${\mathbb{Z}}_2$ invariance of Germanene on MoS${}_2$ from first principles

Abstract

We present a low energy Hamiltonian generalized to describe how the energy bands of germanene ($\overline{\mathrm{Ge}}$) 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 $\overline{\mathrm{Ge}}|$MoS${}_2$ bilayers and MoS${}_2|\overline{\mathrm{Ge}}|$MoS${}_2$ 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 MoS${}_2$ layer(s). Topologically non-trivial gaps for bilayers and trilayers can be almost as large as for a free-standing germanene layer.

References in corpus (12)

• Ultrahigh electron mobility in suspended graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Electronic structure of silicon-based nanostructures
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Spin-orbit gap of graphene: First-principles calculations
• Structural and electronic properties of germanene on MoS${}_2$
• New Family of Robust 2D Topological Insulators in van der Waals Heterostructures
• Quantum spin Hall states in graphene interacting with WS${}_2$ or WSe${}_2$
• Is Silicene the Next Graphene?

Cited by in corpus (4)

• Structural and electronic properties of germanene on MoS${}_2$
• Optimal charge-to-spin conversion in graphene on transition metal dichalcogenides
• Strain-Induced Band Engineering in Monolayer Stanene on Sb(111)
• Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction