Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method.

Figure 1

Electron transport through graphene nanoribbons from source (S) to drain (D) is studied by microwave emulation experiments and tight-binding calculations. Panel (a) shows an armchair ribbon of width 5, while zigzag and zigzag-rhomboid ribbons of width 3 are displayed in panels (b) and (c), respectively. The black and white color shading of the resonators indicate the two different sublattices to which the atoms belong. The contact geometry, i.e., the way source and drain are coupled to the ribbon (dashed lines), has important effects on the transport. Panel (d) shows a photo of the experimental setup for a zigzag ribbon of width 3. On the left-hand side the antenna on the bottom plate is seen, whereas the antenna on the right-hand side is mounted to the top plate (not shown).

Figure 2

Transmission through armchair graphene nanoribbons of length 9 and for increasing widths (from left to right). The ribbons up to a width of 3 are sketched in the insets. The leads (or antenna) through which electrons (or microwaves) are injected and extracted are connected to the black sites at the edges of the ribbons. Experimental data are shown by blue solid lines, while our tight-binding Green's function calculations are indicated by red dashed lines. First row: Connecting leads to all atoms on the zigzag edges, we confirm that the ribbons of width 2 and 5 are metallic, while otherwise the ribbons show a transport gap (gray shaded regions) around $\nu =0$. Second row: Connecting only the outer atoms on the zigzag edges—see the black marked atoms in the insets—the differences between the metallic (width 2 and 5) and semiconducting (width 1, 3 and 4) ribbons become more pronounced. Third row: Connecting only the inner atoms of the zigzag edges to leads, we find a broad transport gaps for all ribbon widths.

Figure 3

Calculated LDOS $D\left(\nu \right)$ in the armchair ribbon indicated by the color shading of the resonators. Close to the Dirac point, the LDOS vanishes on the inner atoms of the confining zigzag edges to the left and right, while it is non-zero on the outer atoms. Note that leads are attached to all sites at the confining zigzag edges to the left and right.

Figure 4

Transmission through zigzag and zigzag-rhomboid ribbons of length 9 and increasing width (from left to right). The more narrow ribbons are sketched in the insets. The leads are attached to the black sites. Top row: Connecting leads to all atoms at the confining armchair edges to the left and right, we observe that all zigzag ribbons are metallic. Bottom row: If leads are connected to the inner atoms of a zigzag-rhomboid ribbon, broad transmission gaps (gray shaded regions) can be observed for all ribbons.

Figure 5

Left: In the zigzag ribbon the calculated LDOS is nonvanishing on all atoms of the confining armchair edges, where the leads are attached. A transport gap cannot be induced by contact engineering. Right: At the edges of the zigzag-rhomboid ribbon, the calculated LDOS is located on the outer atoms and vanishes on the inner atoms.