Departament de Física, Universitat de les Illes Balears, Spin and charge oscillation properties of semiconductor quantum dots from real time simulations Llorenç Serra Departament de Física, Universitat de les Illes Balears, IMEDEA (CSIC-UIB) Outline: * Model of 2d quantum dot * Theoretical framework * Some results * Spin-orbit coupling effects on spin precession Collaborators: A. Puente (Mallorca) M. Valín-Rodríguez (Mallorca) E. Lipparini (Trento) V. Gudmundsson (Reykjavik)

Semiconductor quantum dots Vertical quantum dots GaAs L  10-100 nm z AlxAsGa1-x  1 nm * System of confined electrons in 2D * Possibilities: Control of Geometry (circular, elliptic, rectang..) Size Number of electrons ARTIFICIAL ATOMS

A SIMPLE MODEL: N electrons in 2D confined by Vext(r) conduction electrons in GaAs effective mass m = 0.067 me dielectric constant k = 12.4 interaction e2/kr confinement potential: jellium disk square well harmonic potential effective atomic units

Mean field Ground State Set of orbitals and single-particle energies * Kohn-Sham version of density-functional-theory: exchange-correlation in LSDA (or CDFT) Spin densities: *Hartree-Fock theory: exact exchange but no correlation Numerical methods: Discretization of the xy plane in a grid Iterative solution

Time evolution td-LSDA td-HF After an initial perturbation on the GS keep track of observables in ‘real’ time oscillation frequencies eigenmodes: FIR (charge dipole) spin modes Fourier analysis Alternative to perturbation theory not restricted to small amplitudes or by symmetry

Example: Spin-density oscillation

Collective excitations in deformed systems Dipole Excitation Collective excitations in deformed systems Free N=20 electrons in a deformed parabola wy= 0.75 wx = 0.218 H* p-h transitions Spin Landau damping atract. residual interaction Density Generalized Kohn theorem x,y

* td-(mean field) includes correlation effects * Defines a new correlated ground state (RPA) Applications: * Orbital modes (Lz) * Quadrupole modes (xy) * Absorption patterns in triangular (square) dots * Large amplitude motions * ...

FIR Absorption in polygonal dots

Local absorption patterns: * amplitude of oscillating density * corner and side modes B=1T

Large amplitude motion in tdHF: * non parabolic confinement * CM trajectory * initial rigid displacement * 3 intervals of 9000 steps (12 ps each) * Amplitude shrinks

Energy goes to internal modes

Spin-orbit coupling and spin precession in quantum dots Two sources : *Dresselhaus (bulk asymmetry) *Rashba (nanostructure asymmetry) Coupling constants for 2D bulk: ( E vertical electric field ) ( z0 vertical width ) * g and a0 known from calculations for the bulk (k.p, tight binding) * lR and lD uncertain in nanostructures (sample dependent) in GaAs 2DEG’s: 5 meVA - 50meVA * Tunability of the Rashba strength

*assume given l’s *sp hamiltonians

* spin textures on the ground state * spinorial orbitals: * noncollinear SDFT: * spin textures on the ground state * time evolution

*Analytical solution: neglect interactions vertical magnetic field (Bz) Aleiner-Falk’o transformation * Spin precession: dl = 0 quasi spin-flip * Larmor precession:

* Dreselhaus SO * strong (z0=50A, blue symbols) weak (z0 =85A, green symbols) * zero field offset * rearrangements jumps * results within LSDA

time simulation of spin precession in LSDA:

In a horizontal B: *numerical calculation *first and second levels *circular parabolic confinement

Elliptical dots: transition between Kramers conjugates