pubs.acs.org/JACS Article Molecular Bridge Engineering for Tuning Quantum Electronic Transport and Anisotropy in Nanoporous Graphene César Moreno,* Xabier Diaz de Cerio, Manuel Vilas-Varela, Maria Tenorio, Ane Sarasola, Mads Brandbyge, Diego Peña,* Aran Garcia-Lekue,* and Aitor Mugarza* Cite This: J. Am. Chem. Soc. 2023, 145, 8988−8995 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information 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. ■ INTRODUCTION At the nanoscale, even the most basic quantum size effect, the that regulate the degree of anisotropy of the nanomaterial.24 Quantum simulations on electron propagation in different induction of semiconducting gaps by electron confinement, proposed NPG nanoarchitectures indicate that the interribbon requires ultimate precision. The case of graphene is a dramatic transmission can be switched on/off by the chemical example where deviations of a single atom in width can induce modification of the coupling bridges.25,26 In this work, we present the synthesis of a new nanoporous dramatic variations of the gap of up to a factor of 4.1,2 As a graphene (NPG) structure where such chemical knobs are consequence, local defects or variations in width can severely introduced and where the interribbon coupling strength can be disrupt electron transport properties in nanoscale graphene additionally modulated by a continuous conformational nanoribbons (GNRs).3,4 Fortunately, the atomic engineering transformation of the molecular bridges. The multiple bonding of quantum phenomena in graphene-based nanomaterials configurations of the bisphenylene bridges that bind the started to be a reality a decade ago with the emergence of nanoribbons in this NPG can efficiently switch the interribbon the bottom-up on-surface synthesis (OSS).5−14 In addition to electron flow off by incorporating meta bonds. In the para producing atomically precise homogeneous 1D nanostructures, configuration, the interribbon electron flow is modulated by OSS-based methods can also introduce heteroatoms,15,16 controlling the π−π overlap via the interphenyl twist angle. heterojunctions,17,18 or hybrid components19,20 in the The capability of manipulating the interphenyl twist angle is structure with the same precision, allowing for a precise experimentally inferred from the subtle interplay between the engineering of the electronic properties. steric hindrance and substrate interactions that leads to Recently, an OSS synthetic approach based on the lateral different twist angles in individual ribbons and NPGs with coupling of parallel aligned nanoribbons has endowed this different bridge configurations. This is further corroborated by atomic engineering capability to the synthesis of two- dimensional nanoarchitectures that can be conceived as nanoporous graphene (NPG).21−23 In these intrinsically Received: January 5, 2023 anisotropic structures, when adjacent ribbons are not Published: March 29, 2023 equivalent, band mistmatch can lead to a total confinement of electrons in individual GNRs.23 In contrast, the lateral coupling of equivalent GNRs can lead to sizable interribbon transmission, giving rise to intriguing quantum interferences © 2023 The Authors. Published by American Chemical Society https://doi.org/10.1021/jacs.3c00173 8988 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article 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). ab initio calculations where the effect of substrate interaction is the anthracene units confers to the molecule the 3D staggered directly addressed and the energetics of the twist angle are chiral conformation depicted in Figure 1a, giving rise to the quantitatively analyzed. two possible enantiomers labeled as R/S. The OSS reaction ■ RESULTS AND DISCUSSION The building block of the on-surface synthesized nanoporous procedure carried out in ultrahigh vacuum conditions, summarized in Figure 1, starts with the deposition of the DBP-DBBA precursor on the Au(111) surface held at room graphene is 2,2′-di([1,1′-biphenyl]-4-yl)-10,10′-dibromo-9,9′- temperature. By a subsequent annealing to T1 = 200 °C, bianthracene (DBP-DBBA), a bisanthracene derivative pre- biradicals generated by the thermal debromination cross- cursor that has been synthesized in solution following a couple to form 1D polymeric chains following the well-known procedure similar to that reported for another phenylated Ullmann coupling reaction. The DBP-DBBA units within the derivative21 (see Section 1.1 of the Supporting Information for polymer chain retain the staggering of their bisanthracene core, more details on the synthesis). The steric repulsion between conferring a double protrusion zigzag backbone appearance in 8989 https://doi.org/10.1021/jacs.3c00173 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article 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. the scanning tunneling microscope (STM) images, as shown in bond-resolved (BR) STM image of Figure 1c, resulting in a the close-up image of Figure 1b. Polymer chains self-align in phenylated GNR that we label as Ph-7-13-AGNR. As opposed homochiral close-packed islands following the three equivalent to the 7-13-AGNR, where the chiral information on the orientations imposed by the hexagonal lattice of the underlying precursor is lost upon cyclodehydrogenation, Ph-7-13-AGNR Au(111) surface, as shown in the larger scale image of Figure retains a prochiral configuration (i.e., chiral when confined in 1b left (see Figure S6 for more details). A second annealing 2D) thanks to the side phenyl substituents. We note that the step at T2 = 400 °C converts the polymers into graphene phenyl side group does not affect the band gap, which amounts nanoribbons by undergoing an internal cyclodehydrogenation to ca. 1.0 eV for of the Ph-7-13-AGNR (see Figure S7), that planarizes the structure into the hexagonal lattice of essentially the same value as for the 7-13-AGNR.21 This is in aromatic rings characteristic of graphene. The inner phenylene good agreement with the band structure calculated by density rings of the peripheral bisphenyl groups fuse into the aromatic functional theory (DFT), where the band gap of 0.73 eV backbone giving rise to a periodic modulation of the ribbon obtained for Ph-7-13-AGNR varies little from the 0.74 eV width of alternating pairs of 7 and 13 C atoms, a structure obtained for 7-13-AGNR. The GNRs remain aligned in labeled as 7-13-AGNR in previous studies.21,27,28 The homochiral clusters that follow the three equivalent outermost phenyl rings, on the other hand, remain as single orientations of the atomic lattice of the underlying substrate, bonded peripheral phenyl groups, as can be appreciated in the which enables their lateral coupling by triggering a 8990 https://doi.org/10.1021/jacs.3c00173 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article 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 κc = 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 κc as a function of interphenyl twist angle for pp-NPG, measured at E − EVBM= −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 kc values corresponding to the twist angles in the relaxed free-standing and Au supported structures are indicated with gray and yellow lines. dehydrogenative cross coupling after increasing the temper- as the one shown in Figure 1d (center). The mm bridge is the ature to T3 = 450 °C in a third and final annealing step (Figure most abundant, in agreement with the differences in the 1d). formation energy of the two. In the absence of phenyl side groups, the lateral coupling of Looking into the bridge conformation in more detail by the corresponding 7-13-AGNRs gives rise to a NPG structure using BR-STM images as the ones shown in Figure 2b, one can with two equivalent interribbon coupling configurations.21 see that the appearance of the bridging phenylenes depends on However, the side groups of Ph-7-13-AGNR increase the the bonding configuration. p-Phenylenes appear as sharp coupling degrees of freedom, giving rise to the three contrast features instead of hexagonal rings, a common nonequivalent configurations depicted in Figure 1d. The characteristic of nonplanar molecular groups that interact phenylated GNRs can couple from the para and meta sites, with the CO-functionalized tip used for BR-STM imaging.29 In giving rise to para−para (pp), para−meta (pm), and meta− pure pp bridges, the clockwise/anticlockwise conformation of meta (mm) phenylene bridges. The ortho cross-coupling the two phenyl units with respect to the para bond axis reveals configuration is sterically hindered by the hydrogens at the the interphenyl twist. The appearance of m-phenylenes, adjacent phenyl unit and the fact that it implies the formation instead, resembles that of the planar rings of the backbone. of more than one bond. This selective twist of p-phenylenes, also observed in coupled Interestingly, chiral interactions seem to play a fundamental pairs of phenylated chevron type GNRs,30 cannot be solely role in determining the relative abundance of each coupling explained by steric hindrance arguments, since this affects configuration. From pure energetic arguments and based on similarly both p and m configurations, as it is well-known for the coupling energies obtained for free-standing NPGs, the pm polyphenylene chains.31 Indeed, DFT calculations performed configuration is the most stable, followed by mm and pp, which for the free-standing NPG structures reveal a significant twist are 140 and 510 meV less stable, respectively (see Section 1.4 for the three type of isomers, as shown in Figure 2c. For this of the Supporting Information for details of the calculation). analysis, we define two different twist angles, the first defined However, although we do observe a preference of the mm over by planes of the outermost benzene ring of the GNR backbone the pp configuration, we only find a marginal number of the and the adjacent phenyl (θ) and the second between the two most stable pm configuration. This can be explained by noting phenylenes at the bridge (α). Note that α = 2 × θ only when that this configuration is the only one that requires a the outermost benzene ring remains coplanar to the backbone, heterochiral pair of ribbons (Figure 1d), something that is something that will not be the case due to small nonplanar hindered by the chiral phase separation undergone during the distortions induced at the backbone to accommodate steric polymerization step. The scenario of the chiral hindering of the repulsion, as shown later. As reference, if we compare the pm coupling is supported by the fact that the few pm coupled interphenyl twist angle α = 47° obtained for the pp-NPG with ribbons are always found at the periphery of the NPG sheets, values found in the literature for poly-p-phenylene, we see that the only site where a ribbon of opposite chirality can join a it lies within the α = 40° and 70° calculated for infinite31 and homochiral cluster. Regarding the pp and mm bridge finite32 chains, respectively. When comparing the twist angles configurations, these often appear mixed within a NPG of the free-standing NPG (solid circles) to calculations carried sheet, but one can also find single configuration ensembles out including the Au(111) substrate (dashed circles), we see 8991 https://doi.org/10.1021/jacs.3c00173 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article 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 − EVBM = −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) = TL/TT with twist angle for pp-NPG, where TL and TT are the longitudinal and transversal transmissions, respectively. The horizontal green line corresponds to the effective mass ratio calculated for black phosphorus.38 an overall planarization of the structure, a clear effect of the The conformational flexibility provided by the phenylene interaction with the substrate that competes with steric bridges are expected to affect the interribbon electronic hindrance. The effect is, however, much more pronounced coupling and hence the quantum electron transport across for the m-phenylenes, as found in the experimental data. The the NPG sheets and its anisotropy. We explore that by differences are most visible in the mixed pm bridge, where the analyzing the band structure of the different configurations m-phenylene turns nearly coplanar to the backbone by the and, in the case of pp-NPG, its evolution with the twist angle. interaction with the underlying substrate. In the mm bridges, Figure 3a compares the frontier band structure of free-standing phenyls still have to maintain a minimum tilt in order to avoid NPGs for the three coupling configurations. In this case, the each other, but the twist angles are considerably smaller than structures have been relaxed by imposing coplanarity in order those of the pp bridge. In order to account for the different to account solely for the effect of chemical bonding degree of planarization, one has to pay attention to the configuration. The most notable differences are found between distortion of the backbone structure induced by the twisting. pp-NPG and the other two configurations containing at least The side views of the relaxed structures depicted in Figure 2d one m-phenyl at the bridge. One can see that for pp-NPG the contain the key for such differences. Whereas p-phenylenes do degenerated valence (VB) and conduction (CB) bands split, not significantly distort the backbone structure, m-phenylenes leading to a slight reduction of the band gap and a finite dispersion in the transversal direction (ΓX). All these are induce a substantial out-of-plane distortion at the peripheral manifestations of a finite electron transmission across the units (see Figure 2d for distortion maps). The substrate, in phenylene bridges. In contrast, adding one m-phenyl to the addition to tending to planarize both p and m bridge bridge seems to switch off the interribbon coupling effectively, phenylenes similarly by the local π interaction, also counteracts quenching the band splitting and the transversal band the backbone distortion necessary for the twist of the latter, dispersion. The fact that a single m-phenyl is enough to consequently planarizing m-phenylenes more effectively. effectively quench transmission across the bridge is in A qualitative assessment of the capability of the substrate agreement with calculations reporting that a single meta kink interaction to tune the twist angle can be made by comparing is enough to effectively disrupt electron delocalization across the BR-STM image of the pp bridged NPG with that of the polyphenylene zigzag chains.32 We attribute this quenching of isolated ribbon. We can see that the interaction with the transmission to the destructive interferences produced in the substrate can easily surpass the steric hindrance of the single transport across m-phenylenes, as has been corroborated by neighbor found in the ribbon, as the phenylene appears to be previous electron propagation simulations on theoreticaly coplanar to the backbone in this case (Figure 1c right). This proposed single-phenyl bridged NPG structures.25 Similar observation is corroborated by our DFT analysis of the isolated interference effects have also been found in experimental33−35 Ph-7-13-AGNR (see Figure S8). It is only when we add a and theoretical31,36,37 studies of transport across single- second neighbor in the pp bridges that the steric repulsion molecule junctions with broken or cross conjugation. becomes strong enough to maintain a phenylene twist even in A more quantitative analysis of the interribbon coupling can the presence of the substrate (Figure 2b left). be obtained by measuring the momentum splitting between 8992 https://doi.org/10.1021/jacs.3c00173 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article the otherwise degenerated VB and VB-1 bands (a similar containing at least one m-phenyl at the bridge is evident. In pp- analysis could be carried out with CB and CB+1). The NPG, the injected current spreads across adjacent ribbons, momentum splitting Δk directly relates to the interchannel forming the so-called Talbot interference patterns.24 In coupling coefficient κc that mixes the leaking wave functions of contrast, in the m-phenyl containing NPGs, the current is adjacent ribbons as kc = Δk/4.24 The resulting energy- basically confined within a single ribbon, similar to that found dependent kc(E) of the frontier bands is plotted for all for other meta-bridged NPG structures.25 The interesting configurations in Figure 3b. As reference, we see that, at 0.2 eV situation comes when we turn the conformational degree of below the VB maximum (VBM) (black line in Figure 3b), κc is freedom in the pp-NPG. Here, we see how the divergence of reduced by more than a factor of 5 when we introduce a m- the Talbot interference pattern is gradually reduced as we phenyl in the bridge. increase the interphenyl twist angle and completely fades out In contrast to the abrupt on/off switching of the interribbon close to α = 90°, where π orbitals at the bisphenyl bridge turn coupling provided by this robust chemical knob, the orthogonal. These modulations of the quantum interferences conformational degree of freedom rendered by the interphenyl mimic the continuous evolution of κc found for varying twist angle can enable a more gradual knob. We analyze this by interphenyl twist angle. tracking the evolution of κc in pp-NPG as a function of twist The quantum interferences obtained for the longitudinal angle. For the calculation, we consider the energy 0.2 eV below propagation of injected point charges are indicative of a strong the VBM (black line in Figure 3b), and a rigid backbone, so anisotropy in the electronic transport, and thus, the that α = 2θ. The result is plotted in Figure 3c together with the interphenyl twist can also be seen as a tool for tailoring the total energy variations induced by the phenyl twist. One can overall electronic anisotropy in this nanomaterial. This can be see that the maximum coupling is for the coplanar system measured by computing the longitudinal (TL) and transversal where π overlap is maximized and decays to zero for the (TT) transmissions by using orthogonal pairs of semi-infinite orthogonal bridge configuration (α = 2θ = 90°). Beyond this electrodes corresponding to the pristine, orthogonal unit cell angle, we find a second minima at α = 2θ = 180° where, even if (Figure 4d top) repeated along the transverse and longitudinal the bridge phenyls are coplanar, conjugation is now broken by ribbon directions, respectively. From the 2D transmission their orthogonal configuration with respect to the backbone vector T⃗ = T⃗ L + T⃗ T, one can obtain the anisotropy angle β (see (i.e., θ = 90°). The small maximum between the two nodes sketch in Figure 4d), and the corresponding anisotropy factor p never reaches the absolute maxima of the coplanar = tan(90 − β) = TL/TT. The computed values of p and β are configuration. This trend is perfectly reproduced by a model represented in Figure 4d as a function of interphenyl twist that considers uniquely the π overlap across the bridge with κc angle. One can see that the bridge conformation can modulate = κc(0°) × cos2(θ) × cos(2θ) (blue line in Figure 3c bottom). the anisotropy of the material by an order of magnitude. The From the angular evolution of κc described above, α = 0− whole modulation window is within the strong anisotropy 90° is clearly the region of interest for tuning interribbon regime, well above any experimental value reported for a 2D coupling. Remarkably, the relaxed interphenyl twist angle lies material (p < 3).39−43 The computed transmission ratio can be exactly at the center of this region for the free-standing directly compared to effective mass ratios calculated for other structure, as given by the total energy minimum (Figure 3c 2D materials, which are equivalent within the parabolic band top). The capability to tune the interribbon coupling around approximation. The values obtained for a model anisotropic this value is demonstrated by noting that the reduction of twist 2D material such as black phosphorus38 lie in the lower branch angle from α = 47° to α = 29° found for Au supported NPG of the modulation window of the pp-NPG (see horizontal results in an increase of κc by 44% (thick gray and yellow lines line). in Figure 3c bottom). The angle-dependent energy calculations also provide an estimation of the thermally induced oscillations of the interphenyl twist angle. Whereas thermal effects are ■ CONCLUSIONS In conclusion, with the synthesis of atomically precise negligible at the temperature of the STM experiments (5 K), at nanoporous graphene structures consisting of graphene room temperature, the rotational energy of 1/2kBT = 12.7 meV nanoribbons connected by flexible phenylene bridges, we results in an oscillation of ±8° around the minimum energy open a way of tailoring quantum transport and the anisotropy value for the free-standing case. When supported on Au, these in 2D materials. Our calculations demonstrate that, in contrast values are expected to be even smaller. to the effective interribbon decoupling offered by meta phenyls, The tunability of interribbon coupling and its effect on interesting to confer a robust, absolute 1D anisotropy to the electron transport can be directly visualized by carrying out nanomaterial, para bridges can be designed to tune this quantum simulations of the propagation of electron current anisotropy continuously in a wide range by varying the within the NPG. Figure 4a−c summarizes the results obtained interphenyl twist angle. This could be modulated by external for each configuration and for different twist angles in the case stimuli such as strain or electric fields applied to functionalized of pp-NPG. The color maps displayed here correspond to polar phenylene bridges or more statically by using substrates bond currents; i.e., the electron flow across the pz orbitals of with different degrees of interactions. We foresee that this each carbon atom when electrons are injected from a metallic molecular bridge strategy could also be used to tailor the tip in contact with one of the ribbons of the NPG fragment at phononic anisotropy, leading to novel approaches in the search the bottom end (red dot) and propagate toward a drain of thermoelectric nanomaterials. electrode that connects all ribbons at the top end (see Methods in the Supporting Information for more details). As in the analysis of Figure 3, coplanar pp (Figure 4a right), pm (Figure 4b), and mm (Figure 4c) configurations have been ■ ASSOCIATED CONTENT * Supporting Information sı compared first to disentangle the effects of the two degrees of The Supporting Information is available free of charge at freedom. The difference between the former and the ones https://pubs.acs.org/doi/10.1021/jacs.3c00173. 8993 https://doi.org/10.1021/jacs.3c00173 J. Am. Chem. Soc. 2023, 145, 8988−8995 Journal of the American Chemical Society pubs.acs.org/JACS Article Experimental and theoretical methods, analysis on chiral GOCHIP Projects PCI2019-111890-2 and PCI2019-111933-2 polymer chain assembly, electronic properties of Ph-7- funded by MCIN/AEI/10.13039/501100011033 and co- 13-AGNR, and phenyl planarization of individual funded by the European Union; Grant Nos. TED2021- ribbons (PDF) 132388B-C41, TED2021-132388B-C42, and TED2021- 132388B-C44 funded by MCIN/AEI/10.13039/ ■ AUTHOR INFORMATION Corresponding Authors 501100011033 and the European Union NextGenerationEU/ PRTR; Xunta de Galicia (Centro de Investigación de Galicia accreditation 2019−2022, ED431G 2019/03). X.D.C., A.S., César Moreno − Departamento de Ciencias de la Tierra y and A.G.-L. also acknowledge the financial support received Fisica de la Materia Condensada, Universidad de Cantabria, from the IKUR Strategy under the collaboration agreement 39005 Santander, Spain; Catalan Institute of Nanoscience between Ikerbasque Foundation and DIPC on behalf of the and Nanotechnology (ICN2), CSIC and The Barcelona Department of Education of the Basque Government. C.M. Institute of Science and Technology, 08193 Barcelona, Spain; was supported by Grant RYC2019-028110-I funded by orcid.org/0000-0003-2682-211X; MICIN/AEI/10.13039/501100011033 and by the European Email: cesar.moreno@unican.es Social Fund “ESF Investing in your future”. M.T. was Diego Peña − Centro de Investigación en Química Biolóxica e supported by Grant No. BES-2017-08078 funded by MCIN/ Materiais Moleculares (CiQUS) and Departamento de AEI/10.13039/501100011033 and by “ESF Investing in your Química Orgánica, Universidade de Santiago de Compostela, future”. M.B. acknowledges funding from Villum fonden (VIL 15782 Santiago de Compostela, Spain; orcid.org/0000- 00013340). 0003-3814-589X; Email: diego.pena@usc.es Aran Garcia-Lekue − Donostia International Physics Center, 20018 San Sebastian, Spain; Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain; orcid.org/0000-0001- ■ REFERENCES (1) Yang, L.; Park, C.-H.; Son, Y.-W.; Cohen, M. L.; Louie, S. G. 5556-0898; Email: wmbgalea@ehu.eus Quasiparticle Energies and Band Gaps in Graphene Nanoribbons. Aitor Mugarza − Catalan Institute of Nanoscience and Phys. Rev. Lett. 2007, 99, 186801. 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