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

TL;DR

This study investigates the electronic band structure and band splitting in 2D Ge, Sn, and Pb under electric fields using first-principles, tight-binding, and $k extit{ extbf{p}}$ models, aiming to inform spintronic device design.

Contribution

The paper provides a comprehensive comparison of first-principles, tight-binding, and $k extit{ extbf{p}}$ models for 2D Ge, Sn, and Pb, and offers parameter tables for future nanostructure studies.

Findings

Large band splitting observed under electric fields.

Good agreement among models validates tight-binding parameters.

Transport properties of quantum dots analyzed with spin-orbit coupling.

Abstract

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 $k\cdot p$ 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, $k\cdot p$ 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.