Formalization of the General Model of the Green Economy at the Regional Level

The paper focuses on the study of the problems of the economic and mathematical modeling of the green economy at the regional level. The purpose of the research is the development of economic and mathematical tools for the economic and ecological systems’ modeling at the regional level on the basis of the principles of green economy. The hypothesis of the research is based on the thesis that in the conditions of the exhaustion of natural resources and depletion of natural capital, the technogenic fields, production and consumption waste could be considered as a resource basis for modernization. Such factors’ use leads to the elimination of accumulated environmental damage and substitution of natural resources. The paper describes the approaches to the system modeling problem-solving in order to develop the green economy both in the country and its regions. The urgency of the transition to a green economy is confirmed by the theoretical and practical research on the cyclical development of the socio-eco-economic systems. A number of formalized models and methods for solving the current environmental and economic issues including the economic valuation of accumulated environmental damage, eco-economic assessment of the efficiency of natural resource substitution with resource-substitute are proposed as well as the choice of an optimal set of resources-substitutes taking into account the financial and natural resource constraints. The authors research the typical model of green growth considering the exhaustion of natural resources, technogenic resources deposits involving in economic circulation through the implementation of investment projects on the elimination of accumulated environmental damage. The results could be used in the different regions of Russia for the justification and implementation of investment projects within the framework of the federal target program “Elimination of accumulated environmental damage” in 2015–2026 years.The research has been supported by the Grant of the Russian Foundation for Humanities, Project №14–02–00235а

Minimal conductivity in bilayer graphene

Using the Landauer formula approach, it is proven that minimal conductivity of order of $e^{2}/h$ found experimentally in bilayer graphene is its intrinsic property. For the case of ideal crystals, the conductivity turns our to be equal to $e^{2}/2h$ per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value $1-2/\pi$ is close to the value 1/3 found earlier for the single-layer graphene.Comment: 3 pages, 1 figur

Zitterbewegung, chirality, and minimal conductivity in graphene

It has been recently demonstrated experimentally that graphene, or single-layer carbon, is a gapless semiconductor with massless Dirac energy spectrum. A finite conductivity per channel of order of $e^{2}/h$ in the limit of zero temperature and zero charge carrier density is one of the striking features of this system. Here we analyze this peculiarity based on the Kubo and Landauer formulas. The appearance of a finite conductivity without scattering is shown to be a characteristic property of Dirac chiral fermions in two dimensions.Comment: final version; 4 pages, 1 eps figur

Wave packet revivals in a graphene quantum dot in a perpendicular magnetic field

We study the time-evolution of localized wavepackets in graphene quantum dots under a perpendicular magnetic field, focusing on the quasiclassical and revival periodicities, for different values of the magnetic field intensities in a theoretical framework. We have considered contributions of the two inequivalent points in the Brillouin zone. The revival time has been found as an observable that shows the break valley degeneracy.Comment: 5 pages, 4 figures, corrected typo, To appear in Phys. Rev.

Electronic correlations and crystal structure distortions in BaBiO3

BaBiO3 is a material where formally Bi4+ ions with the half-filled 6s-states form the alternating set of Bi3+ and Bi5+ ions resulting in a charge ordered insulator. The charge ordering is accompanied by the breathing distortion of the BiO6 octahedra (extension and contraction of the Bi-O bond lengths). Standard Density Functional Theory (DFT) calculations fail to obtain the crystal structure instability caused by the pure breathing distortions. Combining effects of the breathing distortions and tilting of the BiO6 octahedra allows DFT to reproduce qualitatively experimentally observed insulator with monoclinic crystal structure but gives strongly underestimate breathing distortion parameter and energy gap values. In the present work we reexamine the BaBiO3 problem within the GGA+U method using a Wannier functions basis set for the Bi 6s-band. Due to high oxidation state of bismuth in this material the Bi 6s-symmetry Wannier function is predominantly extended spatially on surrounding oxygen ions and hence differs strongly from a pure atomic 6s-orbital. That is in sharp contrast to transition metal oxides (with exclusion of high oxidation state compounds) where the major part a of d-band Wannier function is concentrated on metal ion and a pure atomic d-orbital can serve as a good approximation. The GGA+U calculation results agree well with experimental data, in particular with experimental crystal structure parameters and energy gap values. Moreover, the GGA+U method allows one to reproduce the crystal structure instability due to the pure breathing distortions without octahedra tilting

Unconventional quantum Hall effect and Berry’s phase 2pi in bilayer graphene.

There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry’s phase 2pi affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behavior in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies

Theory of Weiss oscillations in the magnetoplasmon spectrum of Dirac electrons in graphene

We present the collective excitations spectrum (magnetoplasmon spectrum) of Dirac electrons in a weakly modulated single graphene layer in the presence of a uniform magnetic field. We consider electric modulation in one-dimension and the magnetic field applied perpendicular to graphene.We derive analytical results for the intra-Landau band plasmon spectrum within the self-consistent-field approach. We find Weiss oscillations in the magnetoplasmon spectrum which is the primary focus of this work. Results are presented for the intra-Landau band magnetoplasmon spectrum as a function of inverse magnetic field. These results are also compared with those of conventional 2DEG. We have found that the Weiss oscillations in the magnetoplasmon spectrum are larger in amplitude compared to those in conventional 2DEG for the same modulation strength, period of modulation and electron density.Comment: 9 pages, 1 figure Phys. Rev. B (accepted for publication