Rodolfo Jalabert
LA RESONANCE PLASMON DANS LES NANOPARTICULES METALLIQUES : un degré de liberté quantique couplé
aux excitations électron-trou
R. Molina (Madrid)G. Weick (Berlin)C. Seoánez (Madrid)G.-L. Ingold (Augsburg)D. Weinmann (Strasbourg)
J.-Y. BigotE. BeaurepaireV. HaltéM. Vomir
P.-A. HervieuxG. ManfrediY. Yin
expérimentateurs à Strasbourg:
• Plasmons au début du XXème• Plasmons dans les années 90• Plasmons pour les artisans de l’antiquité• Plasmons pour les biologistes• Plasmons pour les physiciens nucléaires• Les autres plasmons• Plasmons pour les ingénieurs
(plasmonique)• Plasmons pour la physique
mésoscopique• Plasmons et optique femto-seconde• Plasmons comme excitations collectives• Optique quantique avec les plasmons• Plasmons et spins• Conclusion et prospectives
PLASMONS POUR TOUS ET PARTOUT
• Plasmons au début du XXème
in a metal:
MIE THEORY On the color of gold colloids -
1908
λ >> 2a
resonance pour surface plasmon
• Plasmons dans les années 90
Bréchignac et al, PRL 1993
Photo-absorption cross section of Li clusters,small red-shift with increasing cluste size
PLASMON RESONANCE IN FREE CLUSTERS
(visible)
• Plasmons pour les artisans de l’antiquité
Lycurgus cup, 4th century AD
Chartres cathedral
ABSORPTION AND SCATTERING BY SMALL PARTICLES
• Plasmons pour les biologistes
INTERACTION WITH THE LOCAL ENVIRONMENT
Single-nanoparticle sensors
d-electrons matrix
Feldmann et al, Nano Letters 2007
Biological markers,tracking of individual receptors in neurons
Strong local dipole field
Dahan et al, Science 2003
• Plasmons pour les physiciens nucléaires
GIANT DIPOLE RESONANCE
Photo-absorption cross section of 12C nucleus
• Les autres plasmons
BULK AND SURFACE PLASMONS
bulk plasmon, 3DEG
2D plasmon, 2DEG
electron-hole excitations
Plasmon band, semiconductor multilayer
surface plasmon
Landau damping
= plasmons + optique
• Plasmonique
Plasmon-based miniaturized optical elements
Surface plasmon subwavelength optics
PLASMON PROPAGATION IN MICROSTRUCTURES
Ebbesen et al, Nature 2003
• Plasmons pour la physique mésoscopique• cohérence quantique
• interaction él-él dans un système confiné• régime semi-classique a > λF • évolution temporelle des systèmes finis• décohérence et dissipation des états
collectifs
Kawabata & Kubo, 1966
Time-Dependent Local Density Approximation
R.A. Molina et al., PRB 2002, EPJD 2003
Nonmonotonic behavior !!
Na
SIZE-OSCILLATIONS OF THE LINEWIDTH
Drude, τ‾1
confinement, a < τ vF
Doremus, J. Chem. Phys. 1965
One-particle potential: uniform
jellium background with a
Coulomb tail
COLLECTIVE AND RELATIVE COORDINATES
center of mass: harmonic oscillator
plasmon
relative coordinates: mean field
coupling: dipole field
particle and hole angular-momentum-restricted DOS :
G. Weick et al., PRB 2005 & 2006
in agreement with TDLDA calculations
SEMICLASSICAL APPROACH
Temperature ?
Experiments ?
Half-width for noble metals ?
TDLDA
SPILL-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
• Plasmons et optique femto-seconde
Femto = la bonne échelle pour la dynamique électronique
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-PROBE
pspspsSlowdown of
relaxation at the resonance !
ANOMALY CLOSE TO THE RESONANCE
G. Weick et al., EPL 2007
• Plasmons comme excitations
collectivesDescription quantique du
plasmon
DISCRETE (MATRIX) RPA
Hartree-Fock + Residual interaction :
α, β, γ, and δ : single-particle (Hartree-Fock) states
(symmetrized) Coulomb matrix element
Separable residual interaction :
Diagonalization in the one-particle-hole basis (RPA) :
PLASMON AS A COLLECTIVE EXCITATION
RPA eigenenergies :
C. Seoánez et al., EPJ D 2007
Plasmon = superposition of low-energy e-h coupled to
high-energy e-h
Landau damping γ and Lamb shift δ
Plasmon
E
S(E)TDLDA
• Optique quantique avec les plasmons
reduced density matrix (center of mass system)
REDUCED DENSITY MATRIX FOR THE PLASMON
Rabi frequency
system: plasmon, center of mass,
collective coordinate
bath: high-energy e-h,relative coordinates
coupling: dipole field
excitation: laser field
density matrix of the electron gas
equation of motion for
Markovian approximation justified
BLOCH EQUATIONS FOR THE PLASMON
free evolution coupling (perturbation)
correlation function of the bath:
populations
coherence
COHERENCE EFFECTS FOR THE PLASMON
G. Weick et al., EPJ D 2007
• Plasmons et spins
kinetic: (Thomas-Fermi)
SPIN DIPOLE EXCITATION
exchange-correlation(local)
Hartree = 0
exchange correlation
Spin-dipole frequency:
equilibrium charge
LOCAL APPROXIMATION FOR XC
TDLDA
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
• Conclusion et prospectives
CONCLUSIONS
PERSPECTIVES
Driven nanoparticles: quantum coherence effects, sidebands in the
absorptionPlasmonics: plasmon interaction and transfer between nano-objectsSpin effects: spin-dipole excitation, coupling of charge and spinMagnetic nanoparticles:
fast dynamics of the magnetization, collective excitations
Plasmons in nanoparticles: many-body dynamics, quantum coherence, dissipation
classical and quantum descriptions, collective excitation center of mass and relative coordinates
mesoscopic effects: size-oscillations of the half-width coherence effects: time-dependence of the reduced
DM electronic dynamics in pump-and-probe experiments