2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons

Comparative analysis of absorption resonances between carbynes and cyclo[n]carbons

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo[n]carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and theab initiotime-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following theNring=2Nchain+2rule, which states that the number of atoms in an atomic ringNringis twice the number of atoms on a finite chainNchainwith two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes withN=7and8carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynesN = 7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo[n]carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

Unravelling the Complete Raman Response of Graphene Nanoribbons Discerning the Signature of Edge Passivation

Controlling the edge morphology and terminations of graphene nanoribbons (GNR) allows tailoring their electronic properties and boosts their application potential. One way of making such structures is encapsulating them inside single-walled carbon nanotubes. Despite the versatility of Raman spectroscopy to resolve strong spectral signals of these systems, discerning the response of long nanoribbons from that of any residual precursor remaining outside after synthesis has been so far elusive. Here, the terrylene dye is used as precursor to make long and ultra-narrow armchair-edged GNR inside nanotubes. The alignment and characteristic length of terrylene encapsulated parallel to the tube's axis facilitates the ribbon formation via polymerization, with high stability up to 750 °C when the hybrid system is kept in high vacuum. A high temperature annealing is used to remove the terrylene external molecules and a subtraction model based on the determination of a scaling factor related to the G-band response of the system is developed. This not only represents a critical step forward toward the analysis of the nanoribbon-nanotube system, but it is a study that enables unraveling the Raman signatures of the individual CH-modes (the signature of edge passivation) for GNR for the first time with unprecedented detail.

A theoretical study on the electronic, structural and optical properties of armchair, zigzag and chiral silicon-germanium nanotubes

In this work we have studied infinite size silicon-germanium alloy nanotubes of several types, armchair, zigzag and chiral, by theoretical analysis based on density functional theory as implemented in the SIESTA code, which utilizes a linear combination of atomic orbitals and a generalized gradient approximation proposed by Perdew, Burke and Ernzerhof (GGA-PBE) for the exchange and correlation energy. The structures were relaxed until the atomic forces were less than 0.0001 eV Å-1. The electronic band structure, density of states and cohesive energy were then computed; the optical calculation was run in between 0 and 6 eV, with a broadening of 0.05 eV. The obtained results exhibit the deformation of the structure on the surface, which seems to be related to its stability. The armchair and zigzag tubes are direct band gap semiconductor materials, while chiral nanotubes shift from indirect to direct bandgap semiconductors, depending on their diameter size. Likewise, the bandgap depends on the diameter of the SiGe nanotubes (SiGeNTs). We have associated the absorption curves and the density of states through Van Hove singularities. In summary, our results on the structural and electronic properties of SiGeNTs elucidate their possible applications in thermoelectrics, photovoltaics and nanoelectronics, while the possibility of associating the absorption curves with the density of states provides a method of characterization.