Fate of the Resonating Valence Bond in Graphene

We apply a variational wave function capable of describing qualitatively and quantitatively the so-called ”resonating valence bond” (RVB) in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekulé and Dewar contributions to the chemical bond of the benzene molecule and establish the corresponding RVB energy of these structures ($\simeq 0.01\mathrm{eV}/\mathrm{atom}$). We apply this method to unveil the nature of the chemical bond in undoped graphene, providing an estimate of the RVB energy gain, and show that this picture remains only within a small ”resonance length” of a few atomic units.

Figure 1

2D plot of the AGP pairing function restricted to the molecular orbitals above the HOMO. Color scale in arbitrary units. The arrow indicates the reference position $r_{\uparrow }$ fixed on an atom, colored in red for the sake of clarity.

Figure 2

2D plot of the AGP pairing function for a graphene layer of 48 C atoms restricted to the molecular orbitals above the HOMO (VPPF). Color scale in arbitrary units. The arrow indicates the reference atom.

Figure 3

Ratio between the $s$-wave and the $d$-wave weight in the JAGP WF for the ${\mathrm{CaCuO}}_2$ parent compound of the high-temperature cuprate superconductor ($2\times 2$ supercell).

Figure 4

(a) RVB energy per atom for the graphene layer, as a function of the number of atoms in the supercell ($\Gamma$ point). (b) Ratio of the LUMO/HOMO weight in the AGP, a measure of the RVB character of the bond. Lines are guides to the eye.