**Author details**

**Figure 25.** Qualitative behavior of the *I*–*V* curve for SL under study. Three *I*(*Vx* ) plots under the linear *I*–*V* curve

*Vx Vx* min.

Note finally that the characteristics of the system under study can depend on the gate voltage *Vg* (at different values of the charge carrier density *n*2*D*) owing to the dependence of the renormalized Fermi velocity on *n*2*<sup>D</sup>* [101, 102]. In this case, a controlling factor is the filling of minibands with electrons (holes). For the experimental observations, it is convenient to have partially filled either the lower electronic miniband or the upper hole one (in this case, the higher electronic or lower hole minibands are distinguishable). This takes place if


*<sup>s</sup>* <sup>=</sup> *<sup>ε</sup>s*<sup>1</sup>*dI* <sup>+</sup> *<sup>ε</sup>s*<sup>2</sup>*dI I*

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

*ε* ∗

<sup>2</sup>*<sup>D</sup>* <sup>=</sup> 4/*d*2. This condition can be rewritten in the form of a limitation imposed on

<sup>2</sup>*DLg*/*ε* ∗ *s*,

*<sup>d</sup>* .

*<sup>s</sup>* is the effective dc permittivity of the substrate. For the

correspond to the growth of the transverse voltage *Vy* (from top to bottom).

*n*2*<sup>D</sup> n*<sup>∗</sup>

the gate voltage [90]

234 Graphene - New Trends and Developments

**6. Conclusions**

where *Lg* is the gate thickness and *ε*∗

layered substrate structure (see Fig. 19a), we have

which can help to push the boundaries of science.

Pavel V. Ratnikov∗ and Andrei P. Silin

\*Address all correspondance to: ratnikov@lpi.ru

Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
