Carbon vs silicon polyprismanes: a comparative study of metallic sp3-hybridized allotropes

Polyprismanes are the special type of single-walled nanotubes with an extremely small cross-section in the form of a regular polygon. In the presented study, we considered carbon and silicon polyprismanes that are constructed from carbon and silicon five-, six-, seven- and eight-membered rings, respectively. By means of density functional theory using the periodic boundary conditions, the geometry and electronic characteristics of these tubes were investigated. The results obtained indicate that, with an increase in the effective diameter, carbon polyprismanes undergo an abrupt change in electronic properties, which can be described as a transition from the dielectric to the metallic state. The character of the energy spectrum, as well as the behavior of transmission function near the Fermi level, illustrate that at some critical diameter they begin to exhibit non-typical for the sp(3)-carbon systems metallic nature. In such a case, it has been found from the partial density of electronic states calculation that the overlapping of bands near the Fermi level is mainly due to the 2p state of carbon atoms. Unlike carbon analogs, silicon polyprismanes are metals for any considered diameter. The metallic properties of the silicon polyprismanes arise due to the 3p states of the silicon atoms. Unexpected properties endowed by the prismane morphology discover new prospects of application of carbon and silicon nanostructures as the basic elements of future electronics.