Functionalized germanene as a prototype of large-gap two-dimensional topological insulators

Abstract

We propose two-dimensional (2D) topological insulators (TIs) in functionalized germanenes (GeX, X$\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}$H, F, Cl, Br, or I) using first-principles calculations. We find GeI is a 2D TI with a bulk gap of about 0.3 eV, while GeH, GeF, GeCl, and GeBr can be transformed into TIs with sizable gaps under achievable tensile strains. A unique mechanism is revealed to be responsible for the large topologically nontrivial gap obtained: due to the functionalization, the $\ensuremath{\sigma}$ orbitals with stronger spin-orbit coupling (SOC) dominate the states around the Fermi level, instead of original $\ensuremath{\pi}$ orbitals with weaker SOC. Thereinto, the coupling of the ${p}_{xy}$ orbitals of Ge and heavy halogens in forming the $\ensuremath{\sigma}$ orbitals also plays a key role in the further enlargement of the gaps in halogenated germanenes. Our results suggest a realistic possibility for the utilization of topological effects at room temperature.