Landau quantization $\epsilon=\hbar\omega_{c}m\pm\frac{\delta'}{2}\sqrt{1+\frac{4\hbar^{2}\omega_{c }^{2}\beta^{2}m}{\delta'^{2}}}$ for fermions from mass chiral Dirac equation for the system of doped graphene/insulator/doped graphene and from Schrödinger equation for the two-dimensional materials with spin-orbit interactions in a second quantization is found exactly. Quantum Hall effect in layered graphite as well as in two-dimensional materials with spin-orbit interactions is predicted. Schrödinger equation for pair of two particles of carbon armchair ribbon when magnetic field is applied is analytically solved. The perfect pairing between electron Fermi spheres when magnetic field is applied creating a Cooper pair is found. The conditions under which the bielectron states exist are shown to be concerned with the higher magnetic fields.

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