A graphene-based superlattice formed due to the periodic modulation of the band gap has been investigated. Such a modulation is possible in graphene deposited on a strip substrate made of silicon oxide and hexagonal boron nitride. The advantages and some possible problems in the superlattice under consideration are discussed. A model describing such a superlattice is proposed and the dispersion relation between the energy and momentum of carriers has been obtained using the transfer matrix method within this model.

Monolayer films of transition metal dichalcogenides (in particular, MoS2, MoSe2, WS2, and WSe2) can be considered as ideal systems for the studies of high-temperature electron-hole liquids. The quasi-twodimensional nature of electrons and holes ensures their stronger interaction as compared to that in bulk semiconductors. The screening of the Coulomb interaction in monolayer heterostructures is significantly reduced, since it is determined by the permittivities of the environment (e.g., vacuum and substrate), which are much lower than those characteristic of the films of transition metal dichalcogenides. The multivalley structure of the energy spectrum of charge carriers in transition metal dichalcogenides significantly reduces the kinetic energy, resulting in the increase in the equilibrium density and binding energy of the electron-hole liquid. The binding energy of the electron-hole liquid and its equilibrium density are determined. It is shown that the two-dimensional Coulomb potential should be used in the calculations for the electron-hole liquid.

We study a novel type of graphene-based superlattices formed owing to a periodic modulation of the Fermi surface. Such a modulation is possible for graphene deposited on a striped substrate made of materials with substantially different values of the dc permittivity. Similar superlattices appear also in graphene sheets applied over substrates with a periodic array of parallel grooves. We suggest a model describing such superlattices. Using the transfer-matrix technique, we determine the dispersion relation and calculate the energy spectrum of these superlattices. We also analyze at a qualitative level the current-voltage characteristics of the system under study.

Plasmon collective excitations are studied in a planar graphene superlattice formed by periodically alternating regions of gapless graphene and of its gapped modification. The plasmon dispersion law is determined both for the quasi-one-dimensional case (the Fermi level is located within the minigap) and for the quasi-two-dimensional case (the Fermi level is located within the miniband). The problem concerning the absorption of modulated electromagnetic radiation at the excitation of plasmons is also considered.

We assume that both heterojunctions in the system combining a nanoribbon with gapped graphene sheets are type I junctions (e.g., see [23] for classification of junctions); i.e., the Dirac points in gapless graphene Abstract-A planar quantum well device made of a gapless graphene nanoribbon with edges in contact with gapped graphene sheets is examined. The size quantization spectrum of charge carriers in an asym metric quantum well is shown to exhibit a pseudospin splitting. Interface states of a new type arise from the crossing of dispersion curves of gapless and gapped graphene materials. The exciton spectrum is cal culated for a planar graphene quantum well. The effect of an external electric field on the exciton spec trum is analyzed.