Group-IV nanosheets with vacancies: a tight-binding extended Hückel study

In this work, we present a theoretical study of the electronic properties of group-IV element nanosheets, namely graphene, silicene, germanene and the corresponding hydrogenated structures for the two latter, silicane and germanane. We compare the results of two different calculation methods, Density Functional Theory (DFT) and Extended Hückel Theory (EHT), for both pristine sheets and sheets of silicene and germanene with a single-atom vacancy. We show that EHT offers a remarkably reliable description of the electronic structure of these materials for all cases, thus offering an affordable way for studying large systems for which DFT calculations would be expensive and lengthy.