The stability and electronic structure of bare [001] nanowires of anatase and rutile have been investigated using ab initio density functional calculations. It was found that symmetry plays an important role in both properties below a critical diameter. Up to 2.1 nm in anatase and 3.7 nm in rutile, those {100}-walled anatase and {110}-walled rutile wires are most stable, which retain the nonsymmorphic character of the bulk space group. Our results explain the observed properties of atomic size anatase nanowires. The wires with screw symmetry also show a consistently larger gap in their electronic structures compared to similarly walled wires without it. Additionally, in rutile the indirect or direct character of the band structure is coupled to the presence or absence of the screw axis.
We investigate the effects of external electric fields on the electronic properties of bilayer armchair graphene nano-ribbons. Using atomistic simulations with Tight Binding calculations and the Non-equilibrium Green's function formalism, we demonstrate that (i) in semi-metallic structures, vertical fields impact more effectively than transverse fields in terms of opening larger bandgap, showing a contrary phenomenon compared to that demonstrated in previous studies in bilayer zigzag graphene nano-ribbons; (ii) in some semiconducting structures, if transverse fields just show usual effects as in single layer armchair graphene nano-ribbons where the bandgap is suppressed when varying the applied potential, vertical fields exhibit an anomalous phenomenon that the bandgap can be enlarged, i.e., for a structure of width of 16 dimer lines, the bandgap increases from 0.255 eV to the maximum value of 0.40 eV when a vertical bias equates 0.96 V applied. Although the combined effect of two fields does not enlarge the bandgap as found in bilayer zigzag graphene nano-ribbons, it shows that the mutual effect can be useful to reduce faster the bandgap in semiconducting bilayer armchair graphene nano-ribbons. These results are important to fully understand the effects of electric fields on bilayer graphene nano-ribbons (AB stacking) and also suggest appropriate uses of electric gates with different edge orientations..
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