Theoretical progress in graphene physics has largely relied on the application of a simple nearestneighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that include electron-hole asymmetry and the detailed electronic bands of basic graphene nanostructures (e.g., nanoribbons with different edge terminations) are beyond the capability of such simple model. Here we show that a similarly simple plane-wave solution for the one-electron states of an atom-based two-dimensional potential landscape, defined by a single fitting parameter (the scattering potential), performs better than the standard tight-binding model, and levels to density-functional theory in correctly reproducing the detailed band structure of a variety of graphene nanostructures. In particular, our approach identifies the three hierarchies of nonmetallic armchair nanoribbons, as well as the doubly-degenerate flat bands of free-standing zigzag nanoribbons with their energy splitting produced by symmetry breaking. The present simple planewave approach holds great potential for gaining insight into the electronic states and the electrooptical properties of graphene nanostructures and other two-dimensional materials with intact or gapped Dirac-like dispersions.The two-dimensional (2D) honeycomb carbon-atom lattice known as graphene 1 is a promising material for applications in optical and electronic devices 2-4 . In particular, its peculiar conical electronic dispersion 5,6 and 2D character enable a uniquely large optical tunability 7,8 and a suitable playground for quantum electrodynamics phenomena, such as the relativistic Klein tunneling 9 , as well as a customizable zoo of exotic band structures when decorated with defects 10 , arranged in twisted bilayers 11 , or laterally patterned into ribbons 12,13 . Energy-gap engineering in graphene, an essential prerequisite for nanoelectronics applications, demands controlled and selective sub-lattice perturbations at the atomic scale, such as chemical doping 14,15 or gating 16 , lateral strain 17,18 , and substrate-induced sublattice asymmetry [19][20][21][22] .Graphene nanoribbons (GNRs) have been extensively studied as simple, appealing nanostructures that lead to electronic band features, such as gap opening, due to quantum confinement, and peculiar edge states that can readily be tuned through their width, shape, and edgeterminations 12,13 . The rapidly progressing on-surface chemistry, which allows controlled-synthesis of novel graphene-based nanostructures, such as GNRs with complex architectures 23-28 , combined with the precise mapping of their electronic structures using angle-resolved photomission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS) 29-32 , make GNRs promising candidates for the realization of exotic graphene-based nanodevices [33][34][35] .Theoretical understanding and prediction of extended graphene and GNRs properties has been instrumental in the development of the field. Density-functional theo...

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Two-dimensional honeycomb molecular networks confine a substrate’s surface electrons within their pores, providing an ideal playground to investigate the quantum electron scattering phenomena. Besides surface state confinement, laterally protruding organic states can collectively hybridize at the smallest pores into superatom molecular orbitals. Although both types of pore states could be simultaneously hosted within nanocavities, their coexistence and possible interaction are unexplored. Here, we show that these two types of pore states do coexist within the smallest nanocavities of a two-dimensional halogen-bonding multiporous network grown on Ag(111) studied using a combination of scanning tunneling microscopy and spectroscopy, density functional theory calculations, and electron plane wave expansion simulations. We find that superatom molecular orbitals undergo an important stabilization when hybridizing with the confined surface state, following the significant lowering of its free-standing energy. These findings provide further control over the surface electronic structure exerted by two-dimensional nanoporous systems.

Extracting dielectric fixed charge density on highly doped crystalline-silicon surfaces using photoconductance measurements

Monolayer hexagonal boron nitride (hBN) is attracting considerable attention because of its potential applications in areas such as nano-and opto-electronics, quantum optics and nanomagnetism. However, the implementation of such functional hBN demands precise lateral nanostructuration and integration with other two-dimensional materials, and hence, novel routes of synthesis beyond exfoliation. Here, a disruptive approach is demonstrated, namely, imprinting the lateral pattern of an atomically stepped one-dimensional template into a hBN monolayer. Specifically, hBN is epitaxially grown on vicinal Rhodium (Rh) surfaces using a Rh curved crystal for a systematic exploration, which produces a periodically textured, nanostriped hBN carpet that coats Rh(111)-oriented terraces and lattice-matched Rh(337) facets with tunable width. The electronic structure reveals a nanoscale periodic modulation of the hBN atomic potential that leads to an effective lateral semiconductor multi-stripe. The potential of such atomically thin hBN heterostructure for future applications is discussed.