Tight–Binding Analysis of Electronic Structure of Germanene Sheet and Nanoribbons Including Stone-Wales Defect

In this paper, we investigate the electronic characteristics of germanene using the tight binding approximation. Germanene as the germanium-based analogue of graphene has attracted much research interest in recent years. Our analysis is focused on the pristine sheet of germanene as well as defective monolayer. The Stone-Wales defect, which is one of the most common topological defects in such structures, is considered in this work. Not only the infinite sheet of germanene but also the germanene nanoribbons in different orientations are analyzed. The obtained results show that applying the Stone–Wales defect into the germanene monolayer changes the energy band structure; the E-k curves around the Dirac point are no longer linear, a band gap is opened, and the Fermi velocity is reduced to half of that of defect-free germanene. In the case of nanoribbon structures, the armchair germanene nanoribbons with nanoribbon widths of 3p and 3p+1 reveal the semiconductor behaviour. However, armchair germanene nanoribbon with width of 3p+2 is semi-metal. After applying the Stone–Wales defect, the band gap of armchair germanene nanoribbons with widths of 3p and 3p+1 is reduced and it is increased for the width of 3p+2. Furthermore, there is no band gap in the energy band structure of zigzag germanene nanoribbon and the metallic behaviour is obvious.