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While enormous progress has been achieved in synthesizing atomically precise graphene nanoribbons (GNRs), the preparation of GNRs with fully predetermined length and monomer sequence remains an unmet challenge. Here we report a fabrication method that provides access to structurally diverse and monodisperse “designer” GNRs through utilization of an iterative synthesis strategy, in which a single monomer is incorporated into an oligomer chain during each chemical cycle. Surface-assisted cyclodehydrogenation is subsequently employed to generate the final nanoribbons, and bond-resolved scanning tunneling microscopy is utilized to characterize them.

The design of a spin imbalance within the crystallographic unit cell of bottom-up engineered 1D graphene nanoribbons (GNRs) gives rise to nonzero magnetic moments within each cell. Here, we demonstrate the bottom-up assembly and spectroscopic characterization of a one-dimensional Kondo spin chain formed by a chevron-type GNR (cGNR) physisorbed on Au(111). Substitutional nitrogen core doping introduces a pair of low-lying occupied states per monomer within the semiconducting gap of cGNRs. Charging resulting from the interaction with the gold substrate quenches one electronic state for each monomer, leaving behind a 1D chain of radical cations commensurate with the unit cell of the ribbon. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal the signature of a Kondo resonance emerging from the interaction of

The rational bottom-up synthesis of graphene nanoribbons (GNRs) provides atomically precise control of widths and edges that give rise to a wide range of electronic properties promising for electronic devices such as field-effect transistors (FETs). Since the bottom-up synthesis commonly takes place on catalytic metallic surfaces, the integration of GNRs into such devices requires their transfer onto insulating substrates, which remains one of the bottlenecks in the development of GNR-based electronics. Herein, we report on a method for the transfer-free placement of GNRs on insulators. This involves growing GNRs on a gold film deposited onto an insulating layer followed by gentle wet etching of the gold, which leaves the nanoribbons to settle in place on the underlying insulating substrate. Scanning tunneling microscopy and Raman spectroscopy confirm that atomically precise GNRs of high density uniformly grow on the gold films deposited onto SiO2/Si substrates and remain structurally intact after the etching process. We have also demonstrated transfer-free fabrication of ultrashort channel GNR FETs using this process. A very important aspect of the present work is that the method can scale up well to 12 in. wafers, which is extremely difficult for previous techniques. Our work here thus represents an important step toward large-scale integration of GNRs into electronic devices.

Description, A type of nanoribbon with four-membered rings was synthesized and was found to behave like a hologram of atomic orbitals., The incorporation of nonhexagonal rings into graphene nanoribbons (GNRs) is an effective strategy for engineering localized electronic states, bandgaps, and magnetic properties. Here, we demonstrate the successful synthesis of nanoribbons having four-membered ring (cyclobutadienoid) linkages by using an on-surface synthesis approach involving direct contact transfer of coronene-type precursors followed by thermally assisted [2 + 2] cycloaddition. The resulting coronene-cyclobutadienoid nanoribbons feature a narrow 600-meV bandgap and novel electronic frontier states that can be interpreted as linear chains of effective px and py pseudo-atomic orbitals. We show that these states give rise to exceptional physical properties, such as a rigid indirect energy gap. This provides a previously unexplored strategy for constructing narrow gap GNRs via modification of precursor molecules whose function is to modulate the coupling between adjacent four-membered ring states.

Bottom-up graphene nanoribbons (GNRs) have recently been shown to host nontrivial topological phases. Here, we report the fabrication and characterization of deterministic GNR quantum dots whose orbital character is defined by zero-mode states arising from nontrivial topological interfaces. Topological control was achieved through the synthesis and on-surface assembly of three distinct molecular precursors designed to exhibit structurally derived topological electronic states. Using a combination of low-temperature scanning tunneling microscopy and spectroscopy, we have characterized two GNR topological quantum dot arrangements synthesized under ultrahigh vacuum conditions. Our results are supported by density-functional theory and tight-binding calculations, revealing that the magnitude and sign of orbital hopping between topological zero-mode states can be tuned based on the bonding geometry of the interconnecting region. These results demonstrate the utility of topological zero modes as components for designer quantum dots and advanced electronic devices.

MathemaTB is a package developed to enable tight-binding calculations within Mathematica. The package presents 62 functions dedicated to facilitating these quantum mechanical computations. MathemaTB offers functionalities to carry out matrix manipulation, data analysis and visualizations on molecules, wave functions, Hamiltonians, coefficient matrices, and energy spectra, providing a unique insight into the interplay between geometric and electronic structure. Crystal orbitals, projected dispersions and densities of states can be obtained with only a few lines of code. The effect of different structures, heteroatoms and tight-binding parameters can easily be explored. Calculations can be carried out on molecules (Huckel-type calculations) or on systems with periodicities in one, two or three dimensions. Particularly powerful features are the possibility to plot band structures both along paths (one-dimensional) and over planes (two-dimensional) in reciprocal space, where in each case the localization of the wave function onto different sites, symmetries or basis functions can be visualized with color coding. Further features involve crystal orbital plotting with color coding of the complex phase, mean field Hubbard tight-binding and manipulation of the Hamiltonian matrix with numerical and symbolic elements. The conjunction of tight-binding functions, matrix algebra functions for symmetry, overlap and change of basis, wave function- and dispersion functions and a high degree of interactivity and flexibility makes MathemaTB a useful package for electronic structure calculations. Program summary Program Title: MathemaTB Program Files doi: http://dx.doi.org/10.17632/52bykkbr9n.1 Licensing provisions: LGPL Programming language: Wolfram Mathematica v. 11.0 Supplementary material: MathemaTB manual Nature of problem: The tight-binding method is a useful method for determining the electronic structure in molecules and condensed matter systems. The MathemaTB package provides an implementation of the tight-binding machinery that allows such calculations to be performed in Mathematica. Solution method: A package containing functions to aid in setting up, performing and analyzing tight-binding calculations within Mathematica. The package allows insightful and interactive electronic structure calculations with a high degree of flexibility. Additional comments including restrictions and unusual features: MathemaTB supports molecular and crystal orbitals with color-coding of the complex phase. Supports projected dispersions and local density of states. Allows overlap and change of basis of the Hamiltonian. Supports Hubbard mean field tight-binding. Supports numerical and analytical diagonalization of the Hamiltonian and Hamiltonians with symbolic quantities. Allows plotting the (projected) dispersion in two dimensions. Facilitates simulating differential conductance maps.

The scope of graphene nanoribbon (GNR) structures accessible through bottom-up approaches is defined by the intrinsic limitations of either all-on-surface or all-solution-based synthesis. Here, we report a hybrid bottom-up synthesis of GNRs based on a Matrix-Assisted Direct (MAD) transfer technique that successfully leverages technical advantages inherent to both solution-based and on-surface synthesis while sidestepping their drawbacks. Critical structural parameters tightly controlled in solution-based polymerization reactions can seamlessly be translated into the structure of the corresponding GNRs. The transformative potential of the synergetic bottom-up approaches facilitated by the MAD transfer techniques is highlighted by the synthesis of chevron-type GNRs (cGNRs) featuring narrow length distributions and a nitrogen core-doped armchair GNR (N4-7-ANGR) that remains inaccessible using either a solution-based or an on-surface bottom-up approach alone.

The incorporation of nanoscale pores into a sheet of graphene allows it to switch from an impermeable semimetal to a semiconducting nanosieve. Nanoporous graphenes are desirable for applications ranging from high-performance semiconductor device channels to atomically thin molecular sieve membranes, and their performance is highly dependent on the periodicity and reproducibility of pores at the atomic level. Achieving precise nanopore topologies in graphene using top-down lithographic approaches has proven to be challenging due to poor structural control at the atomic level. Alternatively, atomically precise nanometer-sized pores can be fabricated via lateral fusion of bottom-up synthesized graphene nanoribbons. This technique, however, typically requires an additional high temperature cross-coupling step following the nanoribbon formation that inherently yields poor lateral conjugation, resulting in 2D materials that are weakly connected both mechanically and electronically. Here, we demonstrate a novel bottom-up approach for forming fully conjugated nanoporous graphene through a single, mild annealing step following the initial polymer formation. We find emergent interface-localized electronic states within the bulk band gap of the graphene nanoribbon that hybridize to yield a dispersive two-dimensional low-energy band of states. We show that this low-energy band can be rationalized in terms of edge states of the constituent single-strand nanoribbons. The localization of these 2D states around pores makes this material particularly attractive for applications requiring electronically sensitive molecular sieves.

The field of on-surface synthesis has seen a tremendous development in the past decade as an exciting new methodology towards atomically well-defined nanostructures. A strong driving force in this respect is its inherent compatibility with scanning probe techniques, which allows one to ‘view’ the reactants and products at the single-molecule level. In this article, we review the ability of noncontact atomic force microscopy to study on-surface chemical reactions with atomic precision. We highlight recent advances in using noncontact atomic force microscopy to obtain mechanistic insight into reactions and focus on the recently elaborated mechanisms in the formation of different types of graphene nanoribbons.

We have studied the incommensurate moir\'e structure of epitaxial graphene grown on iridium(111) by dynamic low-energy electron diffraction [LEED $I$($V$)] and noncontact atomic force microscopy (AFM) with a CO-terminated tip. Our LEED $I$($V$) results yield the average positions of all the atoms in the surface unit cell and are in qualitative agreement with the structure obtained from density functional theory. The AFM experiments reveal local variations of the moir\'e structure: The corrugation varies smoothly over several moir\'e unit cells between 42 and 56 pm. We attribute these variations to the varying registry between the moir\'e symmetry sites and the underlying substrate. We also observe isolated outliers, where the moir\'e top sites can be offset by an additional 10 pm. This study demonstrates that AFM imaging can be used to directly yield the local surface topography with pm accuracy even on incommensurate two-dimensional structures with varying chemical reactivity.