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Rashba Spin-Orbit Interaction in Semiconductor Nanostructures (Review)

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Rashba Spin-Orbit Interaction in Semiconductor Nanostructures (Review) Asian Journal of Physical and Chemical Sciences 8(2): 32-44, 2020; Article no.AJOPACS.57016 ISSN: 2456-7779 Rashba Spin-orbit Interaction in Semiconductor Nanostructures (Review) Ibragimov Behbud Guseyn1* 1Institute of Physics, Azerbaijan National Academy of Sciences, Azerbaijan State Oil and Industry University, Azerbaijan. Author’s contribution The sole author designed, analysed, interpreted and prepared the manuscript. Article Information DOI: 10.9734/AJOPACS/2020/v8i230115 Editor(s): (1) Dr. Thomas F. George, University of Missouri - St. Louis One University Boulevard St. Louis, USA. (2) Dr. Shridhar N. Mathad, KLE Institute of Technology, India. Reviewers: (1) Kruchinin Sergei, Ukraine. (2) Subramaniam Jahanadan, Malaysia. (3) M. Abu-Shady, Menoufia University, Egypt. (4) Vinod Prasad, India. (5) Ricardo Luís Lima Vitória, Universidade Federal do Pará, Brazil. Complete Peer review History: http://www.sdiarticle4.com/review-history/57016 Received 25 March 2020 Accepted 01 June 2020 Review Article Published 09 June 2020 ABSTRACT In this work I review of the theoretical and experimental issue related to the Rashba Spin-Orbit interaction in semiconductor nanostructures. The Rashba spin-orbit interaction has been a promising candidate for controlling the spin of electrons in the field of semiconductor spintronics. In this work, I focus study of the electrons spin and holes in isolated semiconductor quantum dots and rings in the presence of magnetic fields. Spin-dependent thermodynamic properties with strong spin- orbit coupling inside their band structure in systems are investigated in this work. Additionally, specific heat and magnetization in two dimensional, one-dimensional quantum ring and dot nanostructures with Spin Orbit Interaction are discussed. Keywords: Spin-orbit interaction; Rashba effect; two dimension electron gas; one-dimensional ring; quantum wire; quantum dot; semiconductor nanostructures. 1. INTRODUCTION last three decades. The spin-orbit interaction is also called spin-orbit coupling or spin-orbit effect. The using of electron spin in electronic devices It means that any interaction of a particle’s spin has been of great interest to scientists during the with its motion. Spin degree of freedom is made _____________________________________________________________________________________________________ *Corresponding author: E-mail: [email protected], [email protected]; Behbud; AJOPACS, 8(2): 32-44, 2020; Article no.AJOPACS.57016 by spin-orbit coupling which is respond to its the dispersion relation for electrons in III-V orbital environment. Moving of the electron in an semiconductor asymmetric quantum wells is external electrical field leads to creating spin- studied within the standard envelope-function orbit interaction and experiences an effective formalism starting from the eight-band Kane magnetic field in its own reference frame, that in model for the bulk [10]. The Rashba spin-orbit turn couples to its spin through the Zeeman splitting in the different subbands is obtained for effect [1]. The magnitude of the spin-orbit both triangular and square asymmetric quantum interaction increases with the atomic number wells. It is shown, that the Rashba splitting in which it is a relativistic effect. The spin-orbit AlAs/GaAs/Ga1−xAlxAs square quantum wells is interaction is found with asymmetry in the of the order of 1 meV and presents a maximum underlying structure in crystals in semiconductors as a function of the well width. In III–V and II–VI systems [2]. In bulk it seems in crystals without semiconductors the spin–orbit interaction has an inversion center (e.g. zinc blende structures) been used successfully to interpret experimental and is called the Dresselhaus spin-orbit results in different quantum wire and well interaction [3]. However, Rashba term is aroused structures. Additionally, it lifts the conduction from the structural asymmetry of the confining state spin-degeneracy [4,11]. Exploiting the spin- potential in heterostructures [4]. Rashba-type orbit interaction in the conventional III–V spin-orbit interaction [4,5] has attracted the most nonmagnetic semiconductors to design basic attention, since it can be manipulated by external and high-speed spintronic devices is reviewed in electric fields, which is of central importance for paper [12]. To achieve this [12], concentrate on applications in spintronics. In a system with spin-dependent electronic characteristics of Rashba spin-orbit interaction, each spin- semiconductor nanostructures. degenerate parabolic band splits into two parabolic bands with opposite spin polarization. 2. RASHBA EFFECT IN TWO- The Rashba-type spin-orbit interaction is usually DIMENSIONAL ELECTRON SYSTEM caused by structure inversion asymmetry which stems from the inversion asymmetry of the Spin-orbit interaction has a vital role in spin confining potential [4,5]. The Rashba-type spin- relaxation, optical phenomena and transport, orbit interaction in systems with inversion which are actively studied for entirely new symmetry breaking is particularly attractive for applications in semiconductor spintronics. Study spintronics applications since itallows for flexible of the effects of spin-orbit interaction in two- manipulation of spin current by external electric dimensional electronic systems exposed to a fields. perpendicular magnetic field and was initially associated with Landau volume levels: the spin- A set of practical information on the cyclotron orbit interaction renormalization of energy resonance and also the combined resonance of dispersions, the interplay among various spin- two-dimensional electron gas at the GaAs- orbit interaction mechanisms, effects of magnetic AlxGa1−xAs heterojunctions’ interface [6,7], transport and electron-electron interaction. In shown that the spin degeneracy was lifted in the general, the Hamiltonian described the spin-orbit inversion layer. For describing this experimental U p information in term of spin-orbit interaction is interaction Hso , in here p developed by the theory [4,5]. In semiconductor is the momentum operator, is the spin-orbit nanostructures, studies of transport phenomena coupling parameter and having a dimension of and spin-dependent confinement have been length squared , which is proportional to the progressing importantly since spintronics interface electric field and is sample dependent, became a focus of recent interest. The first offer is the Pauli matrices vector. The value of of Das and Datta assign that the basic elements determines the contribution of the Rashba spin - of spintronic devices [8]. Several possible orbit coupling to the total electron Hamiltonian. structures with the basic elements were When an external electric field is present, the analyzed. Different kinds of electron spin relativistic correction introduces a relation detection methods have been investigated. between the electron spin and its own Lately the coherent spin transport has been momentum. The coupling of the electron spin showed in heterostructures and homogeneous and its orbital motion lifted the spin degeneracy semiconductors [9]. The most necessary of the two dimensional electron gas energy property of III–V semiconductors to be used in all semiconductor spintronic devices is the spin– bands at k 0 in the absence of a magnetic orbit interaction [3,4]. The spin-orbit splitting in field. This coupling arises due to inversion 33 Behbud; AJOPACS, 8(2): 32-44, 2020; Article no.AJOPACS.57016 asymmetry of the potential which confines the described by Hamiltonian which is given many two dimensional electron gas system. This is books and papers by: p i H so z y x x y (1) Where the z axis is selected perpendicular to the two dimensional electron gas system lying in the x-y plane. In the presence of the Rashba spin orbit term the Hamiltonian of the two-dimensional electron gas systems in the plane (x,y) is given: 2 p H p . z x 2 m (2) The eigenvalues of this Hamiltonian is 2 2 2 E k k k 2 k x k so so 2m 2m (3) 2 2 m k k k k so Here x y is the electron momentum modulus, 2 is a recast form of the spin orbit 2 m so coupling constant and which is neglected due to spin orbit coupling is small. The eigenvectors of the Hamiltonian (1) relative to the spectrum (2) are plane wave’s function of the momentum k ikx k y 1 0 x, y e 1 ie i 2 (4) ikx k y 1 1 x, y e i ie i 2 (5) Scattering geometry of two-dimensional electron gas with Rashba spin-orbit interaction on the spin- orbit lateral superlattice shown in Fig. 1 [13] Fig. 1. Two-dimensional electron gas scattering geometry with Rashba spin-orbit interaction on the spin-orbit lateral superlattice.The reflected r and incoming i spinors are the eigenstates of Rashba hamiltonian with spin-orbit coupling constant 1 and wave vectors belonging to the same Fermi contour [13] 34 Behbud; AJOPACS, 8(2): 32-44, 2020; Article no.AJOPACS.57016 In many two-dimensional electronic systems, the (3D Rashba-like spin splitting) with a helical spin main mechanism of spin relaxation is the polarization around the M points in the Brillouin Dyakonov – Perel spin relaxation mechanism zone of trigonal layered PtBi2 reported [26]. Due [14,15]. In this mechanism, electron spins sense to its inversion asymmetry and reduced an effective momentum dependent magnetic field symmetry at the M point, Rashba-type as well as randomized by electron-scattering events, which Dresselhaus-type spin-orbit interaction co- leads to relaxation
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