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