No Arabic abstract
{gamma}-graphdiyne is a 2D carbon structure beyond graphene: it is formed by sp and sp2 carbon atoms organized as hexagonal rings connected by linear links, and it is predicted to be a semiconductor. The lateral confinement of {gamma}-graphdiyne nanoribbons significantly affects the electronic and vibrational properties. By means of periodic Density Functional Theory (DFT) calculations we investigate here the electronic band structure, the Raman and IR spectra of the {gamma}-graphdiyne 2D crystal and related nanoribbons. We discuss the effect of the functional and basis set on the evaluation of the band gap, highlighting the reliability of hybrid functionals. By joining DFT calculations with a symmetry analysis, we assign in detail the IR and Raman spectra of {gamma}-graphdiyne. On this basis we show the modulation of the gap in nanoribbons of increasing width and different edges (armchair, zigzag). We assess how confinement affects the Raman and IR spectra of such nanoribbons by comparing their vibrational modes with the phonons of the parent 2D crystal. Our symmetry-based classification allows identifying the marker bands sensitive to the edge structure and lateral confinement of nanoribbons of increasing width. These results show the effectiveness of vibrational spectroscopy for the characterization of such nanostructures.
By analytically constructing the matrix elements of an electron-phonon interaction for the $D$ band in the Raman spectra of armchair graphene nanoribbons, we show that pseudospin and momentum conservation result in (i) a $D$ band consisting of two components, (ii) a $D$ band Raman intensity that is enhanced only when the polarizations of the incident and scattered light are parallel to the armchair edge, and (iii) the $D$ band softening/hardening behavior caused by the Kohn anomaly effect is correlated with that of the $G$ band. Several experiments are mentioned that are relevant to these results. It is also suggested that pseudospin is independent of the boundary condition for the phonon mode, while momentum conservation depends on it.
A second-order topological insulator (SOTI) in $d$ spatial dimensions features topologically protected gapless states at its $(d-2)$-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state, it has been attracting great interest, but it remains a challenge to identify a realistic SOTI material in two dimensions (2D). Here, based on combined first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized 2D material graphdiyne as the first realistic example of a 2D SOTI, with topologically protected 0D corner states. The role of crystalline symmetry, the robustness against symmetry-breaking, and the possible experimental characterization are discussed. Our results uncover a hidden topological character of graphdiyne and promote it as a concrete material platform for exploring the intriguing physics of higher-order topological phases.
Using large-scale DFT calculations, we have investigated the structural and electronic properties of both armchair and zigzag graphdiyne nanotubes as a function of size. To provide insight in these properties, we present new detailed calculations of the structural relaxation energy, effective electron/hole mass, and size-scaling of the bandgap as a function of size and chirality using accurate screened-exchange DFT calculations. These calculations provide a systematic evaluation of the structural and electronic properties of the largest graphdiyne nanotubes to date - up to 1,296 atoms and 23,328 basis functions. Our calculations find that zigzag graphdiyne nanotubes (GDNTs) are structurally more stable compared to armchair GDNTs of the same size. Furthermore, these large-scale calculations allow us to present simple analytical formulae to guide future experimental efforts for estimating the fundamental bandgaps of these unique nanotubes as a function of chirality and diameter. While the bandgaps for both the armchair and zigzag GDNTs can be tuned as a function of size, the conductivity in each of these two different chiralities is markedly different. Zigzag GDNTs have wider valence and conduction bands and are expected to have a higher electron- and hole-mobility than their armchair counterparts.
Bottom-up approaches allow the production of ultra-narrow and atomically precise graphene nanoribbons (GNRs), with electronic and optical properties controlled by the specific atomic structure. Combining Raman spectroscopy and ab-initio simulations, we show that GNR width, edge geometry and functional groups all influence their Raman spectra. The low-energy spectral region below 1000 cm-1 is particularly sensitive to edge morphology and functionalization, while the D peak dispersion can be used to uniquely fingerprint the presence of GNRs, and differentiates them from other sp2 carbon nanostructures.
Topological insulators (TIs) are an emerging class of materials that host highly robust in-gap surface/interface states while maintaining an insulating bulk. While most notable scientific advancements in this field have been focused on TIs and related topological crystalline insulators in 2D and 3D, more recent theoretical work has predicted the existence of 1D symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally-confined, semiconducting strips of graphene is determined by their width, edge shape, and the terminating unit cell, and is characterized by a Z2 invariant (similar to 1D solitonic systems). Interfaces between topologically distinct GNRs characterized by different Z2 are predicted to support half-filled in-gap localized electronic states which can, in principle, be utilized as a tool for material engineering. Here we present the rational design and experimental realization of a topologically-engineered GNR superlattice that hosts a 1D array of such states, thus generating otherwise inaccessible electronic structure. This strategy also enables new end states to be engineered directly into the termini of the 1D GNR superlattice. Atomically-precise topological GNR superlattices were synthesized from molecular precursors on a Au(111) surface under ultra-high vacuum (UHV) conditions and characterized by low temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Our experimental results and first-principles calculations reveal that the frontier band structure of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This novel manifestation of 1D topological phases presents an entirely new route to band engineering in 1D materials based on precise control of their electronic topology, and is a promising platform for future studies of 1D quantum spin physics.