rodolfo jalabert charge and spin dipole resonances in metallic nanoparticules : collective versus...
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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
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in a metal:
MIE THEORYMIE THEORY On the color of gold colloids -
1908
λ >> 2a
resonance pour surface plasmon
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Lycurgus cup, 4th century AD
ABSORPTION AND SCATTERING BY SMALL PARTICLESABSORPTION AND SCATTERING BY SMALL PARTICLES
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Bréchignac et al, PRL 1993
(visible)
Photo-absorption cross section of 12C nucleus
Plasmon resonance in free clusters
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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
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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
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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
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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?
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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
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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 !
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ANOMALY CLOSE TO THE RESONANCE ANOMALY CLOSE TO THE RESONANCE
G. Weick et al., EPL 2007
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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
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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
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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
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Markovian approximation justified
BLOCH EQUATIONS FOR THE PLASMON BLOCH EQUATIONS FOR THE PLASMON
free evolution coupling (perturbation)
correlation function of the bath:
populations
coherence
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COHERENCE EFFECTS FOR THE PLASMON COHERENCE EFFECTS FOR THE PLASMON
G. Weick et al., EPJ D 2007
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dipole absorption cross-section
SPIN DIPOLE EXCITATIONSPIN DIPOLE EXCITATION
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exchange-correlation:
Spin-dipole frequency:
LOCAL DENSITY APPROXIMATIONLOCAL DENSITY APPROXIMATION
kinetic: Hartree = 0
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Non uniform ground-state density
Spill-out correction:
SPIN DIPOLE FREQUENCYSPIN DIPOLE FREQUENCY
TDLDA
Equilibrium under external field:
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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
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COUPLED MODES IN OPEN-SHELL CLUSTERSCOUPLED MODES IN OPEN-SHELL CLUSTERS
SP
charge dipoleexcitation SD
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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