Taher Amlaki, Menno Bokdam and Paul J. Kelly, Physical Review Letters **116**, 256805 (2016).

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|MoS_{2} bilayers and MoS_{2}|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 nontrivial gaps for bilayers and trilayers can be almost as large as for a freestanding germanene layer.

Figure 1 S** **Stereographic projection of the phase space of the model Hamiltonian. Black lines represent boundaries between regions where the gap vanishes; phases on either side of the dashed black lines are the same. The scaling of the λ_{so} and λ_{m} variables with R-Z is explained in the text. When germanene is rotated with respect to MoS_{2}, a trajectory is traced out in parameter space which is shown in red for a GeMoS_{2} bilayer and in blue for a MoS_{2}|Ge|MoS_{2} trilayer, where the two MoS_{2} layers are rotated with respect to one another by θ_{1} − θ_{2} = 15°.