Non-linear angle-resolved photoemission of graphite: surface and bulk states

Non-linear angle-resolved photoemission of graphite: surface and bulk states Matteo Montagnese monta@dmf.unicatt.it, http://www.dmf.unicatt.it/elphos Università Cattolica del Sacro Cuore Dipartimento di Matematica e Fisica, Via Musei 41, Brescia, Italy.

Outline THESIS OUTLINE • Introduction: Non perturbative excitations in solids • Image Potential States • Graphite: electronic structure and relation with IPS • Our method: NL-ARPES: experimental setup • Normal emission spectra: IPS and bulk features • Angle-resolved spectra: light induced IPS m* variations • Model calculations: Photoinduced polarization • Conclusions

Introduction NON-PERTURBATIVE DYNAMICS in SOLIDS Ground State and small excitations structure is well understood in many materials SPECTROSCOPIES + ARPES MANY BODY THEORY  + QUASIPARTICLE (QP) Huang, PRL 80, 197 (1998) WHAT ABOUT EXCITATIONS FAR FROM EQUILIBRIUM? RESIDUAL INTERACTION BETWEEN QP – BAND RENORMALIZATION – DYNAMICAL EFFECTS Chemla, Nature 411, 549 2001 STRIVING TO REACH AN UNDERSTANDING & PRECISION FOR THE EXCITED STATES COMPARABLE TO GROUND STATE STRUCTURE PULSED LASER APPARATUS – NONLINEAR OPTICAL TECHNIQUES EFFICIENT, NON PERTURBING PROBE NEEDED

Image Potential States IMAGE POTENTIAL STATES (IPS) Bound surface states of image potential in samples with a bandgap at  Echenique & Pendry, J. Phys. C 11, 2065 (1978) • Pseudo-Rydberg Series in z-direction • Free-electron parallel to surface: k|| - m =me effective mass (2DFEG) Ǻ C= round trip phase change of the wavefunction Adapted from Garcia, PRL 23, 591(1985) EMPTY STATES – LIFETIME DETERMINED BY THE UNDERLYING BULK ( ~ 10-100 fs) BEST STUDIED WITHNL-PE TECHNIQUES

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

Outline THESIS OUTLINE • Introduction: Non perturbative excitations in solids • Image Potential States • Graphite:electronic structure and relation with IPS • Our method: NL-ARPES: experimental setup • Normal emission spectra: IPS and bulk features • Angle-resolved spectra: light induced IPS m* variations • Model calculations: Photoinduced polarization • Conclusions

4.0 IPS π Electrons 0.0 Holes π* -4.0 K G M 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 point @ M point = HIGH ABSORPTION Anisotropic: Surface excitations diffuse poorly in the bulk 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 Lehmann, PRB 60, 17037 (1999) Energy (eV) IPS SENSIBLE TO BULK EXCITATIONS K

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

Outline THESIS OUTLINE • Introduction: Non perturbative exciatations in solids • Image Potential States • Graphite: electronic structure and relation with IPS • Our method: NL-ARPES: experimental setup • Normal emission spectra: IPS and bulk features • Angle-resolved spectra: light induced IPS m* variations • Model calculations: Photoinduced polarization • Conclusions

Our method: NL-ARPES NON-LINEAR PHOTOEMISSION SPECTROSCOPY INTENSE VIS / NEAR-UV LASER PULSES AS PROBE: MULTIPHOTON TRANSITIONS (hv < ) ACCESS TO EMPTY & EXCITED STATES 2st PHOTON Fauster 2003 TIME RESOLVED STUDIES ACCESS to LIFETIMES 1st PHOTON OUR REALIZATION: va=vb SINGLE PULSE MODE Banfi et al. PRL 94, 037601 (2005) ABOVE TRESHOLD PHOTOEMISSION IN SOLIDS CONFIRMED USING 3.14 eV PULSES

ToF e- θ HOPG ToF PARAM: Acc. Angle :  0.83° E = 30meV @ 2 eV EK Our method: NL-ARPES NL-ARPES EXPERIMENTAL SETUP P < 2 10-10 mbar, T=300 K 120 fs; 1 KHz Rep. Rate ћ=3 – 5 eV ; F~100 μJ cm-2 High intensity (>GW cm-2), Spatially coherent light pulses Pulse duration (120fs) << π* excitation lifetime (ps) ACCESS TO THREE IPS QUANTITIES : IPS PE YIELD - IPS LINEWIDTH - IPS EFFECTIVE MASS

Our method: NL-ARPES THREE POSSIBLE EXPERIMENTAL GEOMETRIES: A-B-C C θ=0° =45° Manip Axis B θ=-40° =0  HOPG θ ToF A θ=30° =0

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

Normal Emission spectra MULTIPHOTON TRANSITIONS for IPS AND π* TWO IPS POPULATION PROCESSES MPO=2+1 = 3 Multi Photon Order MPO=1+1 = 2 TWO BULK EXCITATION REGIMES OUT OF RESONANCE With π, π* SADDLE IN RESONANCE IPS IS POPULATED IN A NO-RESONANT WAY BY SCATTERING OF THE HIGH DENSITY OF EXCITED ELECTRONS IN π* BANDS n~1020 cm-3 @ F=100 J cm-2

4.0 MPO TRANSITION @ 4 eV IPS π* Electrons 0.0 Holes π -4.0 K G M Normal Emission spectra VARYING PHOTON ENERGY: STRUCTURE in IPS and π* 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?

Normal Emission spectra PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE π* shoulder feature changes shape And intensity with incident photon energy SHOULDER EXTRACTION FROM DATA no π* FEATURE in 3.52 eV spectrum Used as reference for secondary emission Photoemission intensity (a.u. – linear scale) 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 PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE NON-PERTURBATIVE REGIME 3.60 < hv < 3.90 π* does not change with KE OFF-RESONANCE EXCITATION Int. Width PERTURBATIVE REGIME 3120 K 3.90 < hv < 4.15 INCREASE in Width INCREASE in Teff π* changes with KE 2160 K SADDLE POINT EXCITATION THE IPS is populated by THE SAME π* ELECTRONS

n() 3.6 4.0 4.4 4.8 Normal Emission spectra IPS YIELD AND LINEWIDTH vs. ћ ATћ=4.0 eV PEAK IN THE IPS YIELD STEP IN THE IPS FWHM of 60 meV INTENSITY INCREASE : EXPLAINED BY OPTICAL ABSORPTION + MPO CHANGE 0.4 eV SHIFT : BANDGAP RENORMALIZATION BUT: IPS LINEWIDTH STEP: CHANGE IN LIFETIME? HIGH IPS INTERACTION WITH BULK EXCITATIONS

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

EXCITATION e- Hot e- t 200 ? fs 50 fs 0 n() Angle resolved spectra ROUGH, “SELF-ENERGY” APPROACH ELECTRON POLARIZATION INTERACTION with IPS ? ANSATZ: Primitive cell density FITTING PARAMETERS At k=0 USING KRAMERS-KRONIG RELATIONS: N(ω) x 1020 cm-3 vHs Photon energy

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

Angle resolved spectra GEOMETRY-DEPENDENT SYMMETRY OF IPS DISPERSION A A + C B HIGHER PHOTON ENERGY REQUIRES SYMMETRIC GEOMETRY!

Angle resolved spectra Θmp-DEP. OF PARALLEL POLARIZATION FLUENCE GEOMETRIC EFFECT (SPOT SIZE) + FRESNEL EFFECT (FIELD PROJECTION)

Angle resolved spectra GEOMETRY-DEPENDENT ASYMMETRY EXPLAINED Fresnel Rotating Frame: Geometric projection A B C geometry A and B geometry A Varying θ varying F  varying m*=m*(k) C m* NEARLY CONSTANT for LOW ε2 and/or C geometry : 3.93 eV 3.14 eV

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 2nd order perturbation th. Effective mass at  (orientational average)

ρ(x,y) y (aB) n x (aB) Model calculations SPATIAL PART OF THE CORRUGATION CHARGE: TIGHT BINDING MODEL Periodic Wannier functions of the  bands Excited carrier density

Model calculations Dominant terms: G=NN, n=1 INN(1,1) n≈1020 cm-3 @ F=100 J cm-2 PREDICTION: Δm/m () ≈ 10-4 IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS

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

ELPHOS Lab: Who RESEARCH STAFF Fulvio Parmigiani Gabriele Ferrini Stefania Pagliara Gianluca Galimberti Stefano dal Conte

THANK YOU.

ELPHOS Lab: Where BRESCIA Milano Roma

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

Moos PRL 87, 267402 (2001)

Normal Emission spectra IPS INTENSITY AND LINEWIDTH MEASUREMENTS RESONANCE IN IPS INTENSITY STEP IN IPS LINEWIDTH

PHONONS DISPERSION OF GRAPHTE Mohr PRB 76, 035439

Graphite  BAND SADDLE POINT Zhou, PRB 71, 161403(R) (2005) Taft, PR 138, A197 (1964) EVIDENCE OF HIGH COUPLING of ELECTRONS with PHONONS or DEFECTS DIELECTRIC FUNCTION πM Moos PRL 87, 267402 (2001) ANOMALY in QUASIPARTICLE LIFETIMES due to DISPERSION

Graphite  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 Moos PRL 87, 267402 (2001) Energy- and momentum- conservation hamper decay of M point excitations

n=1 Bulk Vacuum IL U(z) IPS x z e- θ Graphite THE IPS AND THE INTERLAYER STATE In HOPG the IPS is the surface state of the INTERLAYER (IL) BAND Posternak, PRL 52, 863(1984) 1D Periodicity (Kronig-Penney) Photoinduced Polarization High IL(bulk)- IPS coupling Pseudo-Rydberg IPS IL band IPS employed as a probe to the bulk to solve the IL band position controversy Lehman PRB 60, 17 037 (1999) IPS OVERLAPS WITH THE IL BAND = CHANNEL TO HIGHER IPS-BULK COUPLING IS IPS MORE SENSIBLE TO PHOTO-INDUCED POLARIZATIONS?

Our method: NL-ARPES TIME OF FLIGHT DETECTION SCHEME Time of Flight (ToF) detector employed to measure electron kinetic energies. EK=1/2 mev2 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 L KE corrected for CONTACT POTENTIAL SAMPLE WORK FUNCTION MEASURED =4.50 ±0.1eV With hv=6.28 eV CONTACT POTENTIAL

Non-linear angle-resolved photoemission of graphite: surface and bulk states