PhD Dissertation Brescia INFMD.M.F. Dynamics of Non-Equilibrium States in Solids Induced by Ultrashort Coherent Pulses INFM and Università Cattolica del Sacro Cuore Dipartimento di Matematica e Fisica, Via Musei 41, Brescia. Claudio Giannetti

PhD Dissertation Brescia INFMD.M.F. Investigation of Photoinduced non-equilibrium states in Solid State Physics High-Intensity femtosecond coherent pulses Introduction Aim: OPTICAL CONTROL OF ELECTRON INTERACTIONS AND PHASE TRANSITIONS IN SPECIFIC SYSTEMS fs Photodiode reflectivity variation e-e- Spectrometer Photoemission sample

PhD Dissertation Brescia INFMD.M.F. Investigation of Photoinduced non-equilibrium states in solids High-Intensity femtosecond coherent pulses Introduction fs Photodiode reflectivity variation e-e- Spectrometer Photoemission sample pump probe

PhD Dissertation Brescia INFMD.M.F. 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, (2004)] Structural and electronic phase transitions in SOLIDS and MOLECULAR CRYSTALS. [A. Cavalleri et al., Phys. Rev. Lett. 87, (2001)] [E. Collet et al., Science 300, 612 (2003)]

PhD Dissertation Brescia INFMD.M.F. 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 VO 2 By selecting the excitation photon energy it is possible to clarify the physical mechanisms responsible for the photoinduced phase- transition.

PhD Dissertation Brescia INFMD.M.F. 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) Image Potential: Eigenvalues: Ry : Rydberg-like Constant n =1, 2,… m * : electron effective mass

PhD Dissertation Brescia INFMD.M.F. IPS on Ag(100) MEASUREMENTS on IPS Relaxation dynamics IPS effective mass Important test for many-body theories (GW) Electron Green function Screened interaction potential Electron self-energy damping: Γ = 1/ τ = ImΣ * Effective mass: o k + Re Σ *ħ 2 k 2 /2m* Quasi-particle Energy spectrum

PhD Dissertation Brescia INFMD.M.F. ToF e-e- UHV sample 4th 4.2eV 2nd 2.1eV Amplified Ti:Sapphire Oscillator Pulse width: 150 fs Rep. rate: 1kHz Average power: 1W Wavelenght: 790nm ( 1.57eV ) Source : TOPG Tunability nm ( eV) Pulse width 150 fs Average power 50mW Travelling Wave Optical Parametric Generator Energy resolution: 10 2eV IPS on Ag(100) EXPERIMENTAL SET-UP

PhD Dissertation Brescia INFMD.M.F. IPS on Ag(100) NON-LINEAR PHOTOEMISSION on IPS ToF h ν = 4.2 eV > Φ 150 fs E kin = h ν - E n Population of empty states via resonant 2-photon photoemission τ = ħ / Γ Phys. Rev. B 67, (2003)

PhD Dissertation Brescia INFMD.M.F. IPS on Ag(100) ANGLE-RESOLVED PHOTOEMISSION on IPS Phys. Rev. B 67, (2003) m*/m= in agreement with calculated values 2-dimensional free electron gas

PhD Dissertation Brescia INFMD.M.F. Non-Equilibrium Electron Distribution NON-LINEAR PHOTOEMISSION on METALS when h ν < 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

PhD Dissertation Brescia INFMD.M.F. Free-electron dispersion E k || PHOTON ABSORPTION MECHANISMS PROBLEMS: ΔEΔE 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, (2002)] Non-Equilibrium Electron Distribution

PhD Dissertation Brescia INFMD.M.F. Non-Equilibrium Electron Distribution 2-Photon Photoemission with p -polarized light hν=3.14eV Log Scale 10 6 sensitivity I abs =13 μJ/cm 2 Occupied states Non-equilibrium Distribution n=1 IPS hνhν NON-LINEAR PHOTOEMISSION on Ag The excitation of a non-equilibrium electron population results in a high-energy electron tail: E > nhν Φ

PhD Dissertation Brescia INFMD.M.F. submitted to Phys. Rev. B Non-Equilibrium Electron Distribution 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

PhD Dissertation Brescia INFMD.M.F. 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 Non-Equilibrium Electron Distribution submitted to Phys. Rev. B Fermi-liquid

PhD Dissertation Brescia INFMD.M.F. ENERGY TRANSFER non-equilibrium electrons Equilibrium distribution Non-Equilibrium Electron Distribution submitted to Phys. Rev. B Two-temperature model: The heating of the equilibrium distribution can be neglected

PhD Dissertation Brescia INFMD.M.F. IPS as a Probe of Non-Equilibrium Distribution Phys. Rev. Lett 92, (2004) IPS INTERACTING WITH NON-EQUILIBRIUM ELECTRON DISTRIBUTION h ν = 4.28 eV > E n -E F RESONANCE I inc = 30 μJ/cm 2 90% dd ρ e ~ cm -3 h ν = 3.14 eV < E n -E F NO DIRECT POPULATION I inc = 300 μJ/cm 2 0% dd ρ e ~ cm -3 when h ν = 3.14 eV a high-density non-equilibrium electron distribution cohexists with electrons on IPS

PhD Dissertation Brescia INFMD.M.F. IPS as a Probe of Non-Equilibrium Distribution hν=3.15eVhν=3.54eV Shifting with photon energy Δhν=0.39eV n=1 Fermi edge Dispersion of IPS in k || -space Ag(100) E kin = h ν -E bin E bin 0.5 eV n=1 Ag(100) K || =0 IMAGE POTENTIAL STATE Phys. Rev. Lett 92, (2004)

PhD Dissertation Brescia INFMD.M.F. IPS as a Probe of Non-Equilibrium Distribution ELECTRIC DIPOLE SELECTION RULES RESULTS: Ag(100) Dipole selection rules Expected dipole selection rules: J=0 in S -pol J0 in P-pol Violated in non-resonant case Phys. Rev. Lett 92, (2004) EFEF EvEv occupied states empty states Φ n=1 Indirect population of IPS Scattering Assisted Population and Photoemission NO DIPOLE TRANSITION Respected in resonant case

PhD Dissertation Brescia INFMD.M.F. IPS as a Probe of Non-Equilibrium Distribution IPS EFFECTIVE MASS Phys. Rev. Lett 92, (2004) s -polarization m*/m = 0.88±0.04 p -polarization m*/m = 0.88± D electron system interacting with 3-D electron system Role of IPS interaction with the non-equilibrium distribution in W

PhD Dissertation Brescia INFMD.M.F. Insulator-Metal Phase Transition in VO 2 Insulator-to-Metal photoinduced phase transition in VO 2 Solid State properties in highly non- equilibrium regimes

PhD Dissertation Brescia INFMD.M.F. Temperature-Driven IMPT in VO 2 High-T Rutile phase Conductor Low-T Monoclinic phase Insulator: E gap ~0.7 eV T c =340K 3d energy levels [S. Shin et al., Phys. Rev. B 41, 4993 (1990)]

PhD Dissertation Brescia INFMD.M.F. Origin of the Insulating Band-Gap Origin 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 structure stabilizes the distorted Monoclinic phase minimization of the ground-state lattice energy (Peierls or band-like insulator) IMPT Dynamics: a phononic mode drives the phase transition

PhD Dissertation Brescia INFMD.M.F. Photo-Induced IMPT in VO 2 The Insulator-to-Metal phase transition can be induced by ultrashort coherent pulses. τ =150 fs h ν=1.55 eVI=10 mJ/cm 2 [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:

PhD Dissertation Brescia INFMD.M.F. It is the same structural and electronic phase transition? Photo-Induced IMPT in VO 2 Structural YES Electronic ? probe: h ν=1.55 eV structural dynamics τ ~500 fs electronic dynamics τ ~500 fs [A. Cavalleri et al.., Phys. Rev. Lett. 87, (2001)] [M. Becker et al.., Appl. Phys. Lett. 65, 1507 (1994)]

PhD Dissertation Brescia INFMD.M.F. Optical Properties of VO 2 DRUDEHarmonic Oscillator [H. Verleur et al., Phys. Rev. 172, nm ΔR/R ~ -20%

PhD Dissertation Brescia INFMD.M.F. Experimental Set-Up time-resolved ( τ ~150 fs) near-IR (0.5-1 eV) reflectivity PUMP + PROBE three-layer sample

PhD Dissertation Brescia INFMD.M.F. Film thickness: wide-range CW reflectivity Film Thickness E in E out L1L1 L2L2 Best-matching: L 1 =20 nm L 2 =330 nm

PhD Dissertation Brescia INFMD.M.F. Near-IR Reflectivity eV reflectivity: signature of the band-gap Multi-film calculation E in E out L 1 =20 nm L 2 =330 nm L1L1 L2L2

PhD Dissertation Brescia INFMD.M.F. 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

PhD Dissertation Brescia INFMD.M.F. Photo-Induced IMPT Mechanism Which is the mechanism driving the highly non-equilibrium phase transition? d || π*π* hole - doping e-e- with I pump >10 mJ/cm 2 hole-doping ~ % 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!

PhD Dissertation Brescia INFMD.M.F. Photo-Induced IMPT Mechanism d || π*π* hole - doping e-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

PhD Dissertation Brescia INFMD.M.F. Near-IR Photoinduction of the IMPT Pump: 0.95 eV Probe: 1.57 eV-pulses (under gap) ZOOM: IMPT completed in 150 fs: NO thermal effect Metastable metallic phase Two dynamics: τ 1 =200 fs τ 2 =1000 fs

PhD Dissertation Brescia INFMD.M.F. 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!

PhD Dissertation Brescia INFMD.M.F. Near-IR Photoinduction of the IMPT The pump fluence necessary for the IMPT is about constant! No role is played by hole 2400 nm hole-doping ~ 10% P in ~ 16 mJ/cm 1300 nm hole-doping ~ 30% P in ~ 20 mJ/cm 2 Coherent excitation of phonons modes ?

PhD Dissertation Brescia INFMD.M.F. Conclusions We have demonstrated that selecting a particular excitation channel: It is possible to photoinduce the IMPT of VO 2 and clarify the physical mechanisms responsible for the VO 2 electronic properties It is possible to investigate IPS on Ag interacting with a photoinduced non equilibrium electron distribution

PhD Dissertation Brescia INFMD.M.F. Publications G. Ferrini, C. Giannetti, D. Fausti, G. Galimberti, M. Peloi, G.P. Banfi and F. Parmigiani, Phys. Rev. B 67, (2003). G. Ferrini, C. Giannetti, G. Galimberti, S. Pagliara, D. Fausti, F. Banfi and F. Parmigiani, Phys. Rev. Lett. 92, (2004). C. Giannetti, G. Galimberti, S. Pagliara, G. Ferrini, F. Banfi, D. Fausti and F. Parmigiani, Surf. Sci , 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.