AngleAngle--resolved photoemission resolved photoemission spectroscopy (ARPES)spectroscopy (ARPES)

Experimental study of the electronic structure Experimental study of the electronic structure of stronglyof strongly--correlated electron systemscorrelated electron systems

AndrAndrééss Felipe Felipe SantanderSantander--SyroSyro

Centre de Centre de SpectromSpectroméétrietrie NuclNuclééaireaireet de et de SpectromSpectroméétrietrie de Massede Masse

UniversitUniversitéé ParisParis--SudSud

OXITRONICSOXITRONICSOXITRONICS

C. Bareille, F. Fortuna (CSNSM – Orsay)F. Boariu, M. Klein, A. Nüber, F. Reinert (Uni‐Würzburg)P. Lejay (Institut Néel – Grenoble)O. Copie, M. Bibes, N. Reyren, A. Barthélémy (UMPhy – Thales)T. Kondo (Ames‐Lab)F. Bertran, A. Nicolaou, A. Taleb‐Ibrahimi, P. Le Fèvre (SOLEIL)Y. Apertet, P. Lecoeur (IEF ‐ Orsay) S. Pailhès (CEA ‐ Saclay)X. G. Qiu (Chinese Academy of Sciences)G. Herranz (ICMAB ‐ Spain)R. Weht (CNEA ‐ Argentina)M. J. Rozenberg, M. Gabay (LPS – Orsay)

THANKS!THANKS!

1D

2D

3D

Many properties of solids are determined by electrons within a narrow energy slice (~kBT) around EF (dc conductivity, magnetism, superconductivity…)

Fermi Surface

Condensed (crystalline) matter in a nutshell

Room temperature: kBT = 25 meVAdapted from A. Damascelli’s Exciting-2003 lecture and E. Rotenberg’s lecture

Allowed electronic statesRepeated-zone scheme

-kF kF

ARPES principle

F. Reinert and S. Hüfner, New Journal of Physics 7, 97 (2005)

θsin2 kinmE=||kh

Bkin EWhE −−= ν

x

y

z

e-θ

ϕ

Detector

Sample

Kinetic energy analyzer

, Av

νh

Simple example:Cu(111) surface-state

kx

ky

E

Best for 2D or 1D systems

ARPES with He-lampWürzburg University (DE)

(F. Reinert’s team)

ARPES with synchrotron radiationSynchrotron Radiation Center

University of Wisconsin – Madison (USA)

a = 4.129 Åc = 9.58 Å

Data: E. Hassinger et al., PRB B 77, 115117 (2008).Figure: A. Villaume et al., PRB 78, 012504 (2008).

Hidden‐orderLong‐moment AFM

Example of state-of-the art ARPES: The hidden-order transition in URu2i2

[001]

X

P

Y

N

Z

[100]

[010]

ΔΓ Σ

Λ

Σ

0.40.0-0.4k|| (Å

-1)0.40.0-0.4

k|| (Å-1)

0.40.0-0.4k|| (Å

-1)0.40.0

k|| (Å-1)

-80

-60

-40

-20

0

EB (m

eV)

Low

HighT = 26 K T = 18 K = THO T = 13 K T = 10 K

ARPES view across the transition

Spectra along (110)

AFSS, M. Klein, F. L. Boariu, et al., Nature Physics 5, 637 ‐ 641 (2009)

Photoemission in the N-electron system: theoretical snapshot

Photoemission intensity given by Fermi’s golden rule:

( ) ( )νδπε hEEHI Ni

Nf

Ni

(N)int

Nf −−ΨΨ∝

22,h

k

NiΨ N-electron ground state (energy Ei

N) of unperturbed Hamiltonian

NfΨ Excited state (energy Ef

N) of unperturbed Hamiltonian: N-1 electrons in the solid + 1 free electron of energy ε and momentum k

Matrix element:• k-conservation • Symmetries

Energy conservation

• true in the UV for electrons in the bulk• not necessarily true at the surface

indirect transitions interfering with bulk transitions asymmetric line-shapes

[ ] pAA(r)ppA(r) ⋅≈⋅+⋅≈−

mce

mceH e

int 21

Light-matter interaction: perturbation theory + dipole approximation

Dipole approximation: A constant over atomic dimensions

[ ] 0, ≈⋅∇= AAp hi

Electron escape to the surface

ARPES is a surface technique: one needs clean surfaces + work under ultra-high vacuum (better than 10-9 Torr).

λesc (Ekin)= Electron escape depth(average distance traveled by electron without inelastic scattering)

SUDDEN APPROXIMATIONThe ejected electron should be “fast enough” to neglect its

interaction with the hole left behind

Ekin must be large hν must be large

Final state = Plane wave in the vacuum

Furthermore, one has to make sure that the photoemission process itself does not modify

the electronic structure of the material…

Photoemission: many-body effectselectron-electron interaction

Adapted from R. Claessen’s Cargese-2005 lectures

“loss” of kinetic photoelectron energy due to excitation energy stored in the remaining interacting system

electron-phonon interaction

• Shift in energy of the main photoemission line• Broadening of main line (life-time of excited

interacting system)• Transfer of spectral-weight to higher binding

energies (excitations of the remaining interacting system)

Spectra analysis

1 , =≡ hhωBE

( ) ( ) ( ) ( )ωωνω ,,,, 0 kAkk AfII =

( ) ( )( )[ ] ( )[ ]22 ,,

,1,ωωεω

ωπ

ωkk

kkk Σ′′+Σ′−−

Σ′′−=A

Σ ′′Σ′ Energy renormalization

Lifetime of dressed e-Many-body physics

A(k,ω) = Probability of adding or removing one electron at (k,ω)

Interaction effects on ARPES spectra

( ) ( ) ( ) ( )ωωνω ,,,, 0 kAkk AfII =

( ) ( )( )[ ] ( )[ ]22 ,,

,1,ωωεω

ωπ

ωkk

kkk Σ′′+Σ′−−

Σ′′−=A

A(k,ω) = Probability of adding or removing one electron at (k,ω)

Binding energy EB

Σ’’(k,ω)(life-time)

Σ’(k,ω)(renormalization)

EF

εk(ω) I(k,ω)

EF

εk

k

Many-body physics – Effects of the interactions on the band structure:

Example of surface states of Mo(110)

T. Valla et al., PRL 83, 2085 (1999)

Mo(110) band along Mo(110) band along ΓΓNNT = 70 KT = 70 K

Γee ~ ω2

Γe-ph Eliashberg

Γe-imp = const

Polarization = LVSlits = V

Polarization = LHSlits = V

Polarization = LHSlits = H

xy

z

dxy orbital

ARPES: Effects of orbital symmetries

( )22

,N

iNffiM Ψ⋅Ψ∝ pAk

even

-0.4 0.0 0.4 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

10K LH

-0.4 0.0 0.4 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

10K LV

x

y

z

x

y

z

Polar = LVSlits = V

Polar = LHSlits = V

Example: subbands with orbital order at the surface of SrTiO3

Summary of ARPES techniqueWhen it works…

ARPES is a powerful technique for the study of the electronic structure of complex systems

Rapidly developing…

Detailed band structures and Fermi surfacesFermi velocity and effective massGapsMany-body effects

Spin-resolved ARPESTime-resolved ARPESMicro-ARPESLaser-ARPES using UV/X-ray lasers (HHG in noble gases)Ultra-high resolution ARPES using TOF detector

Superficially metallicA 2D electron gas with universal subbands at the 

surface of SrTiO3

Superficially metallicSuperficially metallicA 2D electron gasA 2D electron gas with universal with universal subbandssubbands at the at the 

surface of SrTiOsurface of SrTiO33

Nature Nature 469469, 189, 189‐‐193 (2011).193 (2011).

Preliminaries: A 2D metal that spontaneously forms at the interface between

two insulators

HighHigh‐‐mobility 2DEG at the LaAlOmobility 2DEG at the LaAlO33/SrTiO/SrTiO33 interfaceinterface

A. Ohtomo and H. Y. Hwang, Nature 427, 423 (2004).

LaAlO3: Band insulatorΔ = 5.6 eV

SrTiO3: Band insulator(quantum paraelectric)

Δ = 3.2 eV

(

(

(

(

)-

)+

)0

)0

KT2D

( ) νzcC VVT −∝

Electric field control of the LAO/STO interface ground stateElectric field control of the LAO/STO interface ground state

A. D. Caviglia et al., Nature 456, 624 (2008).

SC

AFM

NFL

HeavyFL

Heavy fermion physicsT

Pressure

SCAFM

FL

NFL

PG

Cuprate superconductivityT

Doping

Why so important?Why so important?2DEGs (e.g. at semiconductor interfaces) are the first step in the 

design of useful micro‐electronic devices, like FETs.

SrTiO3 is the preferred substrate to grow thin films of transition‐metal oxides. 

Transition‐metal oxides have properties that surpass those of semiconductors: high‐temperature superconductivity, colossal magnetoresistance, high thermoelectric power with good conductivity, multiferroic behavior, …

Possibility of combining two or more of these functionalities in a single device through (multi)‐thin films of transition metal oxides. A 2DEG at the interface provides a conduction channel.

Controllable systems to study fundamental aspects of the physics of transition‐metal oxides, which are often “strongly‐correlated electron systems”.

HeteropolarHeteropolar interfaces based on STO:interfaces based on STO:OPEN QUESTIONSOPEN QUESTIONS

What is the origin of the metallic electron gas?

What is its thickness?

What is its dimensionality? (2D, 3D; i.e., can dgas < λF)

What is (are) the mechanisms responsible for (super)conductivity and high mobility?  

M. Baslestic et al., Nature Materials 2008, doi: 10.1038/nmat2223

Extension of 2DEG at LAO/STO interfaceExtension of 2DEG at LAO/STO interface

Metallic 2DEG can also be induced by Metallic 2DEG can also be induced by electrostatic doping of the pure STO surfaceelectrostatic doping of the pure STO surface

K. Ueno et al., Nature Materials 7, 855 (2008)

• Oxygen vacancies

• Polar catastrophe (build‐up of electric field due to the polar LaO layer)

• Electronic reconstruction (charge leakage between LaTiO3 and SrTiO3)

• Atomic diffusion

• Surface reconstruction to avoid polar catastrophe

Scenarios invokedScenarios invoked

Surprise Surprise …… surprisesurprise!!

A 2DEG spontaneously forms at the vacuum-cleaved surface of SrTiO3

Subband structure, carrier density, confinement size similar to those found in other STO-related interfaces

For this 2DEG, the mechanism is well understood door wide open to generate novel 2DEGs in other oxides!

n3D = 1018 cm-3 1019 cm-3 1020 cm-3 1021 cm-3

2π/a

2π/a

n2D = 1014 cm-2

ky

Δ

Γ

Spin-orbit + tetra + ortho + …

E1(dxy)

E1(dxz / yz)

E2(dxz / yz)

-V0 ky

E

EF

Γ

z

-V0

n=1n=2

EF

eFL≈L

SrTiOSrTiO33: bulk : bulk vsvs 2D2D‐‐confined electronic structureconfined electronic structure

dxydyz

dxz

ky

E

EF

Γ

xy

z

light

heavy

AFSS et al, Nature 469, 189‐193 (2011).

-0.4 0.0 0.4 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

n3D < 1013 cm-3

10K LH

-0.4 0.0 0.4 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

10K LV

Metallic 2DEG at the surface of insulating SrTiOMetallic 2DEG at the surface of insulating SrTiO33

x

y

z

x

y

z

Polar = LVSlits = V

Polar = LHSlits = V

AFSS et al, Nature 469, 189‐193 (2011)

-0.4 0.0 0.4 ky (Å

-1)-0.4 0.0 0.4

ky (Å-1)

n3D < 1013 cm-3 n3D ~ 1018 cm-3 n3D ~ 1020 cm-3

20K 20K

-0.4 0.0 0.4 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

10K LV

SrTiOSrTiO33: universal electronic structure at the surface: universal electronic structure at the surface

AFSS et al, Nature 469, 189‐193 (2011)

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 ky (Å

-1)

-0.3

-0.2

-0.1

0.0

E - E

F (e

V)

min

max

10K LH

BΓ102

10K LV

SrTiOSrTiO33: summary of : summary of subbandssubbandsfor the surface 2DEGfor the surface 2DEG

mlight = 0.7me mheavy ≈ 20me

AFSS et al, Nature 469, 189‐193 (2011)

0π/a

2π/a

π/a

-π/a

0π/a

2π/a

-π/a

-2π/a

2π/a

3π/a

4π/a

π/a

2π/a

3π/a

4π/a

k z

k y

kx

min

max

-0.8

-0.4

0.0

0.4

0.8

ky (

Å-1

)

-2.0 -1.0 kx (Å

-1)

-π/a

π/a

Γ102 Γ112Fermi surface and Fermi surface and density of carriersdensity of carriers

n2D-Total = 1.9 – 2.4x1014 cm-2 ≈ 0.29 – 0.35 e/a2

22 2πF

DAn = AF = Fermi surface area

AFSS et al, Nature 469, 189‐193 (2011)

ΔE = E2(dxz) – E1(dxz) = 120 meVmL

* = 0.7me mH* ≈ 20me

F ≈ 83 MV/m

E1(dxy) = -210 meV V0 ≈ 260 meV

eFL ≈ ΔE L ≈ 14.5 Å ≈ 4 u.c.eFLmax = V0 Lmax ≈ 31 Å ≈ 8 u.c.

4 u.c. ≤ L ≤ 8 u.c.

Confinement potential and size of 2DEG: Confinement potential and size of 2DEG: 

z

n = 1

n = 2

E

E = 0

-V0

eFL≈

Lmax

( ) eFzVzV +−= 0

3/23/12

0 41

23

2 ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+−= ∗ eFn

mVE

zn

πh

T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437-672 (1982).

( )

( )BFA

F

FdFne F

D

+=

′′= ∫1

2 0 02

ε

εε

• K. Ueno et al., Nature Mater. 7, 855 (2008). • R. C Neville, B. Hoeneisen, and C. A. Mead. J. Appl. Phys. 43, 2124 (1972).

F [V/m]A(4K) = 4.097 x 10-5

B(4K) = 4.907 x 10-10 m/V

n2D ≈ 0.25 e/a2

Carrier density from confinement potential:Carrier density from confinement potential:

Y. Aiura et al., Surface Science 515, 61-74 (2002)

Valence band bending due to O‐vacancies at the vacuum‐fractured surface of STO

Valence band bending due to OValence band bending due to O‐‐vacancies at the vacancies at the vacuumvacuum‐‐fractured surface of STOfractured surface of STO

ConclusionsConclusions

Observation of subband structure with orbital ordering at the bare surface of STO.

Universal metallic 2DEG. Exists even at the surface of non-doped, bulk-insulating STO!

Characteristics of this 2DEG in quantitative agreement with 2DEGs in STO-based interfaces/heterostructures.

Origin of the observed 2DEG: oxygen vacancies.