In condensed matter/material science papers, I often encountered phrases like structural reconstruction, 3D reconstruction, 3D buckling reconstruction, etc. What do these phrases mean (especially the last one)?
In the "structural reconstruction" context it means that the crystal structure has changed -- often at a surface. In particular a "buckling reconstrction" means that the initially flat layer has changed shape -- buckling into the direction normal to the surface --- because of the Moire-modifield electronic structure.
Surfaces of materials don't look like the inside of the bulk, otherwise you'd have dangling bonds and a ton of energy. So the dangling bonds combine in a certain way to minimize that energy. This is what's called a reconstruction. In silicon, the 111 face usually reconstructs into the 7x7 pattern, which is flat and has steps. A buckling reconstruction is one where some of the atoms pop out of the plane, so the bonds form "ripples" on the surface.
Transition metal dichalcogenides, which you see in that paper, were novel for existing in 2D structures like graphene. I suppose the 3D is emphasizing that the buckling made the 3rd dimension important.