Electronic Transport in Graphene with Aggregated Hydrogen Adatoms

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Such spatial correlation is found to strongly influence the electronic transport properties of disordered graphene. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration $x^{\star }$, which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations.

Figure 1

(a) Atomic structure of a hydrogen adatom covalently bound to graphene. (b) Structures of small clusters of hydrogen adatoms used for fitting the pair potential of Eq. (1). (c) Predicted energy $\tilde{E}$ of aggregation of hydrogen adatoms as a function of aggregation energy $E_{\mathrm{DFT}}$ calculated from first principles for the set of adatom clusters shown in (b).

Figure 2

Representative configurations of (a) randomly distributed and (b) correlated hydrogen adatoms on graphene at $x=5\%$ concentration. (c) Comparison of random and correlated adatoms cluster size distributions $P(x)$ at $x=5\%$ concentration. (d) Cluster size distributions $P(x)$ of correlated hydrogen adatoms at different concentrations. All correlated configurations are obtained by means of Monte Carlo simulations carried out at $T=300\mathrm{K}$.

Figure 3

Density of states of graphene in the presence of (a) randomly distributed and (b) correlated hydrogen adatoms at different concentrations. Local density of states on carbon atoms in the vicinity of (c) an isolated hydrogen adatom and (d) a dimer of hydrogen adatoms. In panels (c) and (d) LDOS referred to as “analyt.” have been obtained using the analytical Green’s function calculations [45].

Figure 4

(a),(b) Averaged conductivity $g_{\text{typ}}$ for the random and correlated adatoms distributions, respectively, as a function of scattering region length $L$ at different energies $E$ and at $x=5\%$ concentration. (c),(d) Conductivity $g$ as a function of energy $E$ calculated using the kernel polynomial method for both adatom distributions at concentration $x=0.5\%$ and $x=5.0\%$, respectively. The dashed lines show the minimum conductivity $g=4/\pi$.

Figure 5

(a) Localization length ${\xi }_{\text{loc}}$ as a function of charge-carrier energy $E$ for the case of random and correlated adatom distribution at $x=5\%$. (b) Charge-carrier localization length ${\xi }_{\text{loc}}$ at low energy ($E=10^{-3}t=2.7\mathrm{meV}$) as a function of simple concentration $x$ and effective concentration $x^{\star }$ for the random and correlated distributions.