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

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.


Sample preparation and on-surface synthesis
The Au(111) single crystal was prepared by repeated sputter-anneal cycles using Ar+ ions at an energy of 1 keV and annealing to 470 • C. Precursors were sublimated from a commercial Dodecon OMBE four-fold Knudsen cell with the crucible at 355 • C and the Au(111) held at room temperature. Sample temperature was measured by using a thermocouple directly in contact to the sample. The base pressure during evaporation was below 1 × 10 −9 mbar.

Experimental details on the imaging method
Bond-resolved STM images were acquired by functionalizing the tip with a CO molecule.
For that, the molecules were first introduced on the Au surface by dosing the cryostat with CO gas at a pressure of 5 × 10 −7 mbar for 30 seconds in a temperature range from 5 to 15 K.
The CO was then picked up by the tip by applying pulses of 2.5 V at random positions or by gentle tip indentations on the Au surface until the resolution was suddenly improved. The higher resolution of these tips are related to dynamic effects in the CO-metallic tip junction as it interacts with the atoms beneath.

Ab-initio Calculations and quantum electron transport simulations
The atomic and electronic structure calculations were performed using DFT as implemented in the SIESTA code. 2,3 To explore the conformational details of phenylene twist at NPG bridges (Fig. 2), and in order to reduce the computational cost, we carried out free-standing and surface supported calculations for a coupled pair of ribbons, where the peripheral phenyls were not included. We used a supercell description of the system, made up of a slab containing 4 layers of a Au(111) 7×6 unit cell with a double ribbon on top of one of the Au surfaces. For all relaxations, the outermost part of the double ribbons were maintained fixed so as to mimic the nanoribbon clustering observed experimentally. For the Au supported relaxations, the top most layer of the substrate was also relaxed. In all cases, forces were less than 0.01 eV/Å. The energy cut-off was fixed at 300 Ry and a 1×5×1 k-mesh was used, where 5 k-points were taken in the direction of the ribbon.
DFT-based total energy calculations for the free-standing systems allowed us to estimate the relative stability of the various bridge configurations. We find that pm is the energetically most favourable conformation (lowest total energy), while the mm and pp have 140 and 510 meV higher total energies, respectively.
For the free-standing calculations of the different phenylene-bridged NPGs (Fig. 3), a 4.751 nm × 0.866 nm supercell was employed, containing 104 carbon atoms and 36 hydrogen atoms. A vacuum region of 20Å was introduced perpendicular to the surface in order to avoid non-physical interactions between periodic images. Core electrons were represented by normconserving Troullier-Martins pseudopotentials, 4 while a linear combination of atomic orbitals (LCAO) was used as a basis set for valence electrons. In particular, a double-ζ polarized (DZP) basis set with a 0.01 Ry energy shift 5 was selected. Exchange-correlation was treated by GGA-PBE. 6 The Brillouin zone was sampled by a 4×15×1 Monkhorst-Pack k-mesh 7 and a mesh-cutoff of 400 Ry was employed to define the real-space grid. Atomic coordinates were optimized until forces between atoms were lower than 0.01 eV/Å and the atomic structure was constrained to remain planar during relaxation. Cell relaxation was performed with a pressure threshold of 0.25 GPa. For the simulations of tilted pp-NPG, atomic structures were built starting from the optimized planar pp-NPG and manually rotating the phenyl rings in the bridges. No further relaxation was performed in these geometries.
Quantum electron transport simulations were carried out using the TRANSIESTA utility TBTRANS, 8 which combines tight-binding (TB) Hamiltonians and Non-equilibrium Green's Functions (NEGF) to compute transport. Accurate "pruned" DFT hamiltonians were constructed using SISL 9 into a reduced set of atomic orbitals: s, p x , p z and p y for carbon atoms sitting in the bridges, and p z , P d xz and P d yz for the rest of carbon atoms (respectively blue and grey atoms in Figs. S4 and S5). P d xz and P d yz refer to polarization (P) orbitals. 10 This

Analysis of interpolymer distance
The interpolymer configuration has been analyzed by studying large and small scale STM images of the polymer chain ensembles. The average interchain distance, which varied in the range of d = 2.0-2.2 nm, has been obtained from Fast Fourier Transforms of the images.
Smaller scale images, on the other hand, have been used to study the relative conformation, by tracking the relative position of the lobes of adjacent polymers. From this analysis one can also obtain the interlobe distance within the chains, which is of a = 0.75 nm, in line what that reported for staggered anthracene polymers. 12 By using these distances to represent the the homochiral and heterochiral assembly configurations, represented in Fig. S6c, it can be concluded that the homochiral one is more favourable.   Fig. 1c. The onset of the CB and VB bands can be identified in the spectrum (red line). The reference spectra acquired on Au(111) is added in shaded gray. dI/dV spectra was acquired using the lock-in technique, with a modulation voltage of 30 mV and a frequency of 2.5 kHz.

Surface-induced planarization of the peripheral phenyl ring in isolated ribbons
For the surface supported calculations to study the planarization of the peripheral phenyl ring, we employed a supercell consisting of 4 layers of a Au(111) 8 × 6 unit cell with a structure formed by 16 C and 12 H atoms placed on top of one of the Au surfaces. The geometry of the overlayer was extracted from the relaxed gas phase structure of Ph-7-13-AGNR and the top most layer of Au and the overlayer were relaxed until the forces were less than 0.04 eV/Å. An energy-cutoff of 300 Ry and a single k point (Γ) were considered. The results summarized in Fig. S8 show how, in the case of individual ribbons, the interaction with the surface dominates over the steric repulsion with the single adjacent ring, resulting in an effective planarization of the structure. This is in contrast to that found in the NPG bridges, as reported in Figs. 2c and d, where the surface-induced planarization is counteracted by the steric repulsion from the two adjacent rings. Fig. S8: a, Schematics of the atomic structure of Ph-7-13-AGNR (left). In order to reduce the computational cost, a representative section, highlighted with a red rectangle, has been used in the relaxation study on the Au(111) surface (right). b, Side view of the structure before (left) and after (right) relaxation on the Au(111) surface. The twisted initial conformation (left) corresponds to that of the relaxed free-standing structure. c, Same structures as those represented in b, with the color code indicating the out-of-plane deviation from the average plane (∆z). The substrate has been removed for clarity.