Electronic band dispersion of graphene nanoribbons via Fourier-transformed scanning tunneling spectroscopy

The electronic structure of atomically precise armchair graphene nanoribbons of width N=7 (7-AGNRs) are investigated by scanning tunneling spectroscopy (STS) on Au(111). We record the standing waves in the local density of states of finite ribbons as a function of sample bias and extract the dispersion relation of frontier electronic states by Fourier transformation. The wave-vector-dependent contributions from these states agree with density functional theory calculations, thus enabling the unambiguous assignment of the states to the valence band, the conduction band, and the next empty band with effective masses of 0.41±0.08me,0.40±0.18me, and 0.20±0.03me, respectively. By comparing the extracted dispersion relation for the conduction band to corresponding height-dependent tunneling spectra, we find that the conduction band edge can be resolved only at small tip-sample separations and has not been observed before. As a result, we report a band gap of 2.37±0.06 eV for 7-AGNRs adsorbed on Au(111).

Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Toward Cove-Edged Low Band Gap Graphene Nanoribbons

Graphene nanoribbons (GNRs), defined as nanometer-wide strips of graphene, have attracted increasing attention as promising candidates for next-generation semiconductors. Here, we demonstrate a bottom-up strategy toward novel low band gap GNRs (E-g = 1.70 eV) with a well-defined cove-type periphery both in solution and on a solid substrate surface with chrysene as the key monomer. Corresponding cyclized chrysene-based oligornerS consisting of the dimer and tetramer are obtained via an Ullmann Coupling followed by oxidative intramolecular cyclodehydrogenation in solution, and much higher GNR homologues via on-surface synthesis. These oligomers adopt nonplanar structures due to the isteric repulsion between the two C-H bonds at the inner cove position. Characterizations by single crystal X-ray analysis, UV-vis absorption spectroscopy, NMR spectroscopy, and scanning tunneling microscopy (STM) are described. The interpretation is assisted by density functional theory (DFT) calculations.

Searching the hearts of graphene-like molecules for simplicity, sensitivity and logic

If quantum interference patterns in the hearts of polycyclic aromatic hydrocarbons (PAHs) could be isolated and manipulated, then a significant step towards realizing the potential of single-molecule electronics would be achieved. Here we demonstrate experimentally and theoretically that a simple, parameter-free, analytic theory of interference patterns evaluated at the mid-point of the HOMO-LUMO gap (referred to as M-functions) correctly predicts conductance ratios of molecules with pyrene, naphthalene, anthracene, anthanthrene or azulene hearts. M-functions provide new design strategies for identifying molecules with phase-coherent logic functions and enhancing the sensitivity of molecular-scale interferometers.

Resolving Atomic Connectivity in Graphene Nanostructure Junctions

We report on the structural characterization of junctions between atomically well-defined graphene nanoribbons (GNRs) by means of low-temperature, noncontact scanning probe microscopy. We show that the combination of simultaneously acquired frequency shift and tunneling current maps with tight binding (TB) simulations allows a comprehensive characterization of the atomic connectivity in the GNR junctions. The proposed approach can be generally applied to the investigation of graphene nanomaterials and their interconnections and is thus expected to become an important tool in the development of graphene-based circuitry.