angle-resolved photoemission spectroscopy (a...
TRANSCRIPT
-
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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