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

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

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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.

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

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

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

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

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

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

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

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

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

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

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

THREE POSSIBLE EXPERIMENTAL GEOMETRIES: A-B-C

C θ=0° =45°

Manip Axis

B θ=-40° =0

HOPG

θ

ToF

A θ=30° =0

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

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

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

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?

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

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

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

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

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

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

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.

GEOMETRY-DEPENDENT SYMMETRY OF IPS DISPERSION

A

A

+

C

B

HIGHER PHOTON ENERGY REQUIRES SYMMETRIC GEOMETRY!

Θmp-DEP. OF PARALLEL POLARIZATION FLUENCE

GEOMETRIC EFFECT (SPOT SIZE) + FRESNEL EFFECT (FIELD PROJECTION)

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

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

* 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)

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

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

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

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

RESEARCH STAFF

Fulvio Parmigiani

Gabriele Ferrini

Stefania Pagliara

Gianluca Galimberti

Stefano dal Conte

* 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

IPS INTENSITY AND LINEWIDTH MEASUREMENTS

RESONANCE IN IPS INTENSITY

STEP IN IPS LINEWIDTH

Mohr PRB 76, 035439

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

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

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?

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

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