Post on 22-Dec-2015
Rodolfo Jalabert
CHARGE AND SPIN DIPOLE RESONANCES CHARGE AND SPIN DIPOLE RESONANCES IN METALLIC NANOPARTICULES : IN METALLIC NANOPARTICULES :
collective versus single-particle excitationscollective versus single-particle excitations
R. Molina (Madrid)G. Weick (Berlin)C. Seoánez (Madrid)G.-L. Ingold (Augsburg)
D. Weinmann P.-A. HervieuxG. ManfrediY. Yin
in a metal:
MIE THEORYMIE THEORY On the color of gold colloids -
1908
λ >> 2a
resonance pour surface plasmon
Lycurgus cup, 4th century AD
ABSORPTION AND SCATTERING BY SMALL PARTICLESABSORPTION AND SCATTERING BY SMALL PARTICLES
Bréchignac et al, PRL 1993
(visible)
Photo-absorption cross section of 12C nucleus
Plasmon resonance in free clusters
Single-nanoparticle sensors
d-electronsd-electrons matrixmatrix
Feldmann et al, Nano Lett. 2007
Plasmon-based miniaturized optical elements
PLASMONICSPLASMONICS
BIOLOGYBIOLOGY
Interaction with the local environment
One-particle potential: uniform
jellium background with a
Coulomb tail
COLLECTIVE AND RELATIVE COORDINATESCOLLECTIVE AND RELATIVE COORDINATES
center of mass: harmonic oscillator
plasmonplasmon
relative coordinates: mean field
coupling: dipole field
Kawabata & Kubo, 1966
Time-Dependent Local Density Approximation
R.A. Molina et al., PRB 2002, EPJD 2003
Nonmonotonic behavior !!
Na
SIZE-OSCILLATIONS OF THE LINEWIDTHSIZE-OSCILLATIONS OF THE LINEWIDTH
Drude, Drude, τ‾τ‾11
confinement, confinement, aa << ττ vvFF
particle and hole angular-momentum-restricted DOS
G. Weick et al., PRB 2005 & 2006
SEMICLASSICAL APPROACHSEMICLASSICAL APPROACH
Temperature?
TDLDA calculations?
Half-width for noble metals?
Semiclassics in the radial problem:
Doremus, J. Chem. Phys. 1965
Experiments?
TDLDA
SPILL-OUT INDUCED RED-SHIFTSPILL-OUT INDUCED RED-SHIFT
Temperature ?
Spill-out from from semiclassics
TDLDA
Lamb shift ?
Jellium model ?
G. Weick et al., PRB 2006
Bréchignac et al, PRL 1993
Differential transmission
Bigot et al., Chem. Phys., 2000
(ps)
(eV)
pscorrelated electrons
collective modesnonthermal regime
e-e & e-surface scattering,
thermal distribution
e-phonons scatteringrelaxation to the lattice
cooling of the distribution
energy transfer to the matrix
TIME RESOLVED EXPERIMENTS, POMP-PROBETIME RESOLVED EXPERIMENTS, POMP-PROBE
pspspsSlowdown of
relaxation at the resonance !
ANOMALY CLOSE TO THE RESONANCE ANOMALY CLOSE TO THE RESONANCE
G. Weick et al., EPL 2007
MATRIX RPA DESCRIPTION OF THE PLASMON MATRIX RPA DESCRIPTION OF THE PLASMON
HF + Residual interaction :
α, β, γ, and δ : single-particle HF states
Separable residual interaction :
E
S(E) PlasmonPlasmon
PLASMON AS A COLLECTIVE EXCITATION PLASMON AS A COLLECTIVE EXCITATION
RPA eigenenergies :
C. Seoánez et al., EPJ D 2007
PlasmonPlasmon = superposition of low-energy e-hlow-energy e-h coupled to
high-energy high-energy e-he-h
C. Yannouleas, R.A. Broglia, Ann. Phys. (N.Y.) 217, 105 (1992)
restricted subspace
additional subspace
reduced density matrix (center of mass system)
REDUCED DENSITY MATRIX FOR THE PLASMONREDUCED DENSITY MATRIX FOR THE PLASMON
Rabi Rabi frequencyfrequency
system: system: plasmon, center of mass,
collective coordinate
bath:bath: high-energy e-h,relative coordinates
coupling:coupling: dipole field
excitation:excitation: laser field
density matrix of the electron gas
equation of motion for
Markovian approximation justified
BLOCH EQUATIONS FOR THE PLASMON BLOCH EQUATIONS FOR THE PLASMON
free evolution coupling (perturbation)
correlation function of the bath:
populations
coherence
COHERENCE EFFECTS FOR THE PLASMON COHERENCE EFFECTS FOR THE PLASMON
G. Weick et al., EPJ D 2007
dipole absorption cross-section
SPIN DIPOLE EXCITATIONSPIN DIPOLE EXCITATION
exchange-correlation:
Spin-dipole frequency:
LOCAL DENSITY APPROXIMATIONLOCAL DENSITY APPROXIMATION
kinetic: Hartree = 0
Non uniform ground-state density
Spill-out correction:
SPIN DIPOLE FREQUENCYSPIN DIPOLE FREQUENCY
TDLDA
Equilibrium under external field:
IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ?IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ?
E
S(E)
Hartree-Fock
HF + residual interaction
~ΔE
1
the spin-dipole is an e-h excitation
COUPLED MODES IN OPEN-SHELL CLUSTERSCOUPLED MODES IN OPEN-SHELL CLUSTERS
SP
charge dipoleexcitation SD
CONCLUSIONSCONCLUSIONS
PERSPECTIVESPERSPECTIVES
Driven nanoparticles: quantum coherence effects, sidebands in the
absorption
Plasmonics: plasmon interaction and transfer between nano-objects
Spin effects: spin-dipole excitation, coupling of charge and spin
Magnetic nanoparticles: fast dynamics of the magnetization, collective
excitations
Plasmons in nanoparticles: many-body dynamics, quantum coherence, dissipation
classical and quantum descriptions, collective excitation mesoscopic effects: size-oscillations of the half-width
electronic dynamics in pump-and-probe experiments