The electronic states of GNRs largely depend on the edge structures (armchair or zigzag). In zigzag edges each successive edge segment is at the opposite angle to the previous. In armchair edges, each pair of segments is a 120/-120 degree rotation of the prior pair. The animation below provides a visualization explanation of both. Zigzag edges provide the edge localized state with non-bonding molecular orbitals near the
Fermi energy. They are expected to have large changes in optical and electronic properties from
quantization. Calculations based on
tight binding theory predict that zigzag GNRs are always metallic while armchairs can be either metallic or semiconducting, depending on their width. Their 2D structure, high electrical and
thermal conductivity and low noise also make GNRs a possible alternative to copper for integrated circuit interconnects. Research is exploring the creation of quantum dots by changing the width of GNRs at select points along the ribbon, creating
quantum confinement. Heterojunctions inside single graphene nanoribbons have been realized, among which structures that have been shown to function as tunnel barriers. Graphene nanoribbons possess
semiconductive properties and may be a technological alternative to
silicon semiconductors capable of sustaining
microprocessor clock speeds in the vicinity of 1 THz
field-effect transistors less than 10 nm wide have been created with GNR – "GNRFETs" – with an Ion/Ioff ratio >106 at room temperature. File:cnt_gnrarm_v3.gif|GNR band structure for armchair type. Tight binding calculations show that armchair type can be semiconducting or metallic depending on width (chirality). File:cnt_zz_v3.gif|GNR band structure for zigzag type. Tight binding calculations predict that zigzag type is always metallic. File:Graphene_Nanoribbons_of_controlled_width.jpg|
TEM micrographs of GNRs of (a) w=15, (b) w=30, (c) w=40 (exfoliating), and (d) w=60 nm deposited on 400 mesh lacey carbon grids and (e) FESEM micrograph of 600 nm ribbon. (f) Electron microscope images of a 120-nm graphene ribbons (FESEM), (g) 50 nm square GQDs (FESEM), (h,i) 25×100 nm2 rectangular GQDs (FESEM), and (j) 8°-angled tapered GNR (or triangular GQD) (FESEM)). The large densities of square and rectangular GQDs (g) showed extensive folding (white arrows). Bar sizes=(a) 250 nm, (b,g,i) 50 nm, (c,d) 500 nm, and (h) 1 μm.
Electronic structure in external fields The electronic properties in external field such as static electric or magnetic field have been extensively studied. The various levels of the tight-binding model as well as first principles calculations have been employed for such studies. For zigzag nanoribbons the most interesting effect under an external
electric field is inducing of half-metallicity. In a simple tight-binding model the effect of the external in-plane field applied across the ribbon width is the band gap opening between the edge states. However, the first principles spin-polarized calculations demonstrate that the spin up and down species behave differently. One spin projection closes the band gap whereas another increases. As a result, at some critical value of field, the ribbon turns into a metallic for one spin projection (up or down) and an insulating for another spin (down or up). In this way, half-metallicity that may be useful for spintronics applications is induced. Armchair ribbons behave differently from their zigzag siblings. They usually feature a band gap that closes under an external in-plane electric field. At some critical value of the field the gap fully closes forming a Dirac cone linear crossing, see Fig. 9d in Ref. This intriguing result have been corroborated by the density functional theory calculations and explained in a simplified tight-binding model. It does not depend on the chemical composition of the ribbon edges, for example both fluorine and chorine atoms can be used for the ribbon edge passivation instead of a usual hydrogen. Also this effect can be induced by chemical co-doping, i.e. by placing nitrogen and boron atoms atop the ribbon at its opposite sides. Modelwise the effect can be explained by a pair of cis-polyacetylene chains placed at a distance corresponding to the ribbon width and subjected to the different gate potentials. Bearded ribbons with Klen-type edges behave in the tight-binding model approximation similar to zigzag ribbons. Namely, the band gap opens between the edge states. Due to chemical instability of this type of the edge configuration, such ribbons are normally excluded from the publications. Whether they can at least hypothetically exhibit half-metallicity in external in-plane fields similar to zigzag nanoribbons is not yet clear. A vast family of cousins of the above ribbons with both similar edges is the class of ribbons combining non-equivalent edge geometries in a single ribbon. One of the simplest examples can be a half-bearded nanoribbon. Such ribbons, in principle, could be more stable than nanoribbons with two bearded edges because they could be realized via asymmetric hydrogenation of zigzag ribbons. In the nearest neighbor tight-binding model and in non-spin-polarized density functional theory calculations such ribbons exhibit chiral anomaly structure. The fully flat band of a pristine half-bearded nanoribbon subjected to the in-plane external electric field demonstrates unidirectional linear dispersions with group velocities of opposite directions around each of the two Dirac points. At high fields, the linear bands around the Dirac points transform into a wiggly cubic-like dispersions. This nontrivial behavior is favorable for the field-tunable dissipationless transport. The drastic transformation from fully flat to linear and then cubic-like band allows for a continuum \vec{k}\cdot\vec{p} model description based on the Dirac equation. The Dirac equation supplemented with the suitable boundary conditions breaking the inversion/mirror symmetry and a single field strength parameter admits an analytic solution in terms of Airy-like special functions. == Mechanical properties ==