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

2. 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.)

3. Conductance à travers de systèmes fortement corrélés

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

5. 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

6. 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!

7. Numerical implementation

8. 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

9. 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.

10. 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 !

11. Interaction-induced non-local effects
universal correction!

12. 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

13. Nanoparticules métalliques

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

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

16. 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

17. 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

18. 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

19. 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

20. SPIN DIPOLE EXCITATION dipole absorption cross-section

21. Décohérence et dissipation

22. Spin echo (Hahn)
H  -H

23. 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 ?

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