Ph.D Thesis defense Brescia, 11 January 2010 Non-linear angle-resolved photoemission of graphite: surface and bulk states Università Cattolica del Sacro Cuore Dipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy. Matteo Montagnese

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Introduction NON-PERTURBATIVE DYNAMICS in SOLIDS Ground State and small excitations structure is well understood in many materials MANY BODY THEORY  + QUASIPARTICLE (QP) SPECTROSCOPIES + ARPES WHAT ABOUT EXCITATIONS FAR FROM EQUILIBRIUM? PULSED LASER APPARATUS – NONLINEAR OPTICAL TECHNIQUES RESIDUAL INTERACTION BETWEEN QP – BAND RENORMALIZATION – DYNAMICAL EFFECTS Huang, PRL 80, 197 (1998) Chemla, Nature 411, STRIVING TO REACH AN UNDERSTANDING & PRECISION FOR THE EXCITED STATES COMPARABLE TO GROUND STATE STRUCTURE EFFICIENT, NON PERTURBING PROBE NEEDED

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Image Potential States IMAGE POTENTIAL STATES (IPS) Bound surface states of image potential in samples with a bandgap at  Pseudo-Rydberg Series in z-direction Free-electron parallel to surface: k|| - m =m e effective mass (2DFEG) Adapted from Garcia, PRL 23, 591(1985) EMPTY STATES – LIFETIME DETERMINED BY THE UNDERLYING BULK (  ~ fs) BEST STUDIED WITH NL-PE TECHNIQUES Echenique & Pendry, J. Phys. C 11, 2065 (1978) Ǻ  C = round trip phase change of the wavefunction

Ph.D Thesis defense Brescia, 11 January 2010 IPS localise in presence of a periodic dipole lattice induced on surface, e.g: C60 on Cu(111) Dutton, JPC 118, 4337 (2003) Miller, Science 297, 1163 (2002) Also, IPS dispersion flattens (up to the dispersionless limit) because of transient reorientation of polar adsorbates thanks to the same hot IPS electrons: τ LOC ≈0.6 – 1 ps IPS MODIFICATIONS DISPERSION FLATTENING (m>m e ) LINEWIDTH BROADENING (EVENTUAL) RIGID SHIFT PURE MIXED Image Potential States

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Graphite BULK STRUCTURE of GRAPHITE Optically active in the 3-4 eV region, due to the π bands van Hove singularity in the J-DOS due to the π bands Saddle M point = HIGH ABSORPTION Anisotropic : Surface excitations diffuse poorly in the bulk Lehmann, PRB 60, (1999) IPS SENSIBLE TO BULK EXCITATIONS   Electrons Holes π π*π* IPS Energy (eV) SADDLE POINTS IPS band not fully studied with NL-ARPES Layered : Possible High IPS-bulk coupling due to the presence of the Interlayer (IL) band

Ph.D Thesis defense Brescia, 11 January 2010 Graphite IPS ON GRAPHITE ZERO QUANTUM DEFECT – 40 fs LIFETIME FOR n=1 IPS VANISHING QUANTUM DEFECT DUE TO THE PRESENCE OF THE INTERLAYER STATE NEARLY-DEGENERATE WITH IPS

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative exciatations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Our method: NL-ARPES INTENSE VIS / NEAR-UV LASER PULSES AS PROBE: MULTIPHOTON TRANSITIONS ( hv <  ) ACCESS TO EMPTY & EXCITED STATES NON-LINEAR PHOTOEMISSION SPECTROSCOPY Fauster 2003 TIME RESOLVED STUDIES ACCESS to LIFETIMES ABOVE TRESHOLD PHOTOEMISSION IN SOLIDS CONFIRMED USING 3.14 eV PULSES Banfi et al. PRL 94, (2005) 1st PHOTON 2st PHOTON OUR REALIZATION: v a =v b SINGLE PULSE MODE

Ph.D Thesis defense Brescia, 11 January 2010 Our method: NL-ARPES NL-ARPES EXPERIMENTAL SETUP 120 fs; 1 KHz Rep. Rate ћ  =3 – 5 eV ; F~100 μJ cm -2 ToF PARAM : Acc. Angle :  0.83°  E = 2 eV E K ToF e-e- θ HOPG P < mbar, T=300 K ACCESS TO THREE IPS QUANTITIES : IPS PE YIELD - IPS LINEWIDTH - IPS EFFECTIVE MASS High intensity (>GW cm -2 ), Spatially coherent light pulses Pulse duration (120fs) << π* excitation lifetime (ps)

Ph.D Thesis defense Brescia, 11 January 2010 Our method: NL-ARPES THREE POSSIBLE EXPERIMENTAL GEOMETRIES: A-B-C A θ=30°  =0 B θ=-40°  =0 C θ=0°  =45° θ  ToF Manip Axis HOPG

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Normal Emission spectra POLARIZATION SELECTION RULES TWO FEATURES : IPS AND BULK π* SHOULDER NORMAL EMISSION SPECTRA (A geom) IPS QUANTUM DEFECT IPS photoemitted only by e  π (  ) photoemitted by e  ( e || ) SHIFT WITH PHOTON ENERGY ћ  =3.14 eV

Ph.D Thesis defense Brescia, 11 January 2010 TWO BULK EXCITATION REGIMES TWO IPS POPULATION PROCESSES MULTIPHOTON TRANSITIONS for IPS AND π* Normal Emission spectra MPO= 2 +1 = 3 MPO= 1 +1 = 2 OUT OF RESONANCE IN RESONANCE With π, π* SADDLE IPS IS POPULATED IN A NO-RESONANT WAY BY SCATTERING OF THE HIGH DENSITY OF EXCITED ELECTRONS IN π* BANDS Multi Photon Order n~10 20 cm F=100  J cm -2

Ph.D Thesis defense Brescia, 11 January 2010 VARYING PHOTON ENERGY: STRUCTURE in IPS and π* Normal Emission spectra USING OPA – NOPA TO SPAN PHOTON ENERGY IN THE 3.2 – 4.2 RANGE LINEAR IPS PHOTOEMISSION RESONANT π  π*  vacuum HOW ABOUT π* INTENSITY AND WIDTH? MPO 4 eV  Electrons Holes π π*π* IPS

Ph.D Thesis defense Brescia, 11 January 2010 PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE no π* FEATURE in 3.52 eV spectrum Used as reference for secondary emission Photoemission intensity (a.u. – linear scale) π* shoulder feature changes shape And intensity with incident photon energy SHOULDER EXTRACTION FROM DATA Subtract the (shifted-normalized) 3.52 eV spectrum from raw data: difference The π* FEATURE spectrum is fitted with a Fermi-Dirac function Normal Emission spectra

Ph.D Thesis defense Brescia, 11 January 2010 PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE NON-PERTURBATIVE REGIME PERTURBATIVE REGIME π* does not change with KE π* changes with KE 3.60 < hv < < hv < 4.15 Normal Emission spectra SADDLE POINT EXCITATION OFF-RESONANCE EXCITATION Int.Width INCREASE in Width INCREASE in T eff 2160 K 3120 K THE IPS is populated by THE SAME π* ELECTRONS

Ph.D Thesis defense Brescia, 11 January 2010 Normal Emission spectra IPS YIELD AND LINEWIDTH vs. ћ  PEAK IN THE IPS YIELD STEP IN THE IPS FWHM of 60 meV AT ћ  =4.0 eV n(  ) INTENSITY INCREASE : EXPLAINED BY OPTICAL ABSORPTION + MPO CHANGE BUT : 0.4 eV SHIFT : BANDGAP RENORMALIZATION IPS LINEWIDTH STEP: CHANGE IN LIFETIME? HIGH IPS INTERACTION WITH BULK EXCITATIONS

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 ANGLE RESOLVED SPECTRA: IPS EFFECTIVE MASS The IPS dispersion has been measured for the first time in HOPG WE FOUND THAT m* DEPENDS on PHOTON ENERGY ћ  Maximum of 4.0 eV IPS MASS RENORMALIZATION on HOPG COULD BE INDUCED BY THE TRANSIENT OPTICAL EXCITATION in π BANDS 2DFEG C GEOMETRY Angle resolved spectra

Ph.D Thesis defense Brescia, 11 January 2010 ANSATZ: FITTING PARAMETERS ROUGH, “SELF-ENERGY” APPROACH n(  ) ELECTRON POLARIZATION INTERACTION with IPS vHs 0 50 fs 200 ? fs e-e- EXCITATION Hot e - t N(ω) x cm -3 Photon energy At k=0 USING KRAMERS-KRONIG RELATIONS: ? Angle resolved spectra Primitive cell density

Ph.D Thesis defense Brescia, 11 January 2010 IPS FWHMIPS EFFECTIVE MASS vHs FITTING RESULTS Previous results allows us to fit C-geometry (symmetric) measurements without further analysis IPS effective mass AND linewidth behaviour are linked by the model. PEAK / STEP IN CORRESPONDENCE OF THE RENORMALIZED VAN HOVE SINGULARITY Angle resolved spectra

Ph.D Thesis defense Brescia, 11 January 2010 Angle resolved spectra GEOMETRY-DEPENDENT SYMMETRY OF IPS DISPERSION HIGHER PHOTON ENERGY REQUIRES SYMMETRIC GEOMETRY! A A B C +

Ph.D Thesis defense Brescia, 11 January 2010 Angle resolved spectra Θ mp -DEP. OF PARALLEL POLARIZATION FLUENCE GEOMETRIC EFFECT (SPOT SIZE) + FRESNEL EFFECT (FIELD PROJECTION)

Ph.D Thesis defense Brescia, 11 January 2010 GEOMETRY-DEPENDENT ASYMMETRY EXPLAINED A and B geometry C geometry Fresnel Geometric projection Rotating Frame: Varying θ  varying F  varying m*=m*(k) m* NEARLY CONSTANT for LOW ε 2 and/or C geometry : 3.14 eV 3.93 eV A B A C Angle resolved spectra

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 Model calculations   * TRANSITION : LASER-INDUCED CORRUGATION AT THE SURFACE Modifications to the effective mass due to the 1-body IPS interaction with the corrugation potential Ground state IPS Periodic corrugation pot. V 2 nd order perturbation th. Effective mass at  (orientational average)

Ph.D Thesis defense Brescia, 11 January 2010 x (a B ) y (a B ) ρ(x,y) Model calculations SPATIAL PART OF THE CORRUGATION CHARGE: TIGHT BINDING MODEL Wannier functions of the  bands Excited carrier density n Periodic

Ph.D Thesis defense Brescia, 11 January 2010 PREDICTION: Δm/m (  ) ≈ n≈10 20 cm F=100  J cm -2 Model calculations IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS I NN (1,1) Dominant terms: G=NN, n=1

Ph.D Thesis defense Brescia, 11 January 2010 Outline THESIS OUTLINE 1.Introduction : Non perturbative excitations in solids 2.Image Potential States 3.Graphite : electronic structure and relation with IPS 4.Our method: NL-ARPES : experimental setup 5.Normal emission spectra : IPS and bulk features 6.Angle-resolved spectra : light induced IPS m* variations 7.Model calculations : Photoinduced polarization 8.Conclusions

Ph.D Thesis defense Brescia, 11 January 2010 LW m* IPS IN GRAPHITE IS SENSIBLE TO LASER INDUCED POLARIZATION n(  ) 5. Role of LAYERED HOPG + HIGH-I LASER PULSES Conclusions 3. Important PHOTOINDUCED modifications of IPS dispersion 4. Evidence of a PHOTOINDUCED  * excitations - IPS INTERACTION (   * SADDLE POINT) 1. Image Potential States on HOPG studied by NL-ARPES FUTURE/2 MEASUREMENTS: TR-ARPES with ToF2D FUTURE/1 COMPUTATIONAL WORK to confirm the coupling dynamics 2. PE YELD – LineWidth – Effective mass measured EXPLORING EXCITED STATE STRUCTURE BY NL-ARPES & SURFACE IPS!

Ph.D Thesis defense Brescia, 11 January 2010 ELPHOS Lab: Who Fulvio Parmigiani Stefania Pagliara Gabriele Ferrini Gianluca Galimberti Stefano dal Conte RESEARCH STAFF

Ph.D Thesis defense Brescia, 11 January 2010 THANK YOU.

Ph.D Thesis defense Brescia, 11 January 2010 Milano BRESCIA Roma ELPHOS Lab: Where

Ph.D Thesis defense Brescia, 11 January 2010 Photoinduced polarization   * TRANSITION : LASER-INDUCED POLARIZATION AT 4 eV: MAXIMUM DENSITY Laser pulse induces a strong charge polarization at the surface. Strenght depends on ћ  F = pulse fluence (J cm -2 ) TIGHT BINDING + Nearly Free Electron Model (quite a message...) IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS BGR 2 ND NN

Ph.D Thesis defense Brescia, 11 January 2010

Moos PRL 87, (2001)

Ph.D Thesis defense Brescia, 11 January 2010 Normal Emission spectra IPS INTENSITY AND LINEWIDTH MEASUREMENTS RESONANCE IN IPS INTENSITY STEP IN IPS LINEWIDTH

Ph.D Thesis defense Brescia, 11 January 2010 PHONONS DISPERSION OF GRAPHTE Mohr PRB 76,

Ph.D Thesis defense Brescia, 11 January 2010 NL-ARPES measurements have been carried out on HOPG with various ћ  ≈ eV IPS PE yield, m* and linewidth VARIATIONS with ћ  have been measured for the first time These findings could be explained by the IPS interaction with Laser-induced bulk polarization in HOPG (π SADDLE POINT) In particular, evidences of a BGR of 0.4 eV and that IPS undergoes a partial localization, both probably induced by the strong laser-driven (π, π*) e-hole pair creation in the first layers. LAYERED CHARACTER of HOPG IMPORTANT: The IPS-IL band hybridization could greatly enhance IPS coupling to the bulk. FUTURE: TIME RESOLVED ARPES measurements w/ ToF2D + NUMERICAL SIMS. Conclusions

Ph.D Thesis defense Brescia, 11 January 2010  BAND SADDLE POINT EVIDENCE OF HIGH COUPLING of ELECTRONS with PHONONS or DEFECTS πMπM Moos PRL 87, (2001) Zhou, PRB 71, (R) (2005) Graphite ANOMALY in QUASIPARTICLE LIFETIMES due to DISPERSION DIELECTRIC FUNCTION Taft, PR 138, A197 (1964)

Ph.D Thesis defense Brescia, 11 January 2010  BAND SADDLE POINT THE ,  * SADDLE POINT is a PECULIAR point for the excited dynamics in graphite - IMPORTANT DEVIATIONS from the FERMI LIQUID BEHAVIOUR of excitations Plateau in the QP relaxation lifetime Time-resolved photoemission -> QP lifetimes Energy- and momentum- conservation hamper decay of M point excitations Moos PRL 87, (2001) Graphite

Ph.D Thesis defense Brescia, 11 January 2010 Posternak, PRL 52, 863(1984) In HOPG the IPS is the surface state of the INTERLAYER (IL) BAND BulkVacuum  n= 1 IPS IL z x U(z) IPS OVERLAPS WITH THE IL BAND = CHANNEL TO HIGHER IPS-BULK COUPLING 1D Periodicity (Kronig-Penney) Pseudo-Rydberg IPS IL band IPS employed as a probe to the bulk to solve the IL band position controversy IS IPS MORE SENSIBLE TO PHOTO-INDUCED POLARIZATIONS? Graphite Lehman PRB 60, (1999) Photoinduced Polarization High IL(bulk)- IPS coupling θ e-e- THE IPS AND THE INTERLAYER STATE

Ph.D Thesis defense Brescia, 11 January 2010 Our method: NL-ARPES Time of Flight (ToF) detector employed to measure electron kinetic energies. E K =1/2 m e v 2 v= L/Δt Scattering from sample used to set zero-time reference Effective ToF lenght L determined by characterization OPTIMAL for SHORT-PULSE LASER SOURCES TIME OF FLIGHT DETECTION SCHEME CONTACT POTENTIAL L KE corrected for CONTACT POTENTIAL SAMPLE WORK FUNCTION MEASURED  =4.50 ±0.1eV With hv=6.28 eV