Z2Invariance of Germanene onMoS2from First Principles

Abstract

We present a low energy Hamiltonian generalized to describe how the energy bands of germanene (Ge) are modified by interaction with a substrate or a capping layer. The parameters that enter the Hamiltonian are determined from first-principles relativistic calculations for Ge|MoS2 bilayers and MoS2|Ge|MoS2 trilayers and are used to determine the topological nature of the system. For the lowest energy, buckled germanene structure, the gap depends strongly on how germanene is oriented with respect to the MoS2 layer(s). Topologically non-trivial gaps for bilayers and trilayers can be almost as large as for a free-standing germanene layer.

Emerging Applications of Elemental 2D Materials

“…In group IV elements, silicene is predicted to have a spin–orbit gap of 1.55 meV, while germanene is predicted to have one of 23.9 meV in freestanding form. Furthermore, this gap is expected to be nearly as large in freestanding bi‐ and trilayer germanene . While silicene and germanene also possess nonzero Z 2 invariants and therefore the possibility for the QSHE, their small spin–orbit splitting makes it only possible at low temperature .…”

“…Similarly, the spin–orbit gap of silicene is predicted to be up to 57 meV due to breaking of sublattice symmetry . The energy of the spin–orbit gap of germanene on MoS 2 is predicted to also depend on the crystallographic orientation of the substrate . As 2D materials interact very strongly with their underlying substrate, which certainly affects the degree of spin–orbit coupling, it has led to the development of passivation strategies to isolate freestanding forms as well as functionalized derivatives of elemental 2D materials.…”

“…Furthermore, this gap is expected to be nearly as large in freestanding bi-and trilayer germanene. [119] While silicene and germanene also possess nonzero Z 2 invariants and therefore the possibility for the QSHE, their small spin-orbit splitting makes it only possible at low temperature. [120] Stanene, however, has been predicted to possess an appreciable spin-orbit gap of around 70 meV.…”

“…[123] The energy of the spinorbit gap of germanene on MoS 2 is predicted to also depend on the crystallographic orientation of the substrate. [119] As 2D materials interact very strongly with their underlying substrate, which certainly affects the degree of spin-orbit coupling, it has led to the development of passivation strategies to isolate freestanding forms [66] as well as functionalized derivatives of elemental 2D materials. For example, Xiong et al modeled electronic properties of stanene nanoribbons (NRs) and found that both bare and edge-hydrogenated NRs were semiconducting in nature, although including spin-orbit coupling had different response to NRs.…”

Recent Progress on Germanene and Functionalized Germanene: Preparation, Characterizations, Applications, and Challenges

“…It was found that the reconstructed germanene on the metallic surface is likely to lose its massless Dirac fermion characteristic due to hybridization, strain, and electronic doping effects . Recently, attempts to epitaxially grow germanene on nonmetallic substrates, including semimetal Sb(111) and semiconducting MoS 2 , were also reported in attempts to achieve its intrinsic electronic properties. The lattice structure of freestanding germanene is displayed in Figure a, in which the buckling degree and bond lengths are 0.7 and 2.44 Å, respectively .…”