**6. Conclusions**

We presented the method for the theoretical research of the electron properties of the planar heterostructures based on graphene, namely, the single heterojunctions, QWs, and SLs. The usage of the gap modifications of graphene in the planar heterostructures is a novel idea which can help to push the boundaries of science.

The valley-polarized currents must exist at the single heterojunctions. The novel phenomena of pseudospin splitting in the energy spectrum of the asymmetric QWs had been theoretically predicted. Some optical properties of the graphene-based QWs was considered (observation of the excitonic lines).

A model describing SL based on graphene on a strip substrate has been proposed. The dispersion relation has been derived, which is transferred to the known nonrelativistic dispersion relation in the passage to the single-band limit. The numerical calculations have been performed for a pair of the nearest electron and hole minibands using the derived dispersion relation. Possible applications of SL as a transistor or a terahertz laser have been pointed out.

We suggested a novel class of graphene-based systems, which are at the same time both photon crystals and graphene SLs with periodically varying Fermi velocity. Such a modulation appears to be possible owing to the renormalization of the Fermi velocity in the energy spectrum of graphene. New prospects become open for the implementation of the technologies based on controlled Fermi velocity. We point out some specific features of the transport phenomena in such systems, in particular, appearance of the sections with negative differential conductivity in the *I*–*V* curves. It is clear that, similarly to photon crystals, these systems should exhibit interesting optical characteristics.
