Ab initio transport fingerprints for resonant scattering in graphene

We have recently shown that by using a scaling approach for randomly distributed topological defects in graphene, reliable estimates for transmission properties of macroscopic samples can be calculated based even on single-defect calculations [A. Uppstu et al., Phys. Rev. B 85, 041401 (2012)]. We now extend this approach of energy-dependent scattering cross sections to the case of adsorbates on graphene by studying hydrogen and carbon adatoms as well as epoxide and hydroxyl groups. We show that a qualitative understanding of resonant scattering can be gained through density functional theory results for a single-defect system, providing a transmission “fingerprint” characterizing each adsorbate type. This information can be used to reliably predict the elastic mean free path for moderate defect densities directly using ab initio methods. We present tight-binding parameters for carbon and epoxide adsorbates, obtained to match the density-functional theory based scattering cross sections.

Figure 1

Two-probe transport geometry consisting of two ideal leads and a central scattering region. The graphene sheet is oriented with the transport along the armchair direction. Upper and lower shadowed (blue/gray) regions indicate the leads. The leftmost adsorbate on the scattering region is on top of a carbon atom and the others show two of the three bridge positions with different orientations with respect to the current.

Figure 2

(a) Ideal electron transmission for a pristine 23-AGNR (dashed line) and transmissions for a 23-AGNR with one hydrogen atom adsorbed on three different locations (solid lines). (b) Scattering cross sections calculated by averaging over all the different adsorbate locations across the ribbon. The vacancy TB model is used. Here and in all the figures below, the Fermi energy is taken to be zero.

Figure 3

(a) Scattering cross sections for a hydrogen atom on AGNRs with different widths. The vacancy TB model is used. (b) Transmission through a 100 nm long 125-AGNR with 0.1$\%$ vacancy defect density. Comparison between results obtained by averaging over an ensemble of 50 samples with random defect locations (thick line) and an estimate from a single defect scattering cross section calculation (thin line). Notice the different energy scales in the two panels.

Figure 4

(a) Scattering cross section for a hydrogen atom on a 23-AGNR. The results of the Anderson impurity hydrogen model with $t_A=-2t$ and $e_A=t/16$ and the vacancy model are shown. (b) Scattering cross section for a hydrogen atom on a bulk geometry from DFT and a 23-AGNR calculated with both the DFT and TB models.

Figure 5

Scattering cross section for a hydrogen atom (dashed line) and a hydroxyl group (solid line) adsorbed on the bulk graphene calculated with DFT. The insets show the corresponding elastic mean free paths for different adatom densities. The scales of the insets have been cut at 1 and 100 nm.

Figure 6

Scattering cross section for an oxygen adatom on bulk graphene (epoxide) averaged over the three different bridge sites. The results of DFT and two TB approaches with different parameter sets are shown. The inset shows the elastic mean free path for different adsorbate concentrations. The scale of the inset has been cut at 1 and 100 nm.

Figure 7

Tight-binding hopping terms $t$ between the two states of the bridge adatom (top) and the two carbon atoms on the graphene plane. The state energies $e$ are also shown.

Figure 8

Mean free paths for epoxide adsorbates at two different concentrations. DFT estimates based on single-defect systems are shown with solid lines, while ensemble-averaged TB results for large-scale many-defect systems are shown with dashed lines. The arrows indicate resonances not captured by the TB model.

Figure 9

Scattering cross section for a carbon adatom on bulk graphene. The inset shows the elastic mean free path as a function of adatom concentration. The scale of the inset has been cut at 1 and 100 nm.