CHARGE AND SPIN DIPOLE RESONANCES
IN METALLIC NANOPARTICULES :
collective versus single-particle excitations
Rodolfo Jalabert
D. Weinmann
P.-A. Hervieux
G. Manfredi
Y. Yin
R. Molina (Madrid)
G. Weick (Berlin)
C. Seoánez (Madrid)
G.-L. Ingold (Augsburg)
MIE THEORY
On the color of gold colloids - 1908
λ >> 2a
in a metal:
resonance pour
surface plasmon
ABSORPTION AND SCATTERING BY SMALL PARTICLES
Lycurgus cup, 4th century AD
Plasmon resonance in free clusters
(visible)
Bréchignac et al, PRL 1993
Photo-absorption cross
section of 12C nucleus
BIOLOGY
Interaction with the
local environment
d-electrons
matrix
Single-nanoparticle sensors
PLASMONICS
Plasmon-based miniaturized
optical elements
Feldmann et al, Nano Lett. 2007
COLLECTIVE AND RELATIVE COORDINATES
relative coordinates: mean field
center of
mass: harmonic
oscillator
One-particle
potential:
uniform jellium
background with
a
plasmon
Coulomb tail
coupling: dipole field
SIZE-OSCILLATIONS OF THE LINEWIDTH
Drude, τ‾1
confinement,
a < τ vF
Kawabata &
Kubo, 1966
Na
Nonmonotonic
behavior !!
Time-Dependent Local
Density Approximation
R.A. Molina et al., PRB 2002, EPJD 2003
SEMICLASSICAL APPROACH
particle and hole angular-momentum-restricted DOS
Semiclassics in the radial problem:
TDLDA calculations? Experiments?
Half-width for noble metals?
Temperature?
G. Weick et al., PRB 2005 & 2006
Doremus, J. Chem. Phys. 1965
SPILL-OUT INDUCED RED-SHIFT
TDLDA
Bréchignac et al, PRL 1993
Lamb shift ?
Jellium model ?
Temperature ?
Spill-out from
from semiclassics
TDLDA
G. Weick et al., PRB 2006
TIME RESOLVED EXPERIMENTS, POMP-PROBE
Differential transmission
(ps)
(eV)
ps
ps
ps
ps
correlated
scattering
energyelectrons
transfer
e-ee-phonons
& e-surface
scattering,
collective
modes
relaxation
tomatrix
the lattice
to the
thermal
distribution
Slowdown
of
relaxation
nonthermal
cooling
of theregime
distribution
at the resonance !
Bigot et al., Chem. Phys., 2000
ANOMALY CLOSE TO THE RESONANCE
G. Weick et al., EPL 2007
MATRIX RPA DESCRIPTION OF THE PLASMON
HF + Residual interaction :
α, β, γ, and δ : single-particle HF states
Separable residual interaction :
S(E)
Plasmon
E
PLASMON AS A COLLECTIVE EXCITATION
C. Yannouleas, R.A. Broglia, Ann. Phys. (N.Y.) 217, 105 (1992)
RPA eigenenergies :
C. Seoánez et al., EPJ D 2007
restricted subspace
Plasmon = superposition of
low-energy e-h coupled to
high-energy e-h
additional subspace
REDUCED DENSITY MATRIX FOR THE PLASMON
system: plasmon,
excitation:
center of mass,
collective coordinate
laser field
Rabi frequency
bath: high-energy e-h,
relative coordinates
density matrix of the electron gas
coupling:
dipole
field
reduced
density
matrix
(center of mass system)
equation of motion for
BLOCH EQUATIONS FOR THE PLASMON
free evolution
coupling (perturbation)
correlation function
of the bath:
Markovian approximation justified
populations
coherence
COHERENCE EFFECTS FOR THE PLASMON
G. Weick et al., EPJ D 2007
SPIN DIPOLE EXCITATION
dipole absorption cross-section
LOCAL DENSITY APPROXIMATION
kinetic:
exchange-correlation:
Spin-dipole frequency:
Hartree = 0
SPIN DIPOLE FREQUENCY
Spill-out
correction:
Non uniform
ground-state density
Equilibrium under
external field:
TDLDA
IS THE SPIN DIPOLE A COLLECTIVE EXCITATION ?
S(E)
~ΔE1
E
Hartree-Fock
HF + residual interaction
the spin-dipole is an
e-h excitation
COUPLED MODES IN OPEN-SHELL CLUSTERS
charge dipole
excitation
SD
SP
CONCLUSIONS
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
PERSPECTIVES
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