Spin-orbit coupling and magnetic spin states in cylindrical quantum dots
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G4.6.1
Spin-orbit coupling and magnetic spin states in cylindrical quantum dots C. F. Destefani,1, 2 Sergio E. Ulloa,1 and G. E. Marques2 2
1 Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701-2979 Departamento de Física, Universidade Federal de São Carlos, 13565-905, São Carlos, São Paulo, Brazil
We make a detailed analysis of each possible spin-orbit coupling of zincblende narrow-gap cylindrical quantum dots built in a two-dimensional electron gas. These couplings are related to both bulk (Dresselhaus) and structure (Rashba) inversion asymmetries. We study the competition between electron-electron and spin-orbit interactions on electronic properties of 2-electron quantum dots.
The creation and manipulation of spin populations in semiconductors has received great attention since the DattaDas proposal of a spin field-effect transistor,1 based on Rashba spin-orbit coupling of electrons in a bidimensional electron gas,2 and the possibility for quantum computation devices using quantum dots (QDs).3 Thus, it is important that every spin-orbit (SO) effect be clearly understood for a full control of spin-flip mechanisms in nanostructures. There are two main SO contributions in zincblende materials. In addition to the structure inversion asymmetry (SIA) caused by the 2D confinement (the Rashba SO), there is a bulk inversion asymmetry (BIA) term in those structures (the Dresselhaus SO).4 An yet additional lateral confinement defining a dot introduces another SIA term with important consequences, as we will see in detail. Although the relative importance of these two effects depends on the material and on sample design (via interfacial fields), only recently have authors begun to consider the behavior of spins under the influence of all effects. The goal of this work is to show how important different types of SO couplings are on the spectra of parabolic QDs built with narrow-gap zincblende materials. We consider both Rashba and a diagonal SIA, as well as the all Dresselhaus BIA terms in the Hamiltonian, in order to study features of the spectrum as function of magnetic field, dot size, and electron-electron interaction. Consider a heterojunction or quantum well confinement potential V (z) such that only the lowest z-subband is occupied. The Hamiltonian for a cylindrical QD, in the absence of SO interactions, is given by H0 = (~2 /2m)k2 + V (ρ) + gµB B · σ/2, where k = −i∇ + eA/(~c), A = Bρ(− sin θ, cos θ, 0)/2 describes a magnetic field B = Bz, m is the effective mass in the conduction band, g is the bulk g-factor, µB is Bohr’s magneton, V (ρ) = mω 20 ρ2 /2 is the (FD) lateral dot confinement, and σ is the Pauli spin vector. The analytical solution of H0 yields the Fock-Darwin p spectrum, EnlσZ = (2n + |l| + 1)~Ω + l~ω C /2 + gµB BσZ /2, with effective (cyclotron) frequency Ω = ω 20 + ω2C /4 are given in terms ofpLaguerre polynomials.5 The lateral, magnetic and effective (ω C = eB/(mc)). p The FD statesp lengths are l0 = ~/(mω 0 ), lB = ~/(mω C ) and λ = ~/(mΩ), respectively. The SIA terms2 for the full co
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