${\mathbb{Z}}_2$ 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.

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• Optimal charge-to-spin conversion in graphene on transition metal dichalcogenides
• Strain-Induced Band Engineering in Monolayer Stanene on Sb(111)
• Discovering new two-dimensional topological insulators from computational screening
• Quantization of spin Hall conductivity in two-dimensional topological insulators versus symmetry and spin-orbit interaction
• Topological phases and twisting of graphene on a dichalcogenide monolayer
• Substrate-supported triplet superconductivity in Dirac semimetals
• Spontaneous breaking of time-reversal symmetry at the edges of 1T' monolayer transition metal dichalcogenides
• Substrate-induced magnetism and topological phase transition in silicene