First-principles calculations were performed to investigate the electronic structure of two-dimensional (2-D) Ge, Sn, and Pb without and with the presence of an external electric field in combination with spin–orbit coupling. Tight-binding calculations based on four orbitals per atom and an effective single orbital are presented to match with the results obtained from first-principles calculations. In particular, the electronic band structure and the band splitting are investigated with both models. Moreover, the simple k·p model is also considered in order to understand the band splitting in the presence of an external electric field and spin–orbit coupling. A large splitting is obtained, which is expected to be useful for spintronic devices. The fair agreement between the first-principle, k· p model, and tight-binding approaches leads to a table of parameters for future tight-binding studies on hexagonal 2-D nanostructures. By using the tight binding parameters, the transport properties of typical 0-D triangular quantum dots between two semi-infinite electrodes in the presence of spin–orbit coupling are addressed.