Pseudo-spin Winding Number in Hydrogenated Graphene

The quantum Hall effect (QHE) has been previously observed in highly resistive hydrogenated graphene, with an estimated hydrogen coverage up to 0.1\% that is sufficient to impart strongly insulating behaviour in zero magnetic field [1]. The opening of an impurity induced gap in graphene upon hydrogenation is anticipated to break local sub-lattice symmetry, and it may thus alter the Berry phase of Shubnikov-de Haas (SdH) oscillations and lead to a different Landau level (LL) sequence. Here we report the observation of SdH oscillations in a magnetic field up to 55 Tesla in graphene samples hydrogenated to different degree. The low temperature electron mobility ranges from $\sim$1 $cm^2/V.s$ to $\sim$1000 $cm^2/V.s$. Analysis of SdH oscillation frequency in 1/B indicates that the LL sequence remains four-fold degenerate. We also observe the $\nu=2$ Hall plateau in all samples. We therefore conclude that the topological part of the Berry phase, meaning the pseudo-spin winding number that determines the LL sequence [2], is preserved in hydrogenated graphene. \\[4pt] [1] J. Guillemette et al, PRL 110, 176801 (2013).\\[0pt] [2] J.N Fuchs et al Eur. Phys. J. B 77, 351-362 (2010).