Electrically Engineered Band Gap in Two-Dimensional Ge, Sn, and Pb: A First-Principles and Tight-Binding Approach

Abstract

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