We explore the transport of the surface states quasielectrons in the 3D topological insulators through the barriers of various origin: the Fermi velocity and the electrostatic barriers. These barriers are believed to be the rectangular and one-dimensional ones. The transmission coefficient T as the function of the quasiparticle energy E and an angle of incidence θ (transmission spectra) is evaluated with the help of the effective Hamiltonian; the conductivity G is calculated on the base of the Landauer–Buttiker formula. It is shown that the value of T and G significantly depends on the ratio of the Fermi velocities in the barrier and out-of-barrier regions α = vF2/vF1. The dependence of these quantities on the strength of the electrostatic potential is analyzed. We find in particular that the effect of supertunneling manifests itself in the considered structure—being markedly dependent on the value of α. The formula which points out the energy value for which the effect of supertunneling takes place, for different α, is presented. For normal angle of the particle incidence, there is the effect analogous to the Klein paradox. The spectra T(E,θ) and G(E) substantially depend on the interplay of α, energy E and the magnitude of the electrostatic potential. Hence, by changing the problem parameters one can flexibly vary the spectra of T(E,θ) and G(E) in wide limits. The obtained results may be useful for the nanoelectronics based on the topological insulators.
Key words: ABSTRACT Graphene Superconductivity Fermi velocity ConductivityThe conductivity of the normal graphene -d-wave superconductive graphene junction is calculated within the framework of the Blonder-Tinkham-Klapwijk formalism [1]. The eigenfunctions, the Andreev and the normal reflection rates are evaluated by solving the Dirac-Bogoliubov-de Gennes equations. The Fermi velocity is believed to be different in the normal and in the superconductive regions [2]. We considered the case of the gapped graphene.Along with the s-wave pairing considered in the papers [16][17] there may take place the unconventional order parameters such as d-wave, p-wave and even f-wave superconductivity [17]. It is clear that the transport in the structures which are described by the non-isotropic pairing symmetry may essentially differ from that of s-pairing. It is demonstrated in this work that for the d-wave superconductivity the characteristics of the considered junction are sensitive to the value of z = υ n /υ s , where υn, υs are the Fermi velocities in the normal and the superconductive graphene respectively. This conclusion refers to the Andreev reflection as well as to the normal one. The first of them is shown to be the dominant process for the formation of the conductivity. These results are true for an arbitrary value of the orientational angle of the d-waves. The dependence of the conductivity on the external electrostatic potential as well as on the Fermi energy is also analyzed. The conductivity G(E) is calculated taking into account the fact that the external potential U is applied to the superconductive part of the given structure.A characteristic feature of the G(E) dependence is the presence of a peak at the energy point which depends on the value of the rotational angle. The value of the maximum (peak) value of G(E) curve steepness essentially depends on the value of the Fermi velocity v F . The dependence of the conductivity on the potential U as well as on the Fermi level EF is analyzed for different values of the rotational angle. The obtained results may be useful for applications in the graphene-based electronics. Національний університет харчових технологій У рамках формалізму Блондера-Тинкхема-Клапвійка розраховується провідність контакту: нормальний графен -d-хвильовий надпровідний графен. Власні функції, коефіцієнти андріївського та нормального відбивання обчислюються за допомогою розв'язування рівняння Дірака-Боголюбова-де Жена. Вважається, що швидкості Фермі набувають різних значень в нормальній і надпровідній областях. Розглядається випадок щільового графена. Крім s-хвильового спарювання, яке розглядалось у [16; 17], можливими є також неконвенційні параметри порядку, такі як d-хвильова, р-хвильова і навіть f-хвильова надпровідності. У статті показано, що характеристики контакту для d-хвильової надпровідності є вельми чутливими до значення / n s
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