Graphene charge carriers behave as massless Dirac fermions, opening the exciting possibility to observe long-range virtual tunneling of electrons in a solid. In granular metals, electron hops arising from series of virtual transitions are predicted to yield observable currents at low-enough temperatures, but to date experimental evidence is lacking. We report on electron transport in granular graphene films self-assembled by hydrogenation of suspended graphene. While the log-conductance shows a characteristic T -1/2 temperature dependence, cooling the samples below 10â€...K drives a triple crossover: a slope break in log-conductance, simultaneous to a substantial increase in magneto-conductance and onset of large mesoscopic conductance fluctuations. These phenomena are signatures of virtual transitions of electrons between distant localized states, and conductance statistics reveal that the high crossover-temperature is due to the Dirac nature of granular graphene charge carriers.
Bibliographical noteFunding Information:
We thank A.H. Castro Neto, V. Pereira, M.A. Cazalilla and J. Martin for helpful discussions. This work was supported by the Singapore Millennium Foundation-NUS Research Horizons award (R-144-001-271-592; R-144-001-271-646), and NUS-YIA (R144-000-283-101).
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