International Workshop on Strong Correl ations and Angle-Resolved

Atsushi Fujimori University of Tokyo

Self-energy from the low to high energy scales in the correlated metal SrVO3

International Workshop on Strong Correlations and Angle-Resolved Photoemission Spectroscopy, 29 July – 2 August 2013, DESY, Hamburg, Germany

Thin film growth and ARPES T. Yoshida*, K. Yoshimatsu**, S. Aizaki, M. Takizawa (U of Tokyo)H. Kumigashira, K. Horiba, K. Ono (KEK-PF) M. Oshima (U of Tokyo)Single crystals H. Eisaki (AIST)DFT calc. P. Mahadevan, K. Gupta (S. N. Bose Inst.)DMFT calc. M.J. Rozenberg, G. Sordi (CNRS)

Present addresses: *Kyoto U, **Tokyo Inst of TechnologySupported by a Grant-in-Aid for Scientific Research S (JSPS)

kFkF

A. Damascelli et al., Rev. Mod. Phys. 2001

Quasi-particle (QP)peak

A(k,)

Band structure

A(k,)

Band electron Correlated electron

Spectral function A(k,) of correlated Fermi liquid

Incoherent part

coherent part(quasi-particle bands)

U

W

W. Metzner and D. Vollhardt, PRL ‚89X.Y. Zhang, M.J. Rozenberg and G. Kotliar, PRL ‘93

Incoherent part(Hubbard bands)

U / W <<1

U / W >1

Dynamical mean field theory (DMFT) of Mott-Hubbard system

W*

Spectral weight 1-z : z

W* = zW

m* 1/W* 1/vF* 1/z

LHB UHB

Bandwidth- and filling-controlled metal-insulator transition

1

Filling-controlled MIT

M. Imada, A. Fujimori and Y. Tokura, Rev. Mod. Phys. 1998

U/W or /W ~ 1

INTE

RA

CTI

ON

STR

ENG

THU

/Wor

/W

n

Bandwidth-controlled MITSrVO3

CaVO3

M. Onoda et al., Solid State Commun. ‘91

Fermi-liquid behaviors of Ca1-xSrxVO3

Electrical resistivity

Ca1-xSrxVO3

I.H. Inoue et al., PRB ‘95

Specific heat

2/ TTcp

SrVO3

CaVO3

H.I. Inoue et al., PRL ‘95

Coherent partIncoherent part(LHB)

Photoemission spectra of the bandwidth-controlled d1 system Ca1-xSrxVO3

SrVO3

CaVO3

A. Sekiyama et al., PRL ‘04

Soft x-ray photoemission

7.1~coh

b

WW

LDA

WbWcoh

2~*

b

Bandwidth Electronic specific heat

Difference between SrVO3 and CaVO3

K. Maiti et al., PRB ‘06

Extraction of bulk spectra

LDA+DMFT calc for SrVO3 and CaVO3

E. Pavarini et al., PRL 04

LDA calculation

LDA+DMFT calculation

H.I. Inoue et al., Phys. Rev. Lett. ‘02

1.5

1.0

0.5

0

-0.5

-1.0

Energ

y (e

V)

43210 X M R ...)cos(cos akaktk yxdxy

X M

R

K. Takegahara et al., J. Electron Spectrosc. 1994

T. Yoshida et al., Phys. Rev. Lett. 2005

dzx

dyz

dxy

...)cos(cos akaktk zydyz ...)cos(cos akaktk xzdzx

EF

Band structure and Fermi surfaces of SrVO3, CaVO3 （d1）

Fermi surfaces

Fermi surfaces of bulk SrVO3 and CaVO3

Secondarycone

dxy

dyz dzxdxy

dyz

T. Yoshida et al., PRB ‘10

ARPES spectra of SrVO3 and CaVO3

SrVO3 CaVO3

Coherent part

Incoherentpart

Coherent part

Incoherentpart

dxydzx dxydzx

T. Yoshida et al., PRB ‘10

ky ky

dyz dyz

Band dispersions

2.1)SrVO(*)CaVO(*

3

3 mm

8.0)SrVO(*)CaVO(*

3F

3F vv

,2* 1 zmm

b

5.0*

F

F zv

v

Outline

• k-dependence of the spectral function and the self-energy

• Self-energy near EF

• Self-energy including Hubbard features

• Remant of ReG(k,)=0 bands

k-dependence of the spectral function and the self-energy

Bulk SrVO3: a = 3.84 ÅK. Yoshimatsu et al.

Epitaxially grown SrVO3 thin film on SrTiO3(001) substrate

SrVO3 filma = 3.905 Å (= SrTiO3)c = 3.82 Å

Reciprocal space mappingof XRD pattern

Atomic force microscope(AFM)

Transmission electronMicroscopy (TEM)

dxy

dzxdyz

Band dispersions

Coherent part

Incoherent part

dzxdzx dxydyz

S. Aizaki et al., PRL ‘12

ARPES spectra of SrVO3 thin film

X

O 2p

V 3d

X

X

ARPES spectra of SrVO3 thin film

incoh.coh

X M

Rkz

kx

ky

X M

X

M

M. Takizawa et al., PRB ‘09

Comparison with DMFT calculation

X X

ARPES intensity map DMFT calc

X X

dxy

dyz

dzx

LDA

Tight biding

Non-int band

incoherentIncoherent

Coherent

2.08.1*

bm

mMass renormalization

M. Takizawa et al., PRB ‘09

Incoherent part:• Finite dispersion• Spectral weight

confined in k<kF

Comparison with DMFT calculation

X X

LDA + DMFT calc

LDA

Tight biding

Non-int band

incoherent

Coherent

I.A. Nekrasov et al., PRB ‘06

m*/mb ~ 2

M. Takizawa et al., PRB ‘09

ARPES intensity map

Model self-energy

S. Aizaki et al.

m*/m=2.0

Momentum kx

0

-1

-2

k-independentmodel self-energy

2)(),(

i

g

k

232k,

g

ig near

• Causal• Fermi-liquid properties:

Application to the free-electron

Self-energy near EF

Kinks in high-Tc cuprates

A. Lanzara et al., Nature ‘01

~70 meV

Band dispersion along (0,0)-()

Self-energy of SrVO3 near EF

Re(k,*k) = *k - k

- 2Im(k,*k)/v

kink

2* 1 zmm

b

5.0*

F

F zv

v

step

LDA

MDC peak

EDC peak

Kink

S. Aizaki et al., PRL ‘12

ARPES A(k,

Re

Im0

Fermi-liquid properties:

Self-energy of SrVO3 near the Fermi level

Re(k,*k) = *k - k

- 2Im(k,*k)/v

kink

2* 1 zmm

b

5.0*

F

F zv

v

step

LDA

MDC peak

EDC peak

Kink

High energy kink/Waterfall?

High energy kink/Waterfall?

S. Aizaki et al., PRL ‘12

ARPES A(k,

Re

Im0

Fermi-liquid properties:

High-energy kink in SrVO3

Self-energy of SrVO3 near the Fermi level

Re(k,*k) = *k - k

- 2Im(k,*k)/v

kink

2* 1 zmm

b

5.0*

F

F zv

v

step

LDA

MDC peak

EDC peak

Kink

High energy kink/Waterfall?

High energy kink/Waterfall?

S. Aizaki et al., PRL ‘12

SrVO3

High energy Kink / Waterfall

Kink

High-energy kink in SrVO3High-energy king in high-Tc cuprates

“Waterfall” inBi2212

J. Graf et al., PRL ‘07

High-energy kink is a general property of correlated metal(Varma, Vollhart…)

Self-energy includingHubbard features

Re(k,)

Im(k,)

(eV)0

Initial input

),(1),(

kk

k G

Self-energy of SrVO3 over a wide energy range

Kramers-Kronig relation

')',(Im'1),(Re

kk GdPG

),( kA ARPES experiment

e-h symmetry assumedRe(k,) antisymmetric,Im(k,) symmetric

),(Im kG

)(1Im1),(

k

kA

Local approx (DMFT)

Agree with Initial input?

No

YesEnd

),(Re kG

),( kk

Dyson equation

)( k

Coh. part

Incoh.part),( kG

A(k,)

(eV)

(eV)

A(k,)

Re(k,)

Im(k,)

self-

ener

gy (e

V)()

Self-energy of SrVO3 over a wide energy range

k = kF

k = kF

k = 0

k = 0

Near EF

Coherent part

Incoherentpart Re()

Im()

Model self-energy

S. Aizaki et al., PRL ‘12

Experimental self-energy compared with LDA+DMFT calculation

I.A. Nekrasov et al., PRB ‘06

(eV)

Re()

Im()

LDA+DMFT calculation

(eV)

Near EF

Re()

Im()

Iteration from ARPES data

U = 3.55 eV

LDA+GW+DMFT calc.

Dynamical screeningR. Sakuma et al., arXiv 13

Im()

Re()

Deriving the bare band dispersion from ARPES data

)(1Im1),(

k

kA

kk

)(Re),(

1ReG

S. Aizaki et al., PRL ‘12

Band energy kARPES A(k,

Simulated A(k,

)0( k

LDA band calc LDA

Coherent part

Incoherent part

Remnant of ReG(k,)=0 bands

S. Sakai et al., PRL ‘09.

Fermi surface and ReG=0 surface

2D Hubbard model for cuprates ReG=0 surface

Fermi surf: ReG=

Hubbard

gap

pseudogap

ReG=0pseudogap

undoped hole-doped

Pseudogap

ReG=(QP band)

LHB

UHB

= =

Self energy from ARPES

k=0

zero

polepole

QP bands and remnant of ReG=0 bands

n nnnn

n iia 11)(

T. Yoshida et al.,

ReG(k,)

ReG=0ReG=

Conclusion

• The kink at ~70 meV is attributed to coupling to optical phonons (cf. Nodal kink in cuprates).

• The kink at ~300 meV is attributed to a self-energy effect (cf. “Waterfall” in cuprates.).

• The self-energy and the spectral function including the incoherent/Hubbard features has been obtained using an iterative procedure.

• Remnant of the ReG=0 bands has been identified, and shown to separate the QP band into the coherent and incoherent features.