Angle-resolved photoemission spectroscopy (A RPES)sadovski.iep.uran.ru/RUSSIAN/LTF/Kourovka_34/... · 2012. 2. 29. · Band dispersion from ARPES k y k x t | ky ky kx 45.8 45.6 45.4-15

Angle-resolvedphotoemission spectroscopy

(ARPES)

Daniil Evtushinsky

Kourovka, 1st of March 2012

Angle-resolved photoemission

sample

i


sample

i

h


sample

fi

i + h – A = f

h


sample

kfki

h

i + h – A = fk||i = k||f

Momentum conservation

Momentum conservationfor semi-infinite case


sample detector

kf

h

ki


sample detector

kf ~1/f

h

ki

E

Angle-resolved photoemissionspectroscopy (ARPES)

BESSY 13 station

Scienta electron analyzer

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


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



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



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


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)

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)…

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


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


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


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


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


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


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


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


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


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


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

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)

Sensitivity to 3D electronic structurevia scanning h

Inosov et al., PRB (2008)

kz-dispersion in iron arsenides

kz-dependence of the superconductinggap in BKFA

3D band structure

Comparison of calculated andmeasured band dispersions

Yaresko (2011)

Tc = 38K

T = 1K


Hole-doped BaFe2As2

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

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

•Completely 3D FS•No band renormalization•Likely conventional superconductivity

Kim et. al., PRB (2012)

SrPd2Ge2

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

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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Angle-resolved photoemission spectroscopy (A RPES)sadovski.iep.uran.ru/RUSSIAN/LTF/Kourovka_34/... · 2012. 2. 29. · Band dispersion from ARPES k y k x t | ky ky kx 45.8 45.6 45.4-15