Theoretical study of the dynamics of atomic hydrogen adsorbed on graphene multilayers

We present a theoretical study of the dynamics of H atoms adsorbed on graphene bilayers with Bernal stacking. First, through extensive density functional theory calculations, including van der Waals interactions, we obtain the activation barriers involved in the desorption and migration processes of a single H atom. These barriers, along with attempt rates and the energetics of H pairs, are used as input parameters in kinetic Monte Carlo simulations to study the time evolution of an initial random distribution of adsorbed H atoms. The simulations reveal that, at room temperature, H atoms occupy only one sublattice before they completely desorb or form clusters. This sublattice selectivity in the distribution of H atoms may last for sufficiently long periods of time upon lowering the temperature down to $0{}^{\circ }\mathrm{C}$. The final fate of the H atoms, namely, desorption or cluster formation, depends on the actual relative values of the activation barriers which can be tuned by doping. In some cases, a sublattice selectivity can be obtained for periods of time experimentally relevant even at room temperature. This result shows the possibility for observation and applications of the ferromagnetic state associated with such distribution.

Figure 1

Binding energy of a H atom on top a C atom in monolayer graphene (a $4\times 4$ supercell) as a function of the distance to the graphene plane. Blue dots correspond to a standard GGA functional while black ones correspond to the vdW-DF, as explained in the text.

Figure 2

Atomic structure of H on bilayer graphene. $\alpha$ (a) and $\beta$ (b) sites top view and $\alpha$ (c) and $\beta$ (d) sites side view detail.

Figure 3

Binding energy curves for a H atom adsorbed on the $\alpha$ (red) and $\beta$ (blue) sites of a bilayer graphene surface (a $4\times 4$ supercell).

Figure 4

Detail of the physisorption binding energy curve for a H atom on top a C atom $(\beta$ site), on hollow, and on bridge position for a bilayer graphene (a $4\times 4$ supercell).

Figure 5

Binding energy of a H atom on bilayer graphene placed along the bond that links the $\alpha$ site to the $\beta$ site for a $4\times 4$ supercell. Despite the appearances, the crossing point is not a saddle point (see lower insets and see text). The true saddle point is depicted with a black dot and the associated structure is shown in the upper inset. (In all insets, the bottom layer is not shown for clarity.)

Figure 6

Time evolution of the relative abundance of H atoms adsorbed on the two graphene sublattices for an initial concentration $C=0.005$ and two representative temperatures (a) $T=300$ and (b) 273 K. Solid lines correspond to isolated H atoms, while dashed and dotted lines correspond to H atoms forming part of dimers (or clusters) through short or long bonds, respectively (see text for a detailed explanation of these two types of bonds). Black solid line refers to desorbed atoms.

Figure 7

Same as in Fig. 6, but only at room temperature for (a) $C=0.0025$ and (b) $0.0125$.

Figure 8

Same as Fig. 6, but for a hole-doped bilayer. The carrier concentration $p$ has been chosen as to make equal the desorption and migration barriers. The H concentration is $C=0.005$ and the temperature is (a) 300 and (b) 273 K.

Figure 9

Same as Fig. 8, but for a larger carrier concentration $p$, which increases even further the desorption barriers and decreases the migration barriers. Two different temperatures are shown: (a) $T=300$ and (b) 273 K. The concentration of H has been here set to $C=0.0066$.