Quantum Field Theory of Graphene with Dynamical Partial Symmetry Breaking

Grushevskaya, H. V.; Krylov, George

doi:10.4236/jmp.2014.510100

Cited by 6 publications

(9 citation statements)

References 42 publications

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“…Let us consider the screening in true two-dimensional (2D) semimetals. As known, [15][16][17] free charge carriers at the Fermi level in these materials are absent.…”

Section: Screening Depending On Charge State Of Mixed-valence Complexesmentioning

confidence: 99%

Enhancement of Raman light scattering in dye-labeled cell membrane on metal-containing conducting polymer film

Grushevskaya

Крылова

Lipnevich

et al. 2016

Int. J. Mod. Phys. B

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An enhanced Raman spectroscopy method based on a plasmon resonance in ultrathin metal-containing LB-film deposited on nanoporous anodic alumina supports has been proposed. This material has been utilized to enhance Raman scattering of light in fluorescent-labeled subcellular membrane structures. It has been shown that the plasmon resonance between vibrational modes of the organometallic complexes monolayers and dye-labeled subcellular structures happens. It makes possible to detect interactions between living cell monolayers and an extracellular matrix.

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“…Let us consider the screening in true two-dimensional (2D) semimetals. As known, [15][16][17] free charge carriers at the Fermi level in these materials are absent.…”

Section: Screening Depending On Charge State Of Mixed-valence Complexesmentioning

confidence: 99%

Enhancement of Raman light scattering in dye-labeled cell membrane on metal-containing conducting polymer film

Grushevskaya

Крылова

Lipnevich

et al. 2016

Int. J. Mod. Phys. B

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“…Let a wavevector k m1, m2 , satisfying either the quantization conditions (II.3) or (II.4), be associated with the reduced wavevector q m1,m2 as the difference between k m1,m2 and the nearest Dirac point (valley) K(K ) of Brillouin zone. The Hamiltonian ĤD is obtained within the quasirelativistic Dirac-Hartree-Fock selfconsistent field approach (see [26,27]). It is a highenergy k • p-Hamiltonian in a q 4 approximation for the quasirelativistic quantum exchange that the latter is series expanded in the vicinity of the Dirac point K( K ) on the absolute value of the difference q = p − K of the quasiparticle momentum p and K( K ) up to the terms of O(q 4 ) inclusively.…”

Section: A "Folding Zone" Approximationmentioning

confidence: 99%

Electronic properties and quasi-zero-energy states of graphene quantum dots

et al. 2021

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In this work, a research has been carried out into the electronic properties of nanostructured graphene. We focus our attention on trapped states of the proposed systems such as spherical and toroidal graphene quantum dots. Using a continuum model, by solving the Dirac-Weyl equation, and applying periodic boundary conditions of two types, i.e. either with zigzag-edges only, or with both armchair-and zigzag-edges, we obtain analytical results for energy levels yielding self-similar energy bands located subsequently one after another on the energy scale. Only for toroidal quantum dots (owing to the lack of curvature) the distribution of electron density is similar to Bohr atomic orbitals. However, although the quasi-zero-energy band exists for both spherical and toroidal quantum dots, no electron density is present on this band for the toroidal quantum dot. This causes the formation of a pseudogap between the hole and electron bands, because of the absence of the electron density at the quantum dot center, like in the case of an ordinary atom. Conversely, the confinement of the charge-carrier density is observed for both geometries of graphene quantum dots.

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“…Then, the emergence of unfolding leads to replica appearance, and further splitting of these replicas gives the octagonal symmetry of the problem, as one can see in Figure 3. Hyperbolic points (saddle points) are located between nodes and at the apex of the Dirac cone (Van-Hove singularities) as one can see in Figure 2a,b [3,[48][49][50]. Therefore, a fractal-like set of Fermi arcs which are shown in Figure 4, is formed in the absence of damping in the system.…”

Section: Harmonic Analysis Of the Problemmentioning

confidence: 99%

“…In Section 2, we propose a semimetal model with coupling between pseudospin and valley currents and prove the pseudo-helicity conservation law. In Section 3, we briefly introduce the approach [3,[35][36][37] and use it in a simple tight-binding approximation to obtain the system of equations for a Majorana secondary quantized field. In Section 4, we support the statement that the squared equation for the constructed field is of the Klein-Gordon-Fock type for different model exchange operators.…”

Section: Introductionmentioning

confidence: 99%

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Massless Majorana-Like Charged Carriers in Two-Dimensional Semimetals

Grushevskaya

Krylov

2016

Symmetry

Self Cite

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Abstract:The band structure of strongly correlated two-dimensional (2D) semimetal systems is found to be significantly affected by the spin-orbit coupling (SOC), resulting in SOC-induced Fermi surfaces. Dirac, Weyl and Majorana representations are used for the description of different semimetals, though the band structures of all these systems are very similar. We develop a theoretical approach to the band theory of two-dimensional semimetals within the Dirac-Hartree-Fock self-consistent field approximation. It reveals partially breaking symmetry of the Dirac cone affected by quasi-relativistic exchange interactions for 2D crystals with hexagonal symmetry. Fermi velocity becomes an operator within this approach, and elementary excitations have been calculated in the tight-binding approximation when taking into account the exchange interaction of π(p z )-electron with its three nearest π(p z )-electrons. These excitations are described by the massless Majorana equation instead of the Dirac one. The squared equation for this field is of the Klein-Gordon-Fock type. Such a feature of the band structure of 2D semimetals as the appearance of four pairs of nodes is shown to be described naturally within the developed formalism. Numerical simulation of band structure has been performed for the proposed 2D-model of graphene and a monolayer of Pb atoms.

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Quantum Field Theory of Graphene with Dynamical Partial Symmetry Breaking

Cited by 6 publications

References 42 publications

Enhancement of Raman light scattering in dye-labeled cell membrane on metal-containing conducting polymer film

Enhancement of Raman light scattering in dye-labeled cell membrane on metal-containing conducting polymer film

Electronic properties and quasi-zero-energy states of graphene quantum dots

Massless Majorana-Like Charged Carriers in Two-Dimensional Semimetals

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