The centrally-symmetric solutions of electronic excitations of semiconductors in the conditions of relativistic like degeneracy of dynamical properties

Suprun, A. D.; Shmeleva, L. V.

doi:10.15407/fm21.01.069

Cited by 12 publications

(14 citation statements)

References 11 publications

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“…At first glance, the dispersion relation (6) for the electron in graphene is not very different from the same relation for simple (one atom per the cell) rectangular lattice [24–27]. In fact, it complicates the situation so that it is not always possible to carry out a full analysis of the dynamic properties of electron in graphene.…”

Section: Resultsmentioning

confidence: 98%

Features of the Generalized Dynamics of Quasiparticles in Graphene

Suprun

Shmeleva

2017

Nanoscale Res Lett

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The general dynamic properties of the electron, as quasiparticle in conduction band of graphene, were analyzed. It is shown that in graphene, these properties essentially differ from similar base properties for crystals with a simple lattice, despite insignificant, on the first sight, difference of dispersion law ε(p). Primarily, crystals with an elementary cell of arbitrary complexity of structure were considered. The obtained general relations were applied further to graphene. Herewith two-dimensional lattice of graphene has been considered as consisting of elementary cells with two atoms. Typically, graphene is considered as crystals consisting of two simple nested sublattices. It has been shown that both considerations lead to the analogous basic results. On the basis of obtained wave Hamiltonian, all the dynamic characteristics of the injected electron, considered as a quasiparticle, were found: speed, tensor of effective dynamic mass, and wave Lagrangian. Also, for some physically actual situations, the dynamic characteristics of an alternative description have been found: a mechanical momentum p m, mechanical Hamiltonian, and mechanical Lagrangian. For these situations, a generalized Louis de Broglie relationship between mechanical p m and wave p momenta was found also.

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Section: Resultsmentioning

confidence: 98%

Features of the Generalized Dynamics of Quasiparticles in Graphene

Suprun

Shmeleva

2017

Nanoscale Res Lett

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“…Taking into consideration the fact that current is to be determined based on the consideration on an injected electron, it is necessary to consider this electron as a free quasi-particle of the classic type within the conductivity band of the primary structure of the protein molecule [19–21]. In this case, each of the eigenvalues E s ( v , k ) for the energies of subzones is to be considered as a classic Hamiltonian of the wave pulse p = ℏ k [21, 22]. …”

Section: Resultsmentioning

confidence: 99%

Current in the Protein Nanowires: Quantum Calculations of the Base States

Suprun¹,

Shmeleva²

2016

Nanoscale Res Lett

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It is known that synthesis of adenosine triphosphoric acid in mitochondrions may be only completed on the condition of transport of the electron pairs, which were created due to oxidation processes, to mitochondrions. As of today, many efforts were already taken in order to understand those processes that occur in the course of donor-acceptor electron transport between cellular organelles (that is, between various proteins and protein structures). However, the problem concerning the mechanisms of electron transport over these organelles still remains understudied. This paper is dedicated to the investigation of these same issues.It has been shown that regardless of the amino acid inhomogeneity of the primary structure, it is possible to apply a representation of the second quantization in respect of the protein molecule (hereinafter “numbers of filling representation”). Based on this representation, it has been established that the primary structure of the protein molecule is actually a semiconductor nanowire. In addition, at the same time, its conduction band, into which an electron is injected as the result of donor-acceptor processes, consists of five sub-bands. Three of these sub-bands have normal dispersion laws, while the rest two sub-bands have abnormal dispersion laws (reverse laws). Test calculation of the current density was made under the conditions of the complete absence of the factors, which may be interpreted as external fields. It has been shown that under such conditions, current density is exactly equal to zero. This is the evidence of correctness of the predictive model of the conductivity band of the primary structure of the protein molecule (protein nanowire). At the same time, it makes it possible to apply the obtained results in respect of the actual situation, where factors, which may be interpreted as external fields, exist.

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“…Without regard for a reaction of the lattice to the excitation [17], the typical Hamiltonian for singleelectronic excitations in simplest solids is determined by the equality [3-6, 16, 18]…”

Section: Basic Relations In Crystals 221 Simple Unit Cellmentioning

confidence: 99%

“…The matrix element n,n+l determines the energy of the resonant exchange interaction. These elements are determined in details in [16,17]. The condition of dynamical minimization of functional (1) is equivalent to the procedure of reduction to the diagonal type of the operator proper to (1) [5].…”

Section: Basic Relations In Crystals 221 Simple Unit Cellmentioning

confidence: 99%

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Some Aspects of Generalized Dynamics of Quasiparticles in Crystals with Unit Cell of Arbitrary Complexity

Suprun¹,

Shmeleva²

2016

Ukr. J. Phys.

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The conditions, under which the general description of the dynamical properties of quasiparticles is almost identical with those of real relativistic particles, are analyzed. Such analysis is, especially, actual today in connection with the growing interest in electronic properties of graphene and other nanostructures of carbon origin (fullerenes, nanotubes, etc.). The development of the traditional applications of quasiparticles (superfluidity, transfer of charge or energy) also requires a generalized analysis of dynamical properties of quasiparticles. The problem of the correlation of quantum and classical methods of description of the quasiparticles in the case of the excited states of crystals is considered. In order to focus attention on the discussed problem, the obtained results are demonstrated on the example of electronic excitations of crystals in the simplest case where other effects are neglected (phonons, defects, high density of excitations, which would require the account for interactions between them, the response of a lattice to excitations, and so forth). It is shown that such excitations can be described in three ways simultaneously. The first is the quantum description of the examined excitations in terms of wave functions and eigenvalues of energy. The second method is classical. It arises from the quantum method and is formulated in terms of the wave momentum. The third method, which follows from the second one, is also a description of the classical type, but is related to the other momentum -the mechanical one. The latter descriptions (the third or second one) make it possible to interpret the experimental data in terms of the usual relativistic dynamics. K e y w o r d s: quasiparticles, dispersive dependence, relativistic approximation, dynamical Dirac model, graphenes.c ○ A.D. SUPRUN, L.V. SHMELEVA, 2016ties of real particles, especially, in connection with the mentioned dynamical Dirac model in graphenes [12].The analysis of the general dynamical properties of free quasiparticles is fulfilled on the basis of one of the major characteristics of the excited states of condensed matter. This is the dispersive dependence of the energy or frequency on a wave vector [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. We will also examine the general conditions, under which the dynamical Dirac model becomes real. The problem of relationship between quantum and classical methods of description of quasiparticles is considered as well. Materials and Methods. Common Remarks About Dynamical Properties of Quasiparticles in Crystals Basic relationsWe will analyze the dependence (k) ≡ ( 1 , 2 , 3 ). Since the wave vector k is always associated with the

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The centrally-symmetric solutions of electronic excitations of semiconductors in the conditions of relativistic like degeneracy of dynamical properties

Cited by 12 publications

References 11 publications

Features of the Generalized Dynamics of Quasiparticles in Graphene

Features of the Generalized Dynamics of Quasiparticles in Graphene

Current in the Protein Nanowires: Quantum Calculations of the Base States

Some Aspects of Generalized Dynamics of Quasiparticles in Crystals with Unit Cell of Arbitrary Complexity

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