Revealing the Local Electronic Structure of a Single-Layer Covalent Organic Framework through Electronic Decoupling.

Covalent organic frameworks (COFs) are molecule-based 2D and 3D materials that possess a wide range of mechanical and electronic properties. We have performed a joint experimental and theoretical study of the electronic structure of boroxine-linked COFs grown under ultrahigh vacuum conditions and characterized using scanning tunneling spectroscopy on Au(111) and hBN/Cu(111) substrates. Our results show that a single hBN layer electronically decouples the COF from the metallic substrate, thus suppressing substrate-induced broadening and revealing new features in the COF electronic local density of states (LDOS). The resulting sharpening of LDOS features allows us to experimentally determine the COF band gap, bandwidths, and the electronic hopping amplitude between adjacent COF bridge sites. These experimental parameters are consistent with the results of first-principles theoretical predictions.

Length-Dependent Evolution of Type II Heterojunctions in Bottom-Up-Synthesized Graphene Nanoribbons.

The ability to tune the band-edge energies of bottom-up graphene nanoribbons (GNRs) via edge dopants creates new opportunities for designing tailor-made GNR heterojunctions and related nanoscale electronic devices. Here we report the local electronic characterization of type II GNR heterojunctions composed of two different nitrogen edge-doping configurations (carbazole and phenanthridine) that separately exhibit electron-donating and electron-withdrawing behavior. Atomically resolved structural characterization of phenanthridine/carbazole GNR heterojunctions was performed using bond-resolved scanning tunneling microscopy and noncontact atomic force microscopy. Scanning tunneling spectroscopy and first-principles calculations reveal that carbazole and phenanthridine dopant configurations induce opposite upward and downward orbital energy shifts owing to their different electron affinities. The magnitude of the energy offsets observed in carbazole/phenanthridine heterojunctions is dependent on the length of the GNR segments comprising each heterojunction with longer segments leading to larger heterojunction energy offsets. Using a new on-site energy analysis based on Wannier functions, we find that the origin of this behavior is a charge transfer process that reshapes the electrostatic potential profile over a long distance within the GNR heterojunction.

Erratum: Self-assembly of ordered graphene nanodot arrays.

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Self-assembly of ordered graphene nanodot arrays.

The ability to fabricate nanoscale domains of uniform size in two-dimensional materials could potentially enable new applications in nanoelectronics and the development of innovative metamaterials. However, achieving even minimal control over the growth of two-dimensional lateral heterostructures at such extreme dimensions has proven exceptionally challenging. Here we show the spontaneous formation of ordered arrays of graphene nano-domains (dots), epitaxially embedded in a two-dimensional boron-carbon-nitrogen alloy. These dots exhibit a strikingly uniform size of 1.6 ± 0.2 nm and strong ordering, and the array periodicity can be tuned by adjusting the growth conditions. We explain this behaviour with a model incorporating dot-boundary energy, a moiré-modulated substrate interaction and a long-range repulsion between dots. This new two-dimensional material, which theory predicts to be an ordered composite of uniform-size semiconducting graphene quantum dots laterally integrated within a larger-bandgap matrix, holds promise for novel electronic and optoelectronic properties, with a variety of potential device applications.The nanoscale patterning of two-dimensional materials offers the possibility of novel optoelectronic properties; however, it remains challenging. Here, Camilli et al. show the self-assembly of large arrays of highly-uniform graphene dots imbedded in a BCN matrix, enabling novel devices.

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm.

The primal-dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1-26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity x-ray illumination is presented.