international workshop on strong correl ations and angle-resolved
TRANSCRIPT
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
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
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
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 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…)
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
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.