Analytical Study of Electronic Structure in Archimedean Type-Spiral Zig-Zag Graphene Nanoscroll

The semiconducting electronic properties of graphene nanoscroll (GNS) are very much related to its geometric structure. The aim of this study is to construct a GNS energy dispersion model within low-energy transport of 1 eV in identifying its electronic properties and carrier statistics. Non-parabolic energy dispersion is used to incorporate the Archimedean type-spiral model, and the band gap is assessed based on chirality and geometry effects. The energy band within low-energy transport indicates that GNS can achieve a quantum conductance limit of ~6.45 kΩ for ballistic transport. On the other hand, the numbers for three minimum sub-bands are attained based on non-parabolic energy dispersion, and the semi-metallic zig-zag GNS is found at chirality (3j + 1, 0). This work consistently predicts the semiconducting properties of the tight-binding model from previous work. The GNS overlapping region strongly affects its electronic properties. Constantly increasing the length of the overlapping region decreases the band gap exponentially, whilst semimetallic GNS forms when the overlap reaches a certain limit. The carrier density with temperature dependence is subsequently assessed at the intrinsic level, and found that the number of carriers in GNS shows a higher rate of increment (exponentially) compared to carbon nanotubes (CNT), in accordance to their diameter. The results are very useful in giving an intuitive understanding on GNS carrier statistics as subject to geometry changes.