Band gaps in incommensurable graphene on hexagonal boron nitride

Devising ways of opening a band gap in graphene to make charge-carrier masses finite is essential for many applications. Recent experiments with graphene on hexagonal boron nitride (h-BN) offer tantalizing hints that the weak interaction with the substrate is sufficient to open a gap, in contradiction of earlier findings. Using many-body perturbation theory, we find that the small observed gap is what remains after a much larger underlying quasiparticle gap is suppressed by incommensurability. The sensitivity of this suppression to a small modulation of the distance separating graphene from the substrate suggests ways of exposing the larger underlying gap

Modeling graphene-substrate interactions

In this thesis I focussed on the interactions between graphene-like materials (grapheme and germanene) and various substrates. The attractive properties of graphene like a high carrier mobility, its single-atomic thickness and its theoretical magic have made graphene a very popular and promising candidate material for numerous applications.\ud However the zero-band gap of intrinsic graphene is a drawback for applications\ud - if not for theoretical physicists! The study of gap opening mechanisms in\ud graphene and how the band structure can be engineered to behave as we wish were\ud the central questions that I have tried to address

Z

We present a low energy Hamiltonian generalized to describe how the energy bands of germanene ($\rm \overline{Ge}$) 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 $\rm \overline{Ge}|$MoS$_2$ bilayers and MoS$_2|\rm \overline{Ge} |$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

Z2 Invariance of Germanene on MoS2 from First Principles

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