Topology concepts have significantly deepened of our understanding in recent years of the electronic properties of one-dimensional (1D) nano structures such as the graphene nanoribbons. Controlling topological electronic properties of GNRs has been d
emonstrated in both theoretical studies and experimental realization. Most previous works rely on classification theory requiring both time reversal and spatial symmetry of a unit cell in the 1D bulk material that is commensurate to its boundary. To access boundary structures that lead to unit cell with no spatial symmetry and to generalize the theory, we propose here another classification scheme, using chiral symmetry, to arrive at a Z classification that is not only applicable to GNRs with arbitrary terminations, but also to any general 1D chiral structures. This theory, combining with Liebs theorem, moreover enables access to the electrons spin degree of freedom, allowing for investigation of spin physics.
The design and fabrication of robust metallic states in graphene nanoribbons (GNRs) is a significant challenge since lateral quantum confinement and many-electron interactions tend to induce electronic band gaps when graphene is patterned at nanomete
r length scales. Recent developments in bottom-up synthesis have enabled the design and characterization of atomically-precise GNRs, but strategies for realizing GNR metallicity have been elusive. Here we demonstrate a general technique for inducing metallicity in GNRs by inserting a symmetric superlattice of zero-energy modes into otherwise semiconducting GNRs. We verify the resulting metallicity using scanning tunneling spectroscopy as well as first-principles density-functional theory and tight binding calculations. Our results reveal that the metallic bandwidth in GNRs can be tuned over a wide range by controlling the overlap of zero-mode wavefunctions through intentional sublattice symmetry-breaking.
We have identified an unusually stable helical coil allotrope of phosphorus. Our ab initio Density Functional Theory calculations indicate that the uncoiled, isolated straight 1D chain is equally stable as a monolayer of black phosphorus dubbed phosp
horene. The coiling tendency and the attraction between adjacent coil segments add an extra stabilization energy of about 12 meV/atom to the coil allotrope, similar in value to the approximately 16 meV/atom inter-layer attraction in bulk black phosphorus. Thus, the helical coil structure is essentially as stable as black phosphorus, the most stable phosphorus allotrope known to date. With an optimum radius of 2.4 nm, the helical coil of phosphorus may fit well and even form inside wide carbon nanotubes.
