Engineering polar discontinuities in honeycomb lattices

Unprecedented and fascinating phenomena have been recently observed at oxide interfaces between centrosymmetric cubic materials, such as LaAlO$_3$ and SrTiO$_3$, where a polar discontinuity across the boundary gives rise to polarization charges and electric fields that drive a metal-insulator transition, with the appearance of free carriers at the interface. Two-dimensional analogues of these systems are possible, and honeycomb lattices could offer a fertile playground, thanks to their versatility and the extensive on-going experimental efforts in graphene and related materials. Here we suggest different realistic pathways to engineer polar discontinuities across interfaces between honeycomb lattices, and support these suggestions with extensive first-principles calculations. Two broad approaches are discussed, that are based on (i) nanoribbons, where a polar discontinuity against the vacuum emerges, and (ii) selective functionalizations, where covalent ligands are used to engineer polar discontinuities by selective or total functionalization of the parent system. All the cases considered have the potential to deliver innovative applications in ultra-thin and flexible solar-energy devices and in micro- and nano-electronics.