PHYSIQUE MESOSCOPIQUE IPCMS - DMONS Rodolfo Jalabert Dietmar Weinmann Post-docs: Jérôme Roccia (DMONS-DON) Guillaume Weick Etudiants: Guido Intronati (Strasbourg – Buenos Aires) Wojciech Szewc

Domaines de recherche : Conductance à travers de systèmes fortement corrélés Relaxation du spin Transport dépendant de spin Nanoparticules métalliques Electronique moléculaire (G.W.) Courants permanents et interactions (D.W.) Décohérence et dissipation (R.J.)

Conductance à travers de systèmes fortement corrélés

Quantum transport universality interactions nano size non-local effects individual object universality interactions size nano

Landauer: conductance from scattering Two terminal conductance: - Separation of sample, leads and reservoirs - Mean field, quasi-particle scattering states at the Fermi energy - Equilibration in the reservoirs leads to dissipation - Contact resistance

Conductance through an interacting region - Is the scattering approach still valid ? without inelastic process (zero temperature) embedding method - How do we calculate the transmission coefficient T ? persistent current for interacting region + leads Ground-state property!

Numerical implementation

Conductance through a correlated region g decreases with U g decreases with LS W = 0 Mott insulator g ≈ 1 for LS odd Perfect conductance only with adiabatic contacts

Even-odd asymmetry and Coulomb blockade LS odd: Resonance NS NS +1 electrons in the interacting region Coulomb blockade resonance (half filling) LS even: Transport involves charging energy U Interacting region is a barrier Observation of a parity oscillation in the conductance of atomic wires: R.H.M. Smit, et al, PRL ’03 Fabry-Perot interference in a nanotube electron waveguide Llang, et al, Nature ’01.

Can we describe an interacting region by an effective one-particle scatterer? R = R+ + R- ohmic composition Quantum mechanics, non-locality S+ S- R ≠ R+ + R- S = S+ * S- Electron-electron interactions S ≠ S+ * S- non local effect !

Interaction-induced non-local effects universal correction!

Conductance quantization 0.7 anomaly M.A. Topinka et al, Nature, 2001 Conductance quantization in a point contact D.A. Wharam et al, J. Phys. C, 1988

Nanoparticules métalliques

On the color of gold colloids - 1908 MIE THEORY On the color of gold colloids - 1908 λ >> 2a in a metal: resonance pour surface plasmon

Plasmon resonance in free clusters (visible) Bréchignac et al, PRL 1993 Photo-absorption cross section of 12C nucleus

TIME RESOLVED EXPERIMENTS, POMP-PROBE Differential transmission (ps) (eV) ps ps ps ps f(E): juste une image naïve “Thermalisation” energy transfer to the matrix e-phonons scattering relaxation to the lattice cooling of the distribution correlated electrons collective modes nonthermal regime e-e & e-surface scattering, thermal distribution Bigot et al., Chem. Phys., 2000

COLLECTIVE AND RELATIVE COORDINATES relative coordinates: mean field center of mass: harmonic oscillator One-particle potential: uniform jellium background with a Coulomb tail plasmon coupling: dipole field

SIZE-OSCILLATIONS OF THE LINEWIDTH Drude, τ‾1 confinement, a < τ vF Kawabata & Kubo, 1966 Na Semiclassical approach gamma^osc: rough estimation (curve: from numerical integration) in addition of gamma^0 Nonmonotonic behavior !! Time-Dependent Local Density Approximation

PLASMON AS A COLLECTIVE EXCITATION RPA eigenenergies : Emphasize the importance & relevance of this result restricted subspace additional subspace Plasmon = superposition of low-energy e-h coupled to high-energy e-h

SPIN DIPOLE EXCITATION dipole absorption cross-section

Décohérence et dissipation

Spin echo (Hahn) H  -H

M(t) = |y0| exp[+i(H0+S)t] exp[-iH0t] |y0|2 Loschmidt echo (fidelity) in the presence of a weak coupling to the environment |yH0(t) |yH(t) |yH0(t) H0 H H0 - H |yH0 , -H (2t) |y0 |y0 H=H0+S environment M(t) = |y0| exp[+i(H0+S)t] exp[-iH0t] |y0|2 How does M(t) depend on H0 , S , and t ?

Time-reversal focusing C. Draeger, M. Fink, PRL 1997