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Nuclear Tunnelling and Dynamical Jahn-Teller Effect in Graphene with Vacancy

We show that the substitutional vacancy in graphene forms a dynamical Jahn-Teller center. The adiabatic potential surface resulting from the electron-lattice coupling was computed using density-functional methods and subsequently the Schrödinger equation was solved for the nuclear motion. Our calculations show a large tunnelling splitting $3 Γ$ of about 86 cm$^{-1}$. %, which is large as compared to the typical strain splitting. The effect results in a large delocalization of the carbon nuclear wave functions around the vacancy leading to a significant broadening of the Jahn-Teller active $sp^2σ$ electron states. The tunnelling splitting should be observable in electron paramagnetic resonance and two-photon resonance scattering experiments.