Diapositiva 1

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Ultrafast Electron Dynamics of non-thermal
population in metals
Claudio Giannetti
INFM and Università Cattolica del Sacro
Cuore Dipartimento di Matematica e Fisica, Via
Musei 41, Brescia.
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Introduction
CW Light
LINEAR PHOTOEMISSION h? gt F ? mapping of
EQUILIBRIUM ELECTRON DISTRIBUTION
Femtosecond Light Pulses NON-LINEAR
PHOTOEMISSION h? lt F ? Mapping
of NON-EQUILIBRIUM ELECTRON DISTRIBUTION
Ag(100)
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Opened Problems
NON-LINEAR PHOTOEMISSION on metals is a powerful
tool to investigate 2 main physical questions
1. PHOTON ABSORPTION MECHANISMS
2. NON-EQUILIBRIUM ELECTRON DYNAMICS
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Photon Absorption
PHOTON ABSORPTION MECHANISMS PROBLEMS
The intraband transition between s-s states
within the same branch is FORBIDDEN for the
conservation of the momentum.

• Recently the excitation mechanism has been
  attributed to
• Laser quanta absorption in electron collisions
  with phonons.
• A.V. Lugovskoy and I. Bray, Phys. Rev. B 60,
  3279 (1999)
• Photon absorption in electron-ion collisions.
• B. Rethfeld et al., Phys. Rev. B 65, 2143031
  (2002)

THE ENERGY ABSORPTION IS DUE TO A THREE-BODY
PROCESS AND NOT TO A DIPOLE TRANSITION
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Photon Absorption
PHOTON ABSORPTION MECHANISMS RESULTS
Ebin (eV)
E-Ef (eV)
SCATTERING-MEDIATED ABSORPTION and PHOTOEMISSION
Evac
Snapshot of the non-equilibrium electron
distribution during the laser pulse duration (150
fs)
k0
EF
Z. Li, and S. Gao, Phys. Rev. B 50, 15394 (1994)
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Introduction
NON-EQUILIBRIUM ELECTRON DYNAMICS PROBLEMS
Time Resolved 2-Photon Photoemission (TR-2PPE)
e
Evac
e
probe
empty states
F
e
delay time
t
Efermi
pump
occupied states
This result is not compatible with Fermi-Liquid
Theory
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Non-Equlibrium Electron Dynamics
NON-EQUILIBRIUM ELECTRON DYNAMICS PROBLEMS
A. At our moderate laser intensities (Iabs13
µJ/cm2), the electron relaxation time t is
consistent with Fermi-Liquid theory?
B. Indirect population of empty states such as
Image Potential States?
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Non-Equlibrium Electron Dynamics
NON-EQUILIBRIUM ELECTRON DYNAMICS RESULTS
Time-Resolved Photoemission Spectroscopy
Photemitted charge autocorrelation of different
energy regions
The Relaxation Time of the high-energy region is
smaller than the pulse timewidth tlt150 fs
This result is compatible with Fermi-Liquid
Theory
(C. Giannetti et al., in preparation.)
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Non-Equlibrium Electron Dynamics
NON-EQUILIBRIUM ELECTRON DYNAMICS RESULTS
Expected dipole selection rules J0 in
S-pol J?0 in P-pol
Dipole selection rules
Violated in non-resonant case
G. Ferrini et al., Phys. Rev. Lett. 92, 2568021
(2004).
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Conclusions
NON-EQUILIBRIUM PHOTOEMISSION SPECTROSCOPY on
Ag(100)

• Role of scattering in the photon absorption
  mechanism

• NON-EQUILIBRIUM electron dynamics at moderate
  laser intensities is well described by
  Fermi-Liquid theory

• Demonstration of indirect population of empty
  states such as IMAGE POTENTIAL STATES

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Responsibles F. Parmigiani, G. Ferrini.
Co-workers F. Banfi, G. Galimberti, S.
Pagliara, E. Pedersoli.
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Experimental Setup
BS
BS
TRANSLATOR
Travelling Wave Optical Parametric Generator
Energy resolution 10 meV _at_ 2eV
pump
probe
delay t
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Introduction
NON-LINEAR PHOTOEMISSION on METALS ?
IMAGE-POTENTIAL STATES (IPS)
IPS 2-dim electron gas in the forbidden gap
of bulk states
2PPE Population and Photoemission from IPS ?
Electronic Decay Dynamics
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2-PPE on Ag(100)
Photoemission Spectra on Ag(100) single crystal
Direct Photoemission
Fermi Edge
h?6.28eV
Ekin h?-F
P-polarized incident radiation
2-Photon Photoemission with P-polarized light
2-P Fermi Edge
h?3.14eV
Ekin 2h?-F
Log Scale 106 sensitivity
h?
Iabs13 µJ/cm2
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High-Energy Background
HIGH ENERGY REGION
Non-linearity order REGION A 2nd order
process REGION B 3rd order process
Ag(100)

• EXPERIMENTAL EVIDENCES
• Region B does not show a flat distribution
• The RATIO Region B/Region A is 10-2
• These results suggest that the 3rd order
  photoemission in the high energy region
• is not a coherent process

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Image Potential State
IMAGE POTENTIAL STATE
Ag(100)
Ekin h?-Ebin Ebin ? 0.5 eV
n1
K0
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3-photon Fermi Edge
3-Photon Fermi Edge Three experimental
evidences...
2 and 3 photon Fermi Edge - ?E h? -
Fermi-Dirac fitting
Non-linearity order 3-photon Fermi edge
vs 2-photon Fermi edge
n3
n2
Energy-shift with photon energy ?E3PFE 3?h?
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Photoemission Process
PHOTOEMISSION PROCESS PROBLEMS
Upon the absorption of two photon the electron
is already free. Which is the absorption
mechanism responsible of the free-free
transition? Evidence of ABOVE THRESHOLD
PHOTOEMISSION on solids
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Photoemission Process
PHOTOEMISSION PROCESS RESULTS
To evaluate the cross section for an n-photon
absorption involving the initial and final states
is proportional to the Transition Matrix Element
in the DIPOLE APPROXIMATION
In this calculation we have to consider the
mixing of the final free electron state with all
the unperturbed Hamiltonian eigenstates? is it
difficult to evaluate the contribution of this
mixing to T(3).
(F. Banfi et al., in preparation.)