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

Ph.D Thesis defense Brescia, 11 January 2010

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

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

Matteo [email protected],

http://www.dmf.unicatt.it/elphos


Outline

THESIS OUTLINE

1. Introduction: Non perturbative excitations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS

4. Our method: NL-ARPES: experimental setup5. Normal emission spectra: IPS and bulk features6. Angle-resolved spectra: light induced IPS m* variations

7. Model calculations: Photoinduced polarization

8. Conclusions


Introduction

NON-PERTURBATIVE DYNAMICS in SOLIDSGround State and small excitations structure is well understood in many materials

MANY BODY THEORY + QUASIPARTICLE (QP)GS 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, 549 2001

STRIVING TO REACH AN UNDERSTANDING & PRECISIONFOR THE EXCITED STATES COMPARABLE

TO GROUND STATE STRUCTURE

EFFICIENT, NON PERTURBING PROBE NEEDED

);(


Outline

THESIS OUTLINE




8. Conclusions


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 =me effective mass (2DFEG)

Adapted from Garcia, PRL 23, 591(1985)

EMPTY STATES – LIFETIME DETERMINED BY THE UNDERLYING BULK( ~ 10-100 fs) BEST STUDIED WITH NL-PE TECHNIQUES

Echenique & Pendry, J. Phys. C 11, 2065 (1978)

Ǻ

C= round trip phase change of the wavefunction


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: τLOC≈0.6 – 1 ps

IPS MODIFICATIONS

DISPERSION FLATTENING (m>me)LINEWIDTH BROADENING(EVENTUAL) RIGID SHIFT

')'(' kkk gdkPURE MIXED

Image Potential States


Outline

THESIS OUTLINE




8. Conclusions


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

Lehmann, PRB 60, 17037 (1999)

IPS SENSIBLE TO BULK EXCITATIONS

Electrons

Holes

4.0

-4.0

0.0

π

π*

IPS

Ener

gy (e

V)

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


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

1. Introduction: Non perturbative exciatations in solids2. Image Potential States3. Graphite: electronic structure and relation with IPS



8. Conclusions


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, 037601 (2005)

1st PHOTON

2st PHOTON

OUR REALIZATION: va=vb

SINGLE PULSE MODE



OP

A

NO

PA

LEEDToF

3-4.2 eV 3-5 eV

UHV chamber

Energy density on sample: 1-2 J cm-2

3.14eV

SHGFHG

SHGSHG

Regenerative Amplifier

Ti:Sa oscillator

500nm cont.

50

0nm

1 K

hz

1 KHz 1 mJ =1.57 eV

76 MHz 10 nJ

Laser system

BS

f

sample

M

Light conversion stage

OP

A

NO

PA

LEEDToF

3-4.2 eV 3-5 eV

UHV chamber

Energy density on sample: 1-2 J cm-2

3.14eV

SHGFHG

SHGSHG


Ti:Sa oscillator

500nm cont.

50

0nm

1 K

hz

1 KHz 1 mJ =1.57 eV

76 MHz 10 nJ

Laser system

SHG


Ti:Sa oscillator

500nm cont.

50

0nm

1 K

hz

1 KHz 1 mJ =1.57 eV

76 MHz 10 nJ

Laser system

BS

f

sample

f

sample

M

Light conversion stage

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 = 30meV @ 2 eV EK

ToF

e-

θ

HOPG

P < 2 10-10 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)



THREE POSSIBLE EXPERIMENTAL GEOMETRIES: A-B-C

A θ=30° =0

B θ=-40° =0

C θ=0° =45°

θ

ToF

Manip Axis

HOPG


Outline

THESIS OUTLINE




8. Conclusions


Normal Emission spectra

POLARIZATION SELECTION RULES

TWO FEATURES : IPS AND BULK π* SHOULDER

NORMAL EMISSION SPECTRA (A geom)

IPS QUANTUM DEFECT

22 )2()1(16

aaRy

E

04.008.0 a

IPS photoemitted only by e

π () photoemitted by e (e||)

SHIFT WITH PHOTON ENERGY

)(cos)( 2ppI

ћ=3.14 eV


TWO BULK EXCITATION REGIMES

TWO IPS POPULATION PROCESSES

MULTIPHOTON TRANSITIONS for IPS AND π*


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 THEHIGH DENSITY OF EXCITED ELECTRONS IN π* BANDS

Multi Photon Order

n~1020 cm-3 @ F=100 J cm-2


VARYING PHOTON ENERGY: STRUCTURE in IPS and π*


USING OPA – NOPA TO SPAN PHOTON ENERGY IN THE 3.2 – 4.2 RANGE

LINEAR IPS PHOTOEMISSIONRESONANT π π* vacuum

HOW ABOUT π* INTENSITY AND WIDTH?

MPO TRANSITION @ 4 eV

Electrons

Holes

4.0

-4.0

0.0

π

π*IPS


PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE

no π* FEATURE in 3.52 eV spectrumUsed as reference for secondary emission

Phot

oem

issio

n in

tens

ity (a

.u. –

linea

r sca

le) 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



PHOTON-DEPENDENT BEHAVIOR OF π* FEATURE

NON-PERTURBATIVE REGIME

PERTURBATIVE REGIME

π* does not change with KE

π* changes with KE

3.60 < hv < 3.90

3.90 < hv < 4.15


SADDLE POINTEXCITATION

OFF-RESONANCEEXCITATION

1/1)(

WEeAEf

Int. Width

INCREASE in WidthINCREASE in Teff

2160 K

3120 K

THE IPS is populated by THE SAME π* ELECTRONS



IPS YIELD AND LINEWIDTH vs. ћ

PEAK IN THE IPS YIELD

STEP IN THE IPS FWHM of 60 meV

AT ћ=4.0 eVn()

3.6 4.0 4.4 4.8

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


Outline

THESIS OUTLINE




8. Conclusions


ANGLE RESOLVED SPECTRA: IPS EFFECTIVE MASS

The IPS dispersion has been measured for the first time in HOPG

*2)(

2||

2

0|| m

kEkEK

WE FOUND THAT m* DEPENDS on PHOTON ENERGY ћ

Maximum of m* @ 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


k

0H )(0 H

ANSATZ:

FITTING PARAMETERS

')'(' kkk gd

ROUGH, “SELF-ENERGY” APPROACH

n()

ELECTRON POLARIZATION INTERACTION with IPS

vHs

0 50 fs 200 ? fs

e-EXCITATION

Hot e-

t

N(ω

) x 1

020 c

m-3

Photon energy

At k=0 USING KRAMERS-KRONIG RELATIONS:

?


Primitive cell density


IPS FWHMIPS EFFECTIVE MASS

vHs

FITTING RESULTSPrevious 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




GEOMETRY-DEPENDENT SYMMETRY OF IPS DISPERSION

HIGHER PHOTON ENERGY REQUIRES SYMMETRIC GEOMETRY!

A A

B C+



Θmp-DEP. OF PARALLEL POLARIZATION FLUENCE

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


GEOMETRY-DEPENDENT ASYMMETRY EXPLAINED

)1()( 0, akFkF BA

20 21)( kb

FkF C

A and B geometry C geometry

A

IF ||

Fresnel

Geometric projection

Rotating Frame:

Varying θ varying F varying m*=m*(k)

m* NEARLY CONSTANT for LOW ε2 and/or C geometry :

3.14 eV 3.93 eV

A

B

A

C



Outline

THESIS OUTLINE




8. Conclusions


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. V2nd order perturbation th.

Effective mass at (orientational average)


x (aB)

y (aB )

ρ(x,y)

Model calculations

SPATIAL PART OF THE CORRUGATION CHARGE: TIGHT BINDING MODEL

Wannier functions of the bands

Excited carrier densityn

T

TTNk

krkrr2

*

2),(),()(),( Periodic


PREDICTION: Δm/m () ≈ 10-4

n≈1020 cm-3 @ F=100 J cm-2

Model calculations

IPS too FAR FROM THE SURFACE; CONSISTENT WITH KNOWN IPS PHYSICS

INN(1,1)

Dominant terms: G=NN, n=1

)]1,1(2)1,1([116

1/* 2142

2

NNNNNN

IIG

mmm


Outline

THESIS OUTLINE




8. Conclusions


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!


ELPHOS Lab: Who

Fulvio Parmigiani

Stefania Pagliara

Gabriele Ferrini

Gianluca Galimberti

Stefano dal Conte

RESEARCH STAFF


THANK YOU.


Milano

BRESCIA

Roma

ELPHOS Lab: Where


Photoinduced polarization

* TRANSITION : LASER-INDUCED POLARIZATION

T

TTNk

krkrr2

*

2),(),()(),( )()( 2 d

c

FN

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

2NDNN


Moos PRL 87, 267402 (2001)



IPS INTENSITY AND LINEWIDTH MEASUREMENTS

RESONANCE IN IPS INTENSITY STEP IN IPS LINEWIDTH


PHONONS DISPERSION OF GRAPHTE

Mohr PRB 76, 035439


BAND SADDLE POINT

EVIDENCE OF HIGH COUPLING of

ELECTRONS with PHONONS or DEFECTS

πM

Moos PRL 87, 267402 (2001)

Zhou, PRB 71, 161403(R) (2005)

Graphite

ANOMALY in QUASIPARTICLE LIFETIMES due to DISPERSION

DIELECTRIC FUNCTION

Taft, PR 138, A197 (1964)


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 lifetimeTime-resolved photoemission -> QP lifetimes

Energy- and momentum- conservation hamper decay of M point excitations

Moos PRL 87, 267402 (2001)

Graphite


Posternak, PRL 52, 863(1984)In HOPG the IPS is the surface state of the INTERLAYER (IL) BAND

Bulk Vacuumn=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

1

)()();();(2

nnnzz

k

z zzdkkzkzL

z

1

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, 17 037 (1999)

Photoinduced PolarizationHigh IL(bulk)- IPS coupling

θe-

THE IPS AND THE INTERLAYER STATE



Time of Flight (ToF) detector employedto measure electron kinetic energies.

EK=1/2 mev2 v= L/Δt

Scattering from sample used to set zero-time referenceEffective 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

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

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