Dynamics of Non-Equilibrium States in Solids
Induced by Ultrashort Coherent Pulses
Claudio Giannetti
INFM and
Università Cattolica del Sacro Cuore
Dipartimento di Matematica e Fisica, Via Musei 41,
Brescia.
INFM
D.M.F.
PhD Dissertation
Brescia 20-12-2004
Introduction
High-Intensity femtosecond coherent
pulses →
Investigation of Photoinduced non-equilibrium
states in solids
pump
sample
Photodiode
Photoemission
e-
10-100 fs
Spectrometer
reflectivity
variation
probe
INFM
D.M.F.
PhD Dissertation
Brescia 20-12-2004
Introduction
High-Intensity femtosecond coherent
pulses →
Investigation of Photoinduced non-equilibrium
states in solids
•Time-resolved non-linear photoemission on METALS.
[W.S. Fann et al., Phys. Rev. Lett. 68, 2834 (1992)]
[U. Höfer et al., Science 277, 1480 (1997)]
[G. Ferrini et al., Phys. Rev. Lett. 92, 2668021 (2004)]
•Structural and electronic phase transitions in SOLIDS
and MOLECULAR CRYSTALS.
[A. Cavalleri et al., Phys. Rev. Lett. 87, 2374011 (2001)]
[E. Collet et al., Science 300, 612 (2003)]
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D.M.F.
PhD Dissertation
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Introduction
OPTICAL CONTROL OF ELECTRON
INTERACTIONS AND PHASE TRANSITIONS
IN TWO SPECIFIC SYSTEMS:
•Image Potential States on Ag(100)
By selecting the excitation photon energy it is possible to investigate
the properties of IPS in different regimes.
•Insulator-Metal phase transition of VO2
By selecting the excitation photon energy it is possible to clarify the
physical mechanisms responsible for the photoinduced phasetransition.
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D.M.F.
PhD Dissertation
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IPS on Ag(100)
IMAGE-POTENTIAL STATES (IPS)
IPS:
2-dim electron gas in the forbidden gap of bulk states
Image Potential:
e2 1
V ( z )  Evac 
4πε0 4 z
Ag(100)
Eigenvalues:
•Ry: Rydberg-like
 2 k||2
Ry
E 2 
n
2m*
P.M. Echenique et al., Surf. Sci. Rep. 52, 219 (2004).
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Constant
•n=1, 2,…
•m* : electron
effective mass
D.M.F.
PhD Dissertation
Brescia 20-12-2004
IPS on Ag(100)
MEASUREMENTS on IPS
•Relaxation dynamics
•IPS effective mass
Important test for many-body theories (GW)


 
dq d ' 
*
 (k ,  )  i 
W (q ,  ' )G (k  q ,    ' )
2
(2 ) 2
Electron
self-energy

G (k ,  ) 
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Screened
interaction potential
1

0
*
   k   (k ,  )
Quasi-particle
Energy spectrum
PhD Dissertation
Electron
Green function
damping:
Γ = 1/τ = ImΣ*
Effective mass:
ok + ReΣ*≈ħ2k2/2m*
D.M.F.
Brescia 20-12-2004
IPS on Ag(100)
EXPERIMENTAL SET-UP
Source:
Amplified Ti:Sapphire Oscillator
Travelling Wave Optical
Parametric Generator
TOPG
Pulse width: 150 fs
Rep. rate: 1kHz
Average power: 1W
Wavelenght: 790nm (1.57eV)
Tunability 1150-1500 nm
(0.8-1.1 eV)
Pulse width 150 fs
Average power 50mW
ToF
Energy resolution: 10 meV @ 2eV
e-
4th
4.2eV
sample
2nd
2.1eV
UHV
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D.M.F.
PhD Dissertation
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IPS on Ag(100)
NON-LINEAR PHOTOEMISSION on IPS
ToF
150 fs
Ekin = hν - En
hν = 4.2 eV > Φ
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τ=ħ/Γ
Population of empty states
via resonant 2-photon photoemission
Phys. Rev. B 67, 235407 (2003)
PhD Dissertation
Brescia 20-12-2004
D.M.F.
IPS on Ag(100)
ANGLE-RESOLVED PHOTOEMISSION on IPS
m*/m=0.970.02
in agreement with
calculated values
2mEKin sin  
k|| 

2
 2 k //
E (k // )  En 
2m*
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→ 2-dimensional
free electron gas
Phys. Rev. B 67, 235407 (2003)
PhD Dissertation
Brescia 20-12-2004
D.M.F.
Non-Equilibrium Electron Distribution
NON-LINEAR PHOTOEMISSION on METALS
when hν < Φ a non-equilibrium electron population is excited
in the s-p bands of Ag
investigation of the non-equilibrium
electron distribution
↓
•Excitation mechanisms
•Relaxation dynamics
•Photoemission processes
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Non-Equilibrium Electron Distribution
PHOTON ABSORPTION MECHANISMS
PROBLEMS:
The intraband transition between s-s
states within the same branch is
FORBIDDEN for the conservation of the
momentum.
E
Δk||
ΔE
Free-electron
dispersion
E
 2k ||2
2m *
k||
Γ
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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D.M.F.
PhD Dissertation
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Non-Equilibrium Electron Distribution
NON-LINEAR PHOTOEMISSION on Ag
The excitation of a non-equilibrium electron population results
in a high-energy electron tail: E > nhνΦ
hν=3.14eV
Occupied
states
n=1 IPS
hν
Non-equilibrium
Distribution
Log Scale
106 sensitivity
2-Photon Photoemission
with p-polarized light
Iabs=13 μJ/cm2
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D.M.F.
PhD Dissertation
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Non-Equilibrium Electron Distribution
We exclude:
• Coherent 3-photon
photoemission
• Direct 3-photon
photoemission
↓
• Scattering-mediated
transition
The high-energy electron tail is a fingerprint of the non-equilibrium electron
distribution at k||≠0
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submitted to Phys. Rev. B
PhD Dissertation
Brescia 20-12-2004
D.M.F.
Non-Equilibrium Electron Distribution
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
τ<150 fs
 N
1
n ( E2 )
 ( E )dn( E )  23fs
Fermi-liquid
n ( E1 )
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 E 
 (E)   0  F 
 E  EF 
submitted to Phys. Rev. B
PhD Dissertation
Brescia 20-12-2004
2
D.M.F.
Non-Equilibrium Electron Distribution
ENERGY TRANSFER
non-equilibrium electrons
↓
Equilibrium distribution
Two-temperature model:
Te
Ce (Te )
 G  (Te  Tl )  P (t )
t
Tl
Cl (Tl )
 G  (Te  Tl )
t
The heating of the equilibrium
distribution can be neglected
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submitted to Phys. Rev. B
PhD Dissertation
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D.M.F.
IPS as a Probe of Non-Equilibrium Distribution
IPS INTERACTING WITH NON-EQUILIBRIUM ELECTRON
DISTRIBUTION
hν = 3.14 eV
< En-EF
NO DIRECT
POPULATION
RESONANCE
Iinc= 300 μJ/cm2
0% d→d
Iinc= 30 μJ/cm2
90% d→d
ρe~ 1020 cm-3
ρe~ 2∙1018 cm-3
hν = 4.28 eV
> En-EF
when hν = 3.14 eV a high-density non-equilibrium electron distribution
cohexists with electrons on IPS
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Phys. Rev. Lett 92, 2568021 (2004)
PhD Dissertation
Brescia 20-12-2004
D.M.F.
IPS as a Probe of Non-Equilibrium Distribution
Ag(100)
Ekin = hν-Ebin
n=1
K||=0
Ebin  0.5 eV
Dispersion of IPS in k||-space
Fermi edge
Shifting with photon energy Δhν=0.39eV
Ag(100)
hν=3.15eV
n=1
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IMAGE POTENTIAL STATE
Phys. Rev. Lett 92, 2568021 (2004)
PhD Dissertation
Brescia 20-12-2004
hν=3.54eV
D.M.F.
IPS as a Probe of Non-Equilibrium Distribution
ELECTRIC DIPOLE SELECTION RULES
RESULTS:
Indirect population of IPS
Ag(100)
Expected dipole selection rules:
J=0 in S-pol
J≠0 in P-pol

n
S
P
Dipole selection rules
Ev
n=1
Scattering Assisted
Population and
Photoemission
EF
Violated
Respected
in non-resonant
in resonant case
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NO DIPOLE
TRANSITION
Phys. Rev. Lett 92, 2568021 (2004)
PhD Dissertation
Brescia 20-12-2004
Φ
empty
states
occupied
states
D.M.F.
IPS as a Probe of Non-Equilibrium Distribution
IPS EFFECTIVE MASS
s-polarization
m*/m = 0.88±0.04
p-polarization
m*/m = 0.88±0.01


 
d
q
d ' 
*
 (k ,  )  i 
W (q ,  ' )G (k  q ,    ' )
2
(2 ) 2
2-D electron system interacting with
3-D electron system
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Role of IPS interaction with the
non-equilibrium distribution in W
Phys. Rev. Lett 92, 2568021 (2004)
PhD Dissertation
Brescia 20-12-2004
D.M.F.
Insulator-Metal Phase Transition in VO2
Insulator-to-Metal photoinduced phase transition in
VO2
Solid State properties in highly nonequilibrium regimes
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Temperature-Driven IMPT in VO2
High-T
Rutile phase
Conductor
Tc=340K
Low-T
Monoclinic phase
Insulator:
Egap~0.7 eV
3d energy levels
[S. Shin et al., Phys. Rev. B 41, 4993 (1990)]
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Origin of the Insulating Band-Gap
Origin of the insulating band-gap:
electron-electron
minimization of the
correlations in the d|| band ground-state lattice energy
(Mott-Hubbard insulator) (Peierls or band-like insulator)
IMPT Dynamics:
the electronic structure
stabilizes the distorted
Monoclinic phase
IMPT Dynamics:
a phononic mode drives
the phase transition
A comprehensive review: [M. Imada et al.., Rev. Mod. Phys. 70, 1039 (1998)]
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Photo-Induced IMPT in VO2
The Insulator-to-Metal phase transition can
be induced by ultrashort coherent pulses.
τ=150 fs
hν=1.55 eV I=10 mJ/cm2
[M. Becker et al.., Appl. Phys. Lett. 65, 1507 (1994)]
Questions opened:
•It is the same structural and electronic phase transition?
•Structural and electronic transitions are simultaneous?
•Which is the mechanism driving the highly
non-equilibrium phase transition?
INFM
D.M.F.
PhD Dissertation
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Photo-Induced IMPT in VO2
•It is the same structural and electronic phase transition?
Structural
YES
probe: hν=1.55 eV
structural
dynamics
τ~500 fs
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Electronic
?
[A. Cavalleri et al.., Phys. Rev.
Lett. 87, 2374011 (2001)]
PhD Dissertation
[M. Becker et al.., Appl. Phys.
Lett. 65, 1507 (1994)]
Brescia 20-12-2004
electronic
dynamics
τ~500 fs
D.M.F.
Optical Properties of VO2
@ 790 nm
ΔR/R ~ -20%
[H. Verleur et al., Phys. Rev. 172, 788 (1968)]
DRUDE
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Harmonic Oscillator
EPj2
EP2
 (E)     2
 2
2
E  iE / 
E

E
j
0 j  iE /  j
PhD Dissertation
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D.M.F.
Experimental Set-Up
time-resolved (τ~150 fs)
near-IR (0.5-1 eV) reflectivity
PUMP + PROBE
three-layer
sample
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Near-IR Reflectivity
0.5-1 eV reflectivity:
signature of the band-gap
Multi-film
calculation
Ein
Eout
L1
L2
L1=20 nm L2=330 nm
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Femtosecond Band-Gap Closing
The Insulator-to-Metal phase transition is
induced by 1.57 eV-pulses
and probed by 0.54 eV-pulses (under gap)
Signature of
Femtosecond
band-gap closing
150 fs
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D.M.F.
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Photo-Induced IMPT Mechanism
•Which is the mechanism driving the highly
non-equilibrium phase transition?
e-
π*
d||
hole - doping
with Ipump>10 mJ/cm2
hole-doping ~ 20-100%
•Removal of the d||
electron-electron correlations→
band-gap collapse and lattice
stabilization
•Coherent excitation of the phonon
responsible of the IMPT→
lattice transition and electronic
rearrangment
In this experimental scheme it is not
possible to discriminate!
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PhD Dissertation
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Photo-Induced IMPT Mechanism
Near-IR photoinduction of the phase transition
π*
e0.7 eV
hole - doping
in the under-gap region
the hole-doping is
highly reduced
d||
we can discriminate between the two
mechanisms
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PhD Dissertation
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Near-IR Photoinduction of the IMPT
Pump: 0.95 eV
Probe: 1.57 eV-pulses (under gap)
Two dynamics: τ1=200 fs
τ2=1000 fs
ZOOM:
IMPT completed in 150 fs:
NO thermal effect
Metastable metallic phase
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D.M.F.
PhD Dissertation
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Near-IR Photoinduction of the IMPT
The Insulator-to-Metal
phase transition can be
induced in the
under-gap region,
through
near-IR pulses
(0.5-1 eV)
The pump fluence
necessary for the IMPT
is about constant!
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D.M.F.
PhD Dissertation
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Conclusions
We have demonstrated that selecting
a particular excitation channel:
•It is possible to investigate IPS on Ag
interacting with a photoinduced non
equilibrium electron distribution
•It is possible to photoinduce the IMPT of VO2
and clarify the physical mechanisms
responsible for the VO2 electronic properties
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D.M.F.
PhD Dissertation
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Publications
•G. Ferrini, C. Giannetti, D. Fausti, G. Galimberti, M. Peloi, G.P. Banfi and F. Parmigiani,
Phys. Rev. B 67, 235407 (2003).
•G. Ferrini, C. Giannetti, G. Galimberti, S. Pagliara, D. Fausti, F. Banfi and F. Parmigiani,
Phys. Rev. Lett. 92, 2568021 (2004).
•C. Giannetti, G. Galimberti, S. Pagliara, G. Ferrini, F. Banfi, D. Fausti and F. Parmigiani,
Surf. Sci. 566-568, 502 (2004).
•G. Ferrini, C. Giannetti, S. Pagliara, F. Banfi, G. Galimberti and F. Parmigiani,
in press on J. Electr. Spectrosc. Relat. Phenom.
•F. Banfi, C. Giannetti, G. Ferrini, G. Galimberti, S. Pagliara, D. Fausti and F. Parmigiani,
accepted for publication on Phys. Rev. Lett.
•C. Giannetti, S. Pagliara, G. Ferrini, G. Galimberti, F. Banfi and F. Parmigiani,
submitted to Phys. Rev. B.
•E. Pedersoli, F. Banfi, S. Pagliara, G. Galimberti, G. Ferrini, C. Giannetti and F. Parmigiani,
in preparation.
INFM
D.M.F.
PhD Dissertation
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