**4.8. Some intermediate conclusions**

Before proceeding to the next section, let us recall some results obtained in this section. We think that it is important for understanding the next results.

We have analyzed the characteristics of planar graphene nanostructures. On the one hand, they retain the unique properties of infinite graphene sheets. On the other hand, bandgap opening makes them important building blocks in carbon-based nanoelectronics, which can be used to control electron motion. Parameters of graphene QWs can easily be manipulated by varying the gapless nanoribbon width or the potential barriers in the adjoining gapped graphene sheets.

We predict pseudospin splitting to occur in asymmetric graphene QWs and interface states to arise from the crossing of dispersion curves of gapless and gapped graphene materials. We have performed calculations of optical properties of planar graphene nanostructures and suggested possible experiments to study the effects in question.

Analysis of pseudospin (valley) characteristics in the heterostructure is simplified by using an effective Hamiltonian having a pseudospin-split energy spectrum. Note that an analogous spectrum was discussed in [63–65]. Therefore, the effective Hamiltonian must contain a Rashba-like spin-orbit coupling. We have developed the effective theory for describing graphene-based systems with the pseudospin splitting.
