Browsing by Author "Suleymanli, B."

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Open Access
Motion of two-dimensional quantum particle under a linear potential in the presence of Rashba and Dresselhaus spin–orbit interactions
(Elsevier Ltd, 2021-11-18) Suleymanli, B.; Nakhmedov, E.; Alekperov, O.; Tatardar, F.; Tanatar, Bilal
The quantum mechanical problem of a particle moving in the presence of electric field and Rashba and/or Dresselhaus spin–orbit interactions (SOIs) is solved exactly. Existence of the SOI removes the spin degeneracy, yielding two coupled Schrödinger equations for spin-up and spin-down spinor eigenfunctions. Fourier-transform of these equations provides two coupled first-order differential equations, which are shown to be reduced to two decoupled Hermite-like equations with complex coefficients. The convergent solutions of the equations are found to be described in the form of so called Hermite series. The recurrence relations and the integral representation of the Hermite series are provided. In the absence of Rashba and Dresselhaus spin–orbit coupling constants, these interconnected equations are decoupled and reduced to two Schrödinger equations for a quantum particle moving in a linear potential, solution of which is described by Airy functions
Open Access
The diagrammatic method of Berezinskii for one-dimensional disordered wire with spin–orbit interaction
(Elsevier BV * North-Holland, 2022-10-29) Suleymanli, B.; Nakhmedov, E.; Tatardar, F.; Tanatar, Bilal
We extend Berezinskii’s diagram technique to the one-dimensional disordered wire containing Rashba and Dresselhaus spin–orbit interactions. The retarded and advanced Green’s functions are factorized in coordinates space in the presence of spin–orbit interactions. This factorization allows us to transform all coordinate dependence of the Green’s functions from lines to the impurity vertices. Our calculations show that all possible impurity vertices giving a contribution to the correlators do not differ from those given in the conventional technique, except that they are written in a 2 × 2 matrix form and the Fermi velocity $v_{F}^{*}$ now depends on the spin–orbit coupling constants. The diagrammatic method of Berezinskii with spin–orbit interaction is used to obtain the distribution of the electron density of the localized state $p_{\infty} \left(\right. y \left.\right)$.