Electronic structure of assembled graphene nanoribbons: Substrate and many-body effects

Experimentally measured electronic band gaps of atomically sharp straight and chevronlike armchair graphene nanoribbons (GNRs) adsorbed on a gold substrate are smaller than theoretically predicted quasiparticle band gaps of their free-standing counterparts [Linden et al., Phys. Rev. Lett. 108, 216801 (2012)]. The influence of the substrate on electronic properties of both straight and chevronlike GNRs is here investigated including many-body effects beyond semilocal density-functional theory. The predicted small electron transfer from a straight or chevronlike GNR to the gold surface is found to lead to a surface polarization at the GNR-metal interface responsible for a significant reduction of the quasiparticle band gap of the GNR. This reduction is quantified using a semiclassical image charge model. By considering both quasiparticle and surface polarization corrections, we obtain theoretical band gaps that are consistent with experimental ones for gold-supported GNRs.

Figure 1

The adsorption geometry of a hydrogenated (a) straight and (b) chevronlike armchair graphene nanoribbon on the Au(111) surface. The straight one has a width of 7 (denoted as AGNR-7) and the chevronlike one is composed of two alternating straight armchair GNRs with widths of 9 and 6 (denoted as AA-96). One unit cell is shown for both cases. Numbers indicate separation distances in $\AA$ between circled C atoms and Au atoms right below them.

Figure 2

Simulated constant current STM images of AGNR-7 on the gold surface at $-1$ eV bias voltage with tip height range given by (a) H${}_{\min }=2.18\AA$, H${}_{\max }=5.18\AA$ and (b) H${}_{\min }=4.42\AA$, H${}_{\max }=6.40\AA$. H${}_{\min }$ and H${}_{\max }$ represent the minimum and maximum tip-substrate distance, respectively. Simulated constant current STM images of AA-96 on the Au(111) surface at $-1$ eV bias voltage with (c) H${}_{\min }=2.20\AA$, H${}_{\max }=5.23\AA$ and (d) H${}_{\min }=4.38\AA$, H${}_{\max }=6.43\AA$.

Figure 3

(a) Electronic band structures of AGNR-7 deposited on a Au(111) substrate. The dots superimposed on the bands correspond to projected bands due to AGNR-7. Panel (b) only shows the dots, for clarity. (d) Electronic band structures of AA-96 deposited on a Au(111) substrate. The dots show the projected bands of AA-96. Panel (e) only shows the projected bands of AA-96 for clarity. The size of the dot is proportional to the amplitude of the projection. (c) and (f) show electronic band structures of free-standing AGNR-7 and AA-96, respectively. Solid (dashed) lines represent bands at the GW (DFT) level.

Figure 4

(a) Plane-averaged difference electronic charge densities $\Delta \rho \left(z\right)={\rho }_{\mathrm{M}|\text{G}}\left(z\right)-{\rho }_{\mathrm{M}}\left(z\right)-{\rho }_{\mathrm{G}}\left(z\right)$ upon formation of the interface for AGNR-7 and AA-96, respectively. (b) Plane-averaged exchange-correlation potential of a clean gold surface and image potential. The origin is set at the first gold layer, and $z_0$ and $z_1$ are fitted by setting the intersection of the two curves at $z_1$. (c) Plane-averaged charge densities for the conduction-band minimum (CB${}_{\min }$) and the valence-band maximum (VB${}_{\max }$) of the free-standing AA-96.