Why don't the twisted bilayers of Mo and W based transition metal dichalcogenides behave like regular semiconductors?

The Mo and W based transition metal dichalcogenides have been known for more than sixty years as examples of solid state lubricants, possible because of the weak van der Waals interactions between the layers which allows one layer to easily slide over the other. It is only recently that one finds unusual phenomena arising in them on doping holes via gating into twisted bilayers, an aspect that we would associate with correlated materials. The untwisted limit has been long understood as a regular semiconductor whose properties are well described by band theory.

We have recently examined the electronic structure of twisted bilayers of Mo and W based transition metal dichalcogenides. In contrast to graphene, we find the emergence of flat bands for several angles of rotation. The origin of this can be linked to patches of various types of stackings - atom-on-atom versus a staggered stacking. The former lead to larger interlayer separations because of larger repulsion between the electrons in the two layers in contrast to the latter. This leads to larger perturbations in some regions of the moire cell. Building on the fact that these materials represent van der Waals structures, and so the perturbation induced by one layer on the other should be small, we explore different twist angles and quantify the perturbation in each instance from the untwisted limit. Surprisingly, at large twist angles we find that we recover the low energy electronic structure of the untwisted limit, while at small angles we find flat band formation as well as other unusual aspects of the electronic structure.