Ultrafast Electron Dynamics
of non-thermal population in metals INFM and
Università Cattolica del Sacro Cuore
Dipartimento di Matematica e Fisica, Via Musei 41, Brescia. Claudio Giannetti
Ultrafast Electron Dynamics
of non-thermal population in metals INFM and
Università Cattolica del Sacro Cuore
Dipartimento di Matematica e Fisica, Via Musei 41, Brescia. Claudio Giannetti
Introduction ToF LINEAR PHOTOEMISSION: hν > Φ
→ mapping of EQUILIBRIUM ELECTRON DISTRIBUTION Femtosecond Light Pulses
NON-LINEAR PHOTOEMISSION: hν < Φ
→ Mapping of
NON-EQUILIBRIUM
ELECTRON DISTRIBUTION CW Light 2-Photon Photoemission
with P-polarized light hν=3.14eV Log Scale
106 sensitivity Iabs=13 μJ/cm2 Occupied
states Non-equlibrium
Distribution n=1 IPS Ag(100)
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
Free-electron
dispersion E k|| Photon Absorption PHOTON ABSORPTION MECHANISMS
PROBLEMS: ΔE Δk|| 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
Photon Absorption PHOTON ABSORPTION MECHANISMS
RESULTS: Ebin (eV) E-Ef (eV) SCATTERING-MEDIATED
ABSORPTION and PHOTOEMISSION scattering scattering scattering k||=0 Evac EF Z. Li, and S. Gao, Phys. Rev. B 50, 15394 (1994) Snapshot of the non-equilibrium electron distribution during the laser pulse duration (150 fs) DEPENDENCE ON POLARIZATION → The models predict a collision term:
in agreement with the measured RATIO (C. Giannetti et al., in preparation.) (IP/IS)3=0.69
Rtheor=0.29
Rexp=0.22±0.1
Introduction Evac Efermi occupied states empty states scattering hν hν photoemission decay dynamics of non-equilibrium electron distribution in Au film:
PUMP: hν=1.84eV, Iabs=120μJ/cm2
PROBE: hν=5.52eV W.S. Fann et al., Phys. Rev B 46, 13592 (1992). Time Resolved 2-Photon Photoemission (TR-2PPE) pump probe delay time τ e– e– e– Φ NON-EQUILIBRIUM ELECTRON DYNAMICS
PROBLEMS: This result is not compatible with Fermi-Liquid Theory
Non-Equlibrium Electron Dynamics NON-EQUILIBRIUM ELECTRON DYNAMICS
PROBLEMS: A. At our moderate laser intensities (Iabs=13 μJ/cm2),
the electron relaxation time τ is consistent with
Fermi-Liquid theory? B. Indirect population of empty states such as Image Potential States?
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:
τ<150 fs (C. Giannetti et al., in preparation.) This result is compatible with Fermi-Liquid Theory
Non-Equlibrium Electron Dynamics NON-EQUILIBRIUM ELECTRON DYNAMICS
RESULTS: G. Ferrini et al., Phys. Rev. Lett. 92, 2568021 (2004). Ag(100) Dipole selection rules Expected dipole selection rules:
J=0 in S-pol
J≠0 in P-pol Violated in non-resonant case EF Ev occupied
states empty
states Φ n=1 Indirect population of IPS Scattering Assisted
Population
NO DIPOLE TRANSITION
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
Responsibles:
F. Parmigiani,
G. Ferrini. Co-workers:
F. Banfi,
G. Galimberti,
S. Pagliara,
E. Pedersoli.
Introduction NON-LINEAR PHOTOEMISSION on METALS
→ IMAGE-POTENTIAL STATES (IPS) Ag(100) U. Hofer et al., Science 277, 1480 (1997). Ebin=
0.5eV IPS: 2-dim electron gas in the forbidden gap of bulk states 2PPE: Population and Photoemission from IPS
→ Electronic Decay Dynamics
2-PPE on Ag(100) Fermi Edge Direct Photoemission 2-Photon Photoemission
with P-polarized light 2-P Fermi Edge Photoemission Spectra on Ag(100) single crystal hν=6.28eV Ekin= hν-Φ hν=3.14eV Ekin= 2hν-Φ hν Log Scale
106 sensitivity Efermi Evac occupied
states empty
states Φ n=1 Iabs=13 μJ/cm2 P-polarized incident radiation
High-Energy Background HIGH ENERGY REGION: Non-linearity order
REGION A: 2nd order process
REGION B: 3rd order process 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 Ag(100)
Image Potential State Δhν=0.39eV hν=3.15eV hν=3.54eV Shifting with photon energy m*/m0.880.04 n=1 Fermi edge Dispersion of IPS in k||-space Ag(100) Ekin = hν-Ebin
Ebin 0.5 eV n=1 Ag(100) K||=0 IMAGE POTENTIAL STATE
3-photon Fermi Edge 2 and 3 photon Fermi Edge:
- ΔE = hν
- Fermi-Dirac fitting Energy-shift with photon energy:
ΔE3PFE = 3·Δhν Non-linearity order:
3-photon Fermi edge vs
2-photon Fermi edge 3-Photon Fermi Edge: Three experimental evidences... n=2 n=3
Photoemission Process PHOTOEMISSION PROCESS
PROBLEMS: Efermi Evac occupied
states empty
states Φ n=1 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
Photoemission Process PHOTOEMISSION PROCESS
RESULTS: To evaluate the cross section for an
n-photon absorption involving the initial and final states: Efermi Evac occupied
states empty
states Φ n=1 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). Rough Estimate T(3)/T(2)10-6
Experimental Value T(3)/T(2)10-4 Is another mechanism involved? (F. Banfi et al., in preparation.)
Comments