Germanene and stanene on two-dimensional substrates: Dirac cone and Z2 invariant

Abstract

By using the combination of the ab initio density functional theory and data mining of the Inorganic Crystal Structure Database, a series of monolayer materials are found to be suitable substrates for germanene or stanene, including some of the $\mathrm{Cd}{\mathrm{I}}_{2}$-type materials, CuI, and GaGeTe. All of the found materials, when they are used as the substrate, can almost preserve the quasifreestanding geometry, stability, and band structure of germanene or stanene. Among them, $\mathrm{Cd}{\mathrm{I}}_{2}$ and $\mathrm{Zn}{\mathrm{I}}_{2}$ can open a relatively large band gap of 0.16--0.18 (0.13--0.16) eV [without (with) spin-orbit coupling] in germanene, while preserving Dirac-cone-like band structures. Moreover, the ${Z}_{2}$ invariants of germanene on CuI and stanene on $\mathrm{Ca}{\mathrm{I}}_{2}$ are found to be nontrivial. The interaction between germanene and substrates can be well modeled by the low-energy tight-binding Hamiltonian of germanene under external fields. Our analysis based on the tight-binding Hamiltonian shows that suitable substrates mainly act like a ``pseudoelectric'' field on germanene, and that strong linear correlations are seen among the ``pseudoelectric'' field, extrinsic Rashba coefficient, and charge transfer.