Energy levels of a parabolically confined quantum dot in the presence of spin-orbit interaction

Kuan, Wen-Hsuan; Tang, Chi-Shung; Xu, W.

doi:10.1063/1.1710726

Cited by 49 publications

(31 citation statements)

References 27 publications

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“…So, controlling and calculating the spin-related effects are attractive and important not only from the fundamental scientific point of view, but also because of their effects on the electronic and optical properties of these structures (Lo 2009;Kuan et al 2004;Winkler 2003;Japaridze et al 2009;Debald and Kramer 2005;Mehdiyev et al 2009;Paaske et al 2010).…”

Section: Introductionmentioning

confidence: 99%

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

2011

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In this article simultaneous effects of external electric field and spin-orbit interaction on the linear and the nonlinear optical properties of a cubic quantum dot are studied. Based on the non-degenerate perturbation method, energy eigenvalues and eigenfunctions of the system under the influence of spin-orbit interaction are calculated. Furthermore, the linear and the nonlinear optical absorption coefficients and refractive index changes are obtained using the compact density matrix approach and iterative method. Our results show that, due to the spin-orbit interaction, resonant peak values of the optical absorption coefficients and refractive index changes decrease and occur at lower values of the incident photon energy. The variation of these optical parameters depend on the spin-orbit interaction strength, dot dimensions and external electric field.

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Section: Introductionmentioning

confidence: 99%

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

2011

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“…8,9,10,11,12 However, despite its potential interest for SO coupled low-dimensional systems, the specific 2D Coulomb problem appears to have been only marginally considered in the literature.…”

mentioning

confidence: 99%

“…Equation (2) commutes with the z-projection of the total angular momentum J z =L z + σ z /2, whereL z = −i∂/∂φ, so that the eigenfunctions of (2) can be chosen to be simultaneously eigenfunctions ofĴ z . Since H in polar coordinates allows for separation of variables, its eigenfunctions have therefore the following form: 8,9,10,11,12 Ψ j (r, φ) = f …”

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confidence: 99%

Energy levels of a two-dimensional hydrogen atom with spin-orbit Rashba interaction

Grimaldi

2008

Phys. Rev. B

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Electronic bound states around charged impurities in two-dimensional systems with structural inversion asymmetry can be described in terms of a two-dimensional hydrogen atom in the presence of a Rashba spin-orbit interaction. Here, the energy levels of the bound electron are evaluated numerically as a function of the spin-orbit interaction, and analytic expressions for the weak and strong spin-orbit coupling limits are compared with the numerical results. It is found that, besides the level splitting due to the lack of inversion symmetry, the energy levels are lowered for sufficiently strong spin-orbit coupling, indicating that the electron gets more tightly bound to the ion as the spin-orbit interaction increases. Similarities and differences with respect to the two-dimensional Fröhlich polaron with Rashba coupling are discussed.PACS numbers: 71.70. Ej, 73.21.Fg, 73.20.Hb The two-dimensional (2D) hydrogen atom, i. e., an electron constrained to move in a plane and subjected to an attractive Coulomb potential, 1,2,3,4,5 is a theoretical construction which, besides being of interest in itself, has also important physical realizations. It can describe indeed the effect of a charged impurity in 2D systems such as quantum wells and surface states, or in extremely anisotropic three-dimensional crystals, 1 as well as excitons in semiconductor 2D heterostructures. 5The spin-orbit (SO) interaction, arising from the structural and/or bulk inversion asymmetries, characterizes several of the above mentioned low-dimensional systems, 6 and gives rise to energy level splittings ranging from a few to hundreds of meV, depending on the material characteristics (see for example Ref. [7]). Furthermore, the possibility of tuning the SO interaction in semiconductor quantum wells by means of external applied voltages represents the key feature for application in spintronics. Given this situation, it becomes therefore natural to assess how the properties of a 2D hydrogen atom are affected by the SO interaction.Several studies have already been devoted to the effect of the SO coupling in electrons interacting with central potentials, such as those describing hard-wall or parabolic quantum dots. 8,9,10,11,12 However, despite its potential interest for SO coupled low-dimensional systems, the specific 2D Coulomb problem appears to have been only marginally considered in the literature.12 In this Brief Report, the 2D Coulomb problem is numerically solved for an electron interacting with a Rashba potential, that is the SO coupling arising from structural inversion asymmetry in the direction perpendicular to the 2D plane.13 It is found that the Rashba interaction removes partially the initial degeneracy of the 2D hydrogen atom, and the resulting energy levels are two-fold degenerate due to the time-reversal invariance of the model. Furthermore, it is shown that the SO interaction renders the electron more tightly bound to the ion, confirming a general trend observed for other central potentials and for 2D electrons coupled to phonons.The ...

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“…11,37 In several recent works, the Rashba spin-orbit coupling in QD systems was explored by several different groups (see Refs. [38][39][40][41][42]). However, the influence of the coupled magneto-thermoelectroelasticity in QDs has been largely neglected in the literature and we intend to cover this gap.…”

Section: Introductionmentioning

confidence: 99%

Coupled Magneto-Thermo-Electromechanical Effects and Electronic Properties of Quantum Dots

Prabhakar¹,

Melnik²,

Neittaanmäki³

et al. 2013

j comput theor nanosci

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For the first time, we systemically analyze the influence of magneto-thermo-electromechanical effects on the band structure calculations by using the fully coupled model. We focus on three different types of quantum dots (QDs): (a) ferroelectric, (b) piezomagnetic, and (c) magnetoelectric, with and without wetting layers (WLs). We demonstrate that the influence of such coupled effects in the general fully coupled framework for studying properties of QDs can be significant and we quantify these effects in each case. For example, in magnetic GaN/BaTiO 3 QDs, we found that the influence of electromechanical effects on the band structure calculations and the spin splitting energy are practically independent of temperature. However, in piezoelectric AlN/GaN QDs, the influence of temperature on the electromechanical effects, electronic properties and spin splitting energy is significant. In particular, in piezoelectric AlN/GaN QDs, the intra-subband energy (i.e., the energy difference between ground and first excited states) decreases with the increase in temperature.

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Energy levels of a parabolically confined quantum dot in the presence of spin-orbit interaction

Cited by 49 publications

References 27 publications

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

Simultaneous effects of spin-orbit interaction and external electric field on the linear and nonlinear optical properties of a cubic quantum dot

Energy levels of a two-dimensional hydrogen atom with spin-orbit Rashba interaction

Coupled Magneto-Thermo-Electromechanical Effects and Electronic Properties of Quantum Dots

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