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The physical implementation of devices based on semiconductor quantum dots requires external fields to manipulate the spectrum and the wavefunctions of the trapped electrons.
Increasing the magnetic field orthogonal to the plane of a parabolic quantum dot, the total spin increases, up to full spin
polarization (FSP) ( Maximum Density Droplet state). Rashba spin-orbit interaction due to an orthogonal external electric field turns the crossing of energy levels into an anticrossing and gradually tilts the spin polarization from the vertical direction at the dot centre, to a radial in plane direction at the border of the dot. The lowest lying excitation is a collective spin mode with the spin density reversed at the centre of the dot, healing back to the radial in plane orientation at the boundary. This excitation was recognized some time ago by us and put in connection with the skyrmion excitation occurring in a Quantum Hall Ferromagnetic Disk at filling close to one. The energy gap increases with increasing spin-orbit coupling.
Far-infrared optical excitation of quantum dots with parabolic confinement is discouraging because it only couples (within dipole approximation) to center of mass excitation modes (Kohn theorem), which are equally spaced in energy and do not depend on electron-electron interaction. However spin-orbit coupling violates this rule and the spin collective excitation can be monitored in this way. The intensities of the absorption peaks satisfy the optical sum rule, giving direct information on the total number of electrons inside the dot and on the nature of the spin-orbit interaction. Deviations from paraboliticity are discussed. [*] P.Lucignano, B.Jouault, A. Tagliacozzo,"Far infrared absorption of noncenter-of-mass modes and an optical sum rule in a few-electron quantum dot with Rashba spin-orbit coupling, Phys. Rev. B75, 153310 (2007). [*] P.Lucignano,B.Jouault, A.Tagliacozzo and B.L.Altshuler:" Rashba control for the spin excitation of a fully spin polarized quantum dot". Phys.Rev.B71,121310(R)(2005) [*] P.Lucignano,B.Jouault,A.Tagliacozzo, "Spin exciton in a quantum dot with spin-orbit coupling at high magnetic fields", Phys.Rev B69,045314 (2004) |
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