Excitonic gap, phase transition, and quantum Hall effect in graphene

We suggest that physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of an excitonic gap. The experimental form of the Hall conductivity is reproduced and the main characteristics of the dynamics are described. Predictions of the behavior of the gap as a function of temperature and a gate voltage are made.Comment: Revtex4, 10 pages, 4 figures, text essentially extended, one figure and references added; v3: to match PRB versio

Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps

By combining analytic and numerical methods, edge states on a finite width graphene ribbon in a magnetic field are studied in the framework of low-energy effective theory that takes into account the possibility of quantum Hall ferromagnetism (QHF) gaps and dynamically generated Dirac-like masses. The analysis is done for graphene ribbons with both zigzag and armchair edges. The characteristic features of the spectrum of the edge states in both these cases are described. In particular, the conditions for the existence of the gapless edge states are established. Implications of these results for the interpretation of recent experiments are discussed.Comment: 13 pages, 7 figures. v2: analysis for ribbons with armchair edges added, to appear in Phys. Rev.

Landau level collapse in graphene in the presence of in-plane radial electric and perpendicular magnetic fields

It is known that in two-dimensional relativistic Dirac systems placed in orthogonal uniform magnetic and electric fields, the Landau levels collapse as the applied in-plane electric field reaches a critical value $\pm E_c$. We study this phenomenon for a distinct field configuration with in-plane constant radial electric field. The Dirac equation for this configuration does not allow analytical solutions in terms of known special functions. The results are obtained by using both the WKB approximation and the exact diagonalization and shooting methods. It is shown that the collapse occurs for positive values of the total angular momentum quantum number, the hole (electron)-like Landau levels collapse as the electric field reaches the value $+(-) E_c/2$. The investigation of the Landau level collapse in the case of gapped graphene shows a number of distinctive features in comparison with the gapless case.Comment: 14 pages, 5 figures; final version published in PR

Formation and study of the RRAM memory elements by local anodic oxidation method

This work was supported by RFBR according to the research project № 18-37-00299 and by Grant of the President of the Russian Federation No. MK-2721.2018.8

The investigation of regularities of the memristor effect of oxide nanosized titanium structures from the parameters of local anodized oxidation

This work was supported by Grant of the President of the Russian Federation No. MK-2721.2018.8. and by RFBR according to the research project № 18-37-00299