Molecular Bridge Engineering for Tuning Quantum Electronic Transport and Anisotropy in Nanoporous Graphene

Abstract

Recent advances on surface-assisted synthesis have demonstrated that arrays of nanometer wide graphene nanoribbons can be laterally coupled with atomic precision to give rise to a highly anisotropic nanoporous graphene structure. Electronically, this graphene nanoarchitecture can be conceived as a set of weakly coupled semiconducting 1D nanochannels with electron propagation characterized by substantial interchannel quantum interferences. Here, we report the synthesis of a new nanoporous graphene structure where the interribbon electronic coupling can be controlled by the different degrees of freedom provided by phenylene bridges that couple the conducting channels. This versatility arises from the multiplicity of phenylene cross-coupling configurations, which provides a robust chemical knob, and from the interphenyl twist angle that acts as a fine-tunable knob. The twist angle is significantly altered by the interaction with the substrate, as confirmed by a combined bond-resolved scanning tunneling microscopy (STM) and ab initio analysis, and should accordingly be addressable by other external stimuli. Electron propagation simulations demonstrate the capability of either switching on/off or modulating the interribbon coupling by the corresponding use of the chemical or the conformational knob. Molecular bridges therefore emerge as efficient tools to engineer quantum transport and anisotropy in carbon-based 2D nanoarchitectures.

Figure 1

Schematic illustration and STM images of the synthetic steps for the generation of phenylene-bridged NPG. (a) Molecular structure of the DBP-DBBA precursor. (b) Self-assembled arrays of linear polymer chains obtained after the Ullmann coupling reaction induced at step T₁ = 200 °C. Image size: 150 × 150 nm² (left); 6.3 × 6.3 nm² (right). (c) Planarization of the polymers into phenylated GNRs obtained by triggering cyclodehydrogenation at step T₂ = 400 °C. The phenylene side groups and 7-13-AGNR backbone structure are resolved in the BR-STM image shown in grayscale. Image size: 20 × 20 nm² (left); 3 × 3 nm² (right). The two possible prochiral configurations are indicated in one of the unit cells as S and R. (d) Formation of NPG by the lateral fusion of GNRs achieved by inducing interribbon dehydrogenative cross coupling at the final step T₃ = 450 °C. The chirality S/R of each GNR is indicated on top. The STM images at the bottom show large scale NPG domains (left), a pure meta–meta domain (center), and a mixture of the three bridge configurations (right). Image size: 98.3 × 98.3 nm² (left), 13.4 × 10 nm² (center), and 8.5 × 8.5 nm² (right).

Figure 2

Phenylene twist at NPG bridges. (a) Schematics of the three type of bridge configurations, with the selective twist found by STM for the para-phenylenes indicated by arrows. (b) BR-STM close-up images of the corresponding bridge configurations. The sharp features observed at para-phenylene sites are attributed to the out-of-plane tilt induced by the twist. In the pp bridge, the two phenyl units are tilted toward opposite directions with respect to the para bond axis (dashed yellow line). (c) Phenyl-ribbon twist angle θ (color circles) and interphenyl twist angle α (black circles), obtained by DFT for freestanding (solid circles) and Au-supported (open circles) NPGs. Angles are defined in (a) (see text for further description). (d) Side views of the corresponding atomic structures, where the interphenyl twist and the local distortion of the backbone can be appreciated by the out-of-plane distortion indicated in the red/blue color scale.

Figure 3

Electronic properties of phenylene-bridged NPG. (a) Electronic band structures of free-standing pp-, pm-, and mm-NPG. ΓY and ΓX correspond to the longitudinal (i.e., along the ribbon) and transversal directions of the 2D nanostructures. To account solely for the effect of the chemical bond, the structures are forced to remain coplanar in the relaxation. Atomistic models of the corresponding unit cells are displayed below. (b) Interchannel coupling coefficient κ_c = Δk/4 obtained from the momentum difference of the frontier bands. (c) Evolution of total energy relative to the coplanar configuration (top) and interchannel coupling coefficient κ_c as a function of interphenyl twist angle for pp-NPG, measured at E – E_VBM= −0.2 eV (horizontal line in (b)). The catafused benzene of the backbone is forced to be coplanar with the rest of the backbone, so that α = 2θ. The k_c values corresponding to the twist angles in the relaxed free-standing and Au supported structures are indicated with gray and yellow lines.

Figure 4

Bridge engineering of current injection. (a–c) Bond current maps in large-scale NPG fragments comprising seven 75 nm long graphene nanoribbons. The maps show the propagation of currents injected at E – E_VBM = −0.2 eV at the lower end of the central ribbon (red dot) for different interphenyl twist angles of pp-NPG (a) and coplanar pm-NPG (b) and mm-NPG (c). The color bar is saturated above 5% of the maximum value in order to detect the interference patterns produced by the current transmitted across the ribbons. (d) Evolution of the anisotropy ratio p = tan(90 – β) = T_L/T_T with twist angle for pp-NPG, where T_L and T_T are the longitudinal and transversal transmissions, respectively. The horizontal green line corresponds to the effective mass ratio calculated for black phosphorus.