dynamics of non-equilibrium states in solids induced by ultrashort coherent pulses

PhD Dissertation Brescia 20-12-2004 INFM D.M.F.

Dynamics of Non-Equilibrium States in SolidsInduced by Ultrashort Coherent Pulses

INFM and

Università Cattolica del Sacro CuoreDipartimento di Matematica e Fisica, Via Musei 41, Brescia.

Claudio Giannetti


Investigation of Photoinduced non-equilibrium states in solids

High-Intensity femtosecond coherent pulses →

Introduction

10-100 fs

Photodiode

reflectivity variatione-Spectrometer

Photoemissionsamplepump

probe


Investigation of Photoinduced non-equilibrium states in solids

High-Intensity femtosecond coherent pulses →

Introduction

•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)]


OPTICAL CONTROL OF ELECTRON INTERACTIONS AND PHASE TRANSITIONS

IN TWO SPECIFIC SYSTEMS:

Introduction

•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 phase-transition.


IPS on Ag(100)

IMAGE-POTENTIAL STATES (IPS)

P.M. Echenique et al., Surf. Sci. Rep. 52, 219 (2004).

IPS: 2-dim electron gas in the forbidden gap of bulk states

Ag(100)

zπεeEzV vac 4

14

)(0

2

Image Potential:

*

2||

2

2 2mk

nRyE

Eigenvalues: •Ry: Rydberg-likeConstant•n=1, 2,…•m* : electron effective mass


IPS on Ag(100)

MEASUREMENTS on IPS

)',()',(2

')2(

),( 2*

qkGqWdqdik

•Relaxation dynamics•IPS effective mass

Important test for many-body theories (GW)

),(1),(

*0

kkG

k

Electron Green functionScreened

interaction potential

Electronself-energy

damping:Γ = 1/τ = ImΣ*

Effective mass:o

k + ReΣ*≈ħ2k2/2m*Quasi-particleEnergy spectrum


ToF

e-

UHV

sample

4th4.2eV

2nd2.1eV

Amplified Ti:Sapphire Oscillator

Pulse width: 150 fsRep. rate: 1kHzAverage power: 1WWavelenght: 790nm (1.57eV)

Source: TOPG Tunability 1150-1500 nm

(0.8-1.1 eV) Pulse width 150 fs Average power 50mW

Travelling Wave Optical Parametric Generator

Energy resolution: 10 meV @ 2eV

IPS on Ag(100)

EXPERIMENTAL SET-UP


IPS on Ag(100)

NON-LINEAR PHOTOEMISSION on IPS

ToF

hν = 4.2 eV > Φ

150 fs

Ekin = hν - En

Population of empty states via resonant 2-photon photoemission

τ = ħ / Γ

Phys. Rev. B 67, 235407 (2003)


IPS on Ag(100)

ANGLE-RESOLVED PHOTOEMISSION on IPS

Phys. Rev. B 67, 235407 (2003)

*

2//

2

// 2)(

mkEkE n

sin2||

KinmEk

m*/m=0.970.02in agreement with calculated values

→ 2-dimensionalfree electron gas


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


*

2||

2

2mk

E

Free-electrondispersion

E

k||Γ

PHOTON ABSORPTION MECHANISMSPROBLEMS:

ΔE

Δk||

The intraband transition between s-s states within the same branch is FORBIDDEN for the conservation of the momentum.

THE ENERGY ABSORPTION IS DUE TO A THREE-BODY PROCESS AND NOT TO A DIPOLE TRANSITION

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)]




2-Photon Photoemissionwith p-polarized light

hν=3.14eV

Log Scale106 sensitivity

Iabs=13 μJ/cm2

Occupied states

Non-equilibrium Distribution

n=1 IPS

hν

NON-LINEAR PHOTOEMISSION on AgThe excitation of a non-equilibrium electron population results

in a high-energy electron tail: E > nhνΦ

PhD Dissertation Brescia 20-12-2004 INFM D.M.F.submitted to Phys. Rev. B


We exclude:

• Direct 3-photon photoemission

• Coherent 3-photon photoemission

↓• Scattering-mediated

transition

The high-energy electron tail is a fingerprint of the non-equilibrium electron distribution at k||≠0


NON-EQUILIBRIUM ELECTRON DYNAMICSRESULTS:

Time-Resolved Photoemission SpectroscopyPhotemitted charge autocorrelation of different energy regions

The Relaxation Time of the high-energy region is

τ<150 fs


submitted to Phys. Rev. B

fs23)()()(

)(

12

1

En

En

EdnEN 2

0)(

F

F

EEEE Fermi-liquid


ENERGY TRANSFER non-equilibrium electrons

↓Equilibrium distribution


submitted to Phys. Rev. B

Two-temperature model:

)()(

)()()(

lel

ll

lee

ee

TTGtTTC

tPTTGtTTC

The heating of the equilibrium distribution can be neglected


IPS as a Probe of Non-Equilibrium Distribution

Phys. Rev. Lett 92, 2568021 (2004)

IPS INTERACTING WITH NON-EQUILIBRIUM ELECTRON DISTRIBUTION

hν = 4.28 eV> En-EF

RESONANCE

Iinc= 30 μJ/cm2

90% d→d

ρe~ 2∙1018 cm-3

hν = 3.14 eV< En-EF

NO DIRECTPOPULATION

Iinc= 300 μJ/cm2

0% d→d

ρe~ 1020 cm-3

when hν = 3.14 eV a high-density non-equilibrium electron distribution cohexists with electrons on IPS



hν=3.15eV hν=3.54eV

Shifting with photon energy Δhν=0.39eV

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

Phys. Rev. Lett 92, 2568021 (2004)



ELECTRIC DIPOLE SELECTION RULESRESULTS:

n

P

S

Ag(100)

Dipole selection rules

Expected dipole selection rules: J=0 in S-polJ≠0 in P-pol

Violated in non-resonant case

Phys. Rev. Lett 92, 2568021 (2004)

EF

Ev

occupied states

emptystates

Φn=1

Indirect population of IPS

Scattering Assisted Population and Photoemission

NO DIPOLETRANSITIONRespected in resonant case



)',()',(2

')2(

),( 2*

qkGqWdqdik

IPS EFFECTIVE MASS

Phys. Rev. Lett 92, 2568021 (2004)

s-polarizationm*/m = 0.88±0.04

p-polarizationm*/m = 0.88±0.01

2-D electron system interacting with 3-D electron system

Role of IPS interaction with the non-equilibrium distribution in W


Insulator-Metal Phase Transition in VO2Insulator-Metal Phase Transition in VO2

Insulator-to-Metal photoinduced phase transition inVO2

Solid State properties in highly non-equilibrium regimes


Temperature-Driven IMPT in VO2

High-TRutile phaseConductor

Low-TMonoclinic phase

Insulator:Egap~0.7 eV

Tc=340K

3d energy levels

[S. Shin et al., Phys. Rev. B 41, 4993 (1990)]


Origin of the Insulating Band-GapOrigin of the insulating band-gap:

A comprehensive review: [M. Imada et al.., Rev. Mod. Phys. 70, 1039 (1998)]

electron-electron correlations in the d|| band(Mott-Hubbard insulator)

IMPT Dynamics:the electronic structurestabilizes the distorted

Monoclinic phase

minimization of theground-state lattice energy

(Peierls or band-like insulator)

IMPT Dynamics:a phononic mode drives

the phase transition


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)]

•It is the same structural and electronic phase transition?

•Which is the mechanism driving the highly non-equilibrium phase transition?

•Structural and electronic transitions are simultaneous?

Questions opened:


•It is the same structural and electronic phase transition?Photo-Induced IMPT in VO2

StructuralYES

Electronic?

probe: hν=1.55 eVstructuraldynamicsτ~500 fs

electronicdynamicsτ~500 fs

[A. Cavalleri et al.., Phys. Rev. Lett. 87, 2374011 (2001)]

[M. Becker et al.., Appl. Phys. Lett. 65, 1507 (1994)]


Optical Properties of VO2

j jj

PjP

iEEEE

iEEEE

//)( 2

02

2

2

2

DRUDE Harmonic Oscillator

[H. Verleur et al., Phys. Rev. 172, 788 (1968)]

@ 790 nmΔR/R ~ -20%


Experimental Set-Up

time-resolved (τ~150 fs)near-IR (0.5-1 eV) reflectivity

PUMP + PROBE

three-layer sample


Near-IR Reflectivity0.5-1 eV reflectivity:

signature of the band-gap

Multi-film calculation

Ein Eout

L1=20 nm L2=330 nm

L1

L2


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


Photo-Induced IMPT Mechanism

•Which is the mechanism driving the highly non-equilibrium phase transition?

d||

π*

hole - doping

e-

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 rearrangmentIn this experimental scheme it is not possible to discriminate!


Photo-Induced IMPT Mechanism

d||

π*

hole - doping

e-

Near-IR photoinduction of the phase transition

0.7 eV

in the under-gap region

the hole-doping is highly reduced

we can discriminate between the two mechanisms


Near-IR Photoinduction of the IMPT

Pump: 0.95 eVProbe: 1.57 eV-pulses (under gap)

ZOOM:IMPT completed in 150 fs:NO thermal effect

Metastable metallic phase

Two dynamics: τ1=200 fsτ2=1000 fs


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!


Conclusions

We have demonstrated that selecting a particular excitation channel:

•It is possible to photoinduce the IMPT of VO2 and clarify the physical mechanisms responsible for the VO2 electronic properties

•It is possible to investigate IPS on Ag interacting with a photoinduced non equilibrium electron distribution


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.

dynamics of non-equilibrium states in solids induced by ultrashort coherent pulses

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