Browsing by Author "Tatardar, F."

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Open Access
Josephson current between two p-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields
(Elsevier, 2020) Nakhmedov, E.; Süleymanlı, B. D.; Alekperov, O. Z.; Tatardar, F.; Mammadov, H.; Konovko, A. A.; Saletsky, A. M.; Shukrinov, Y. M.; Sengupta, K.; Tanatar, Bilal
Josephson current between two one-dimensional nanowires with proximity induced p-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-reflection is realized by means of two different channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters’ phase differences φ and oscillates with 4π period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with 4π period not only with φ but also with orientational angle of the in-plane magnetic field θ resulting in a magneto-Josephson effect. In the presence of Rashba spin-orbit coupling (SOC) and normal-to-plane magnetic field h, a forbidden gap is shown to open in the dependence of Andreev bound state energies on the phases φ and θ at several values of SOC strength and magnetic field, where Josephson current seems to vanish. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from these channels and discuss experiments which can test our theory.
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 $p_{\infty} \left(\right. y \left.\right)$.