Electronic structure of single-wall silicon nanotubes and silicon   nanorribons: Helical symmetry treatment and effect of dimensionality
  Helical method of tube formation for band structure calculations and Hartree-Fock self-consistent field method (HF-SCF) modified for periodic solids have been applied in study of electronic properties of single-wall silicon nanotubes (SWSiNT), graphene-like parent 2D-hP silicone sheet and nanoribbons (SiNR). The results obtained for nanotubes of the length of ${\approx}$ 358 \AA in diameter range ${\approx}$ 3.7 \AA -- 116 \AA of different helicity-types have shown that only small-diameter SWSiNTs up to} ${\varphi}${6.3 \AA ~ are metallic due to the effect of curvature which induces coupling of}{${\sigma}$}{and}{${\pi}$}{orbitals. From the calculated band structures follow that irrespective of helicity, the SWSiNTs of larger diameter are all small-gap semiconductors with direct gap between the Dirac-like cones of}(${\pi}$\textsuperscript{*}, ${\pi}$) bands{.}Gap of SWSiNTs exhibits, however, an oscillatory-decreasing character with increase of the tube diameter. In the oscillatory series, minima of the gap in {\textquotedblleft}saw-teeth{\textquotedblright} pattern are reached for helicity numbers m \textsubscript{a} that are an integer multiple of 3, whilst m\textsubscript{a} value itself directly determine the fold-number of particular tubular rotational axis symmetry. Oscillations are damped and gap decreases toward {${\approx}$ 0.33 eV} for tube diameter {${\approx}$ 116 \AA .} {Irrespective of the width, the SiNRs are all small-gap semiconductors, characteristic by oscillatory decreasing gap with increasing ribbon widths. The gap of SWSiNTs and SiNRs is tuneable through modulation of tube diameter or ribbon width, respectively. 
Pavol Banacky, Jozef Noga, Vojtech Szocs
cond-mat.mes-hall cond-mat.mtrl-sci