifying positions of the nearest neighbors of a carbon atom on sublattice $A$.

Figure 2

The conduction-band dispersion ${\epsilon }_c\left(\mathbf{k}\right)$ for the {17, 5} antidot lattice. The inset shows the $L$-dependence $\left(9\le L\le 17\right)$ of the conduction bandwidth $W_c$ for $R=5$.

Figure 3

The phonon density of states for the {17, 5} antidot lattice, obtained using the 4NNFC (solid line) and VFF (dashed line) methods.