Angle-resolvedphotoemission spectroscopy
(ARPES)
Daniil Evtushinsky
Kourovka, 1st of March 2012
Angle-resolved photoemission
sample
i
Angle-resolved photoemission
sample
i
h
Angle-resolved photoemission
sample
fi
i + h – A = f
h
Angle-resolved photoemission
sample
kfki
h
i + h – A = fk||i = k||f
Momentum conservation
Momentum conservationfor semi-infinite case
Angle-resolved photoemission
sample detector
kf
h
ki
Angle-resolved photoemission
sample detector
kf
h
ki
Angle-resolved photoemission
sample detector
kf ~1/f
h
ki
E
Angle-resolved photoemissionspectroscopy (ARPES)
BESSY 13 station
Scienta electron analyzer
Sample preparation
Sample preparation
hν
e-
UE 112 LowE1meV*10JANIS1K
SES R40001meV*0.1°
BESSY 13 station
Unitary ARPES image
Electronic band dispersion
Unitary ARPES image
Band dispersion from ARPES(
k y)
k x=c
onst
|
ky
ky
kx
45.8
45.6
45.4
-15 -10 -5 0 5 10 15
3500
3000
2500
2000
1500
1000
500
min
max
ky
kx
(kx, ky)
(kx, ky)=0
2H-TaSe2
kxk y
EK
TiSe2
Another typical experimentaldata set: 1T-TiSe2
151050-5-1 0
95
94
93
92
91
Kin
etic
ene
rgy
(eV
)
Momentum
kxk y
EK
TiSe2
Another typical experimentaldata set: 1T-TiSe2
Beamline
Excitation energy range5.
85.
65.
45.
25.
0
Kine
tic e
nerg
y (e
V)
-5 0 5
h=9 eV
Bi2Se3
BSCCO
h=200 eV
Cuprates
Fermi surface
Aebi et al. (1996) Borisenko et al. (1999)
d-wave
Shen et al. (1993) Ding et al. (1996)
Effects of interaction with bosonic mode
Inosov et al., PRB (2006)Fedorov et al. (1999)
Pseudogap
Kondo et al., Nature (2009)
ARPES data analysis
Ideal and measured signal
Nodal Direction of cuprates
No gap
Voigt fit of energy-momentum cut
Evtushinsky et al., PRB (2006)
Spectral Function Extraction fromARPES Data
I(k, ) A(k, )R(k, )
Inte
nsity
-0.05 0.00 0.05
k - km (Å-1)
L G
- 0.01 eV
- 0.1 eV
We measure I(k, )We are interested inA(k, )We need to remove R(k, )
Spectral line shapef --- LorentzianR --- Gaussian
g --- Voigt profile
Voigt profile in optical spectroscopy
Linewidthfrom Voigt Fit
60
50
40
30
20
10
0
HW
HM
(1/
Å)
-0.3-0.2-0.10.0(eV)
Voigt fit:
WV WG WG
f
WL WLf
Lorentz fit:
Wlor
Bi-2212 OP 89K, T = 110–135 Ka
Evtushinsky et al., PRB (2006)
60
50
40
30
20
10
0
HW
HM
(1/
Å)
-0.3-0.2-0.10.0(eV)
Voigt fit:
WV WG WG
f
WL WLf
Lorentz fit:
Wlor
Bi-2212 OP 89K, T = 110–135 Ka
Intrinsic width,WL
Evtushinsky et al., PRB (2006)
Linewidthfrom Voigt Fit
60
50
40
30
20
10
0
HW
HM
(1/
Å)
-0.3-0.2-0.10.0(eV)
Voigt fit:
WV WG WG
f
WL WLf
Lorentz fit:
Wlor
Bi-2212 OP 89K, T = 110–135 Ka
Resolution:WG=const
Evtushinsky et al., PRB (2006)
Linewidthfrom Voigt Fit
Comparison to the low-energy high-resolution data
0.03
0.02
0.01
0.00
W (
1/Å
)
-0.15-0.10-0.050.00 (eV)
Kordyuk PRL 2004WL
Koralek PRL 2006
a
Bi-2212 OP 89 KT = 30 K
J. D. Koralek et al., PRL 2006
R(h)-1/2
R6eV LASER/R27eV synchrotron=0.25
Temperature dependence of scattering rateΣ"(ω=0,T)
20
15
10
5
0HW
HM
(1/
Å)
3002001000
T (K)
Voigt Gauss Lorentz
width decreases!Overall Intrinsic width increases
Temperature dependenceof scattering rate
Evtushinsky et al., PRB (2006)
ARPES on charge-density-wavecompounds
Phase diagram
Morosan et al., Nat. Phys. (2006); PRB (2008)
- π / a π / a0
E F
normal state, V=0
- π / a π / a0
4 V
E F
modulated state, V 0
- π / a π / a0
E F
A(k, ω)
Electronic structure modification bymodulating potential
Band dispersion of 2H-TMDs
2H-TaSe2
CDW-induced Change in ElectronicStructure
180K
30K
New Parts of Fermi surface
Fermi surface nesting andsuperstructure formation
( ) ( ) k q
nesting vectorin the momentum space
periodicity of the superstructurein the coordinate space
Charge ordering in 2H-TaSe2 andNbSe2
Davis et al.
S. V. Borisenko et al., PRL (2008)
S. V. Borisenko et al., PRL (2009)
D. S. Inosov et al., NJP (2008)
2H-TaSe2
2H-NbSe2 2H-NbSe2
Magnetic ordering in Gd2PdSi3 andTb2PdSi3
D. S. Inosov et al., PRL (2009)
Charge-orbital ordering inLa0.5Sr1.5MnO4
D. V. Evtushinsky et al., PRL (2010)
Comparison to complementarymeasurements of electronic
structure
ARPESElectron transport,thermodynamics, etc.
ε(k) Φ[ε(k)]dk∫
Electron dynamics in applied fieldBloch wave packet
Electronic response to the weakexternal field
where
Can be expressedin a similar way
Resistivity , Hall coefficient RH, and magnetoresistance /
Calculated and measured RH forsimple metals
RH (10-10 m3/C)
T. P. Beaulac, PRB (1981)http://www.phys.ufl.edu/fermisurface/
Hall effect in 2H-TaSe2 and NbS2
Evtushinsky et al., PRL (2008)
Hall effect in 2H-TaSe2 and NbS2
Evtushinsky et al., PRL (2008)
Band dispersion of 2H-TMDs
2H-NbSe2, 2H-NbS22H-TaSe2
ARPES on iron-basedsuperconductors
Iron-based superconductors
Fermi surfaces of iron-basedsuperconductors
S. Raghu et al., PRB (2008)D. J. Singh, PRB (2008)A. Nekrasov et al., JETP (2008)…
Fermi surfaces of iron-basedsuperconductors
Electronic bands at Fermi level
Ene
rgy
Momentum
Γ X
Fermi surface of Ba1-xKxFe2As2
(kx, ky)
Zabolotnyy et al., Nature (2009)Evtushinsky et al., JPSJ (2011)
Zabolotnyy et al., Nature (2009);Physica C (2009)Evtushinsky et al., NJP (2009);JPSJ (2011)
Band dispersion near Fermi levelin Ba1-xKxFe2As2 from ARPES
Propellers again
T. Sato et al., 0810.3047
17th of October
L. Wray et. al.,arXiv:0812.2061
11th of December15th of August
L. Wray et al.,arXiv:0808.2185
V. B. Zabolotnyy et al.,arXiv:0808.2454
18th of August
Hall and FS in parent
Borisenko et al., PRL (2009)
LiFeAs: no nesting, no magnetism,superconductivity
LiFeAs map
Band renormalization in LiFeAs
~3
Superconducting gap extractionfrom ARPES spectra
Opening of the superconducting gapin electronic dispersion
TTc
Superconducting gap in ARPES spectra
15.68eV
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
827
826
825
824
823
Inte
nsity
(ar
b. u
.)
15.68eV15.6615.6415.6215.60
Kinetic energy (eV)
T=1K
Superconducting gap in ARPES spectra
15.67
15.66
15.65
15.64
15.63
Kine
tic e
nerg
y (e
V)
0.50ky, 1/Å0.450.400.350.30
Momentum (1/Å)
Fermi level
15.68eV
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
T=1K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
300
250
200
150
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=22K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
300
250
200
150
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=22K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
350
300
250
200
150In
tens
ity (
arb.
u.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=20K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
500
400
300
200In
tens
ity (
arb.
u.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=18K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
600
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=16K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
600
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=14K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
600
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=12K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
600
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=10K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
500
400
300
200In
tens
ity (
arb.
u.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=8K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
500
400
300
200In
tens
ity (
arb.
u.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=6K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=4K
Superconducting gap opening inARPES spectra
15.74eV
15.72
15.70
15.68
15.66
15.64
15.62
15.60
Kine
tic e
nerg
y (e
V)
0.7ky, 1/Å0.60.50.40.30.2
Momentum (1/Å)
600
500
400
300
Inte
nsity
(ar
b. u
.)
15.74eV15.7215.7015.6815.6615.6415.6215.60
Kinetic energy (eV)
T=2K
Gap extraction from ARPES dataFit of IEDC
Evtushinsky et al., PRB (2009)Dynes et al., PRL (1978)
Ene
rgy
Momentum
Gap extraction from ARPES data
Evtushinsky et al., PRB (2009)Dynes et al., PRL (1978)
below Tc
Ene
rgy
? = 10 meV
= 10 meV
Fit vs. Symmetrization
Superconducting gapin Ba1-xKxFe2As2
Fermi surfaces of iron-basedsuperconductors
Hole-doped BaFe2As2
Superconducting gap distributionfor Ba1-xKxFe2As2 (Γ FS sheets)
Hole-doped BaFe2As2
Gap on propeller-like structure
Hole-doped BaFe2As2
Gap on propeller-like structure
Gap anisotropy
Anisotropy of gap for -barrels
Momentum dependence of thesuperconducting gap in Ba1-xKxFe2As2
Fermi surface and gap distribution incuprate superconductors
Superconducting gap in LiFeAs from fit ofARPES spectra
Superconducting gap of 1.7meV in underdopedBa1-xNaxFe2As2 with Tc=10K
Evtushinsky et al., NJP (2009)
Coupling strength, 2/kBTc, in iron-arsenidesuperconductors
P. Szabo et al., PRB (2009)
Ba1-xKxFe2As2
R. S. Gonnelli et al., PRB (2009)
LaFeAsO1−xFx SmFeAsO1−xFx
R. S. Gonnelli et al., Physica C (2009)
Ba1-xKxFe2As2
C. Ren et al., PRL (2008)
Ba1-xKxFe2As2
Comparison to complementarymeasurements of electronic
structure in superconducting state
ε(k), (k) Φ[ε(k), (k)]dk∫
ARPESSR, Hc1,specific heat, etc.
Superfluid density in Ba1-xKxFe2As2 fromARPES
Khasanov et al., PRL (2009)Evtushinsky et al., NJP (2009)
Chandrasekhar and Einzel, Ann. Physik (1993)
Superfluid densityin LiFeAs
Inosov et al., PRL (2010)
3D
Sensitivity to 3D electronic structurevia scanning h
Inosov et al., PRB (2008)
kz-dispersion in iron arsenides
kz-dispersion in iron arsenides
kz-dependence of the superconductinggap in BKFA
kz-dependence of the superconductinggap in BKFA
3D band structure
Comparison of calculated andmeasured band dispersions
Yaresko (2011)
Comparison of calculated andmeasured band dispersions
Tc = 38K
T = 1K
Comparison of calculated andmeasured band dispersions
Hole-doped BaFe2As2
Comparison of calculated andmeasured band dispersions
Zeroing matrix element due tosymmetry reasons
wave, propagatingto detector
initial state of electronin crystal
polarization ofincoming light
Zeroing matrix element due tosymmetry reasons
Comparison between of and measuredband dispersions
Special role of iron 3dxz,yz orbitals inmagnetism
Yi et al., PNAS (2011)
Node-like behavior in BFAP
al. et Feng (2011)
Ba1-xNaxFe2As2
Ba1-xNaxFe2As2hν=80eVhν=80eV
Ba1-xKxFe2As2
Fermi surface
Gap on the inner Γ-barrel in Ba1-xNaxFe2As2
2500
2000
1500
1000
500
40.8640.8440.8240.8040.78eV
EDC85 7K EDC86 16K EDC87 26K EDC88 30K EDC89 35K EDC90 40K EDC91 45K
40.90
40.85
40.80
40.75
40.70
40.65
40.60
eV
151050-5-10-15deg
1200
1000
800
600
400
200
40.9040.8540.8040.7540.7040.6540.60eV
40.90
40.85
40.80
40.75
40.70
40.65
40.60
eV
151050-5-10-15deg
2000
1500
1000
500
40.9040.8540.8040.7540.7040.6540.60eV
Gap on the electron-like pocket inBa1-xNaxFe2As2
45.95
45.90
45.85
45.80
45.75
45.70
eV
-6 -4 -2 0 2 4 6deg
1200
1000
800
600
400
200
45.9545.9045.8545.8045.7545.70eV
Gap on the outer Γ-barrel in Ba1-xNaxFe2As2
80
60
40
20
0
-20
meV
-0.6-0.5-0.4-0.3-0.2-0.10.0ky, 1/Е
Surface sensitivity
Surface component of photoemissionsignal in YBCO
V. Zabolotnyy et al., PRB (2006)
Surface component in BKFA
Surface component in BKFA
Surface component in BKFA
Surface component in BKFA
Absence of surface states in LiFeAs
Absence of surface states in LiFeAs
bulk slab
Lankau et al., PRB (2011)
Surface sensitivity:
•no surface states at the Fermi level observedin 111 and 122 iron arsenides
•surface layer may be non-superconducting,but band dispersion doesn’t differ from the bulk
SrPd2Ge2
Kim et. al., PRB (2012)
Experiment Theory
SrPd2Ge2
Kim et. al., PRB (2012)
Experiment Theory
•Completely 3D FS•No band renormalization•Likely conventional superconductivity
Kim et. al., PRB (2012)
SrPd2Ge2
Mode
DOS of stronglycoupled
superconductor
Mode effects on the spectra ofBa1-xKxFe2As2 below Tc
kink_energy = 23 meV
Christianson et al., Nature (2008)
= 10 meVM = 13-14 meV
Kink in Ba1-xNaxFe2As2
1K
1K40K
4.54.03.53.02.5
40.82
40.80
40.78
40.76
eV
40.84
40.82
40.80
40.78
40.76
40.74
40.72
eV
7654321deg
40.84
40.82
40.80
40.78
40.76
40.74
40.72
eV
7654321deg
40K
Mode effect at X-pocketin Ba1-xKxFe2As2
Tc = 38K
T = 40K T = 1K
T = 40K T = 1K
Fusion of bogoliubons
Fusion of bogoliubons
Fusion of bogoliubons
Fine structure of electronic spectrum below Tc
Temperature dependence: fastersaturation for the larger gap
Relation between energy scales ofband structure and superconductivity
Conclusions for iron-based• Various Fermi surface shape for different iron-based
superconductors
• Large and small superconducting gaps in Ba1-xKxFe2As2and other materials, large 2/kTc
• Correlation of superconducting gap magnitude withorbital composition: importance of iron 3dxz,yz
Acknowledgements
V. B. ZabolotnyyA. A. KordyukT. K. KimJ. Maletz
S. AswarthamI. MorozovS. WurmhelG. BehrC. HessR. HübelA. KoitzschM. Knupfer
B. Büchner
S. V. Borisenko
A. VarykhalovE. RienksR. Follath
DFG Research Unit 538
D. S. InosovA. N. YareskoA. V. BorisG. L. SunD. L. SunV. HinkovC. T. LinB. Keimer
H. Q. LuoZ. S. WangH. H. Wen
Acknowledgements
S. V. Borisenko
A. A. Kordyuk
V. B. Zabolotnyy
R. Follath
B. Büchner
thank you for your attention
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