Phase fluctuation in AF order and its effect on the pseudo-gap in

electron doped cuprates

Chang Young Kim Yonsei University

Outline

1. Review

2. ARPES results

3. Spin-fermion model

4. AF phase fluctuation model

5. Conclusion

What interacts with electronsin HTSCs?

k

k'

?

Lattices, spins, etc

k

k' -k

-k'

Cooper pair

Information in spectral functionsElectron-phonon coupling

Ashcroft, Mermin “Solid State Physics”T. Valla, Science, 1999

“kink”

‘kink’ in the spectral function

Controversies in h-doped HTSCs

- Similar energy scalesSuperconducting gap, Pseudo gap, Phonons, Magnetic resonance mode

Q=(0.5,0.5)

H. He et al. PRL (2001)

Strong kink in Bi2212

A. Gromko et al., PRB

Energy scales in e-doped HTSCs

High E kink (~500 meV)

Low E kink (~50 meV)Pseudo gap ( ~ 100 meV)

Magnetic resonance mode (~10 meV?)Superconducting gap (~3 meV)

B. Moritz et al., NJP

Spin resonance mode?

S. Wilson, Nature 442, 59 (2006)

Phonons in e-doped HTSCs

Nodal

Anti-nodal

Isotropic e-phonon coupling ( S. R. Park, PRL 101, 117006 (2008) )

Wish to look at pseudo-gap

High E kink (~500 meV)

Low E kink (~50 meV)Pseudo gap ( ~ 100 meV)

Spin resonance mode (~10 meV?)Superconducting gap (~3 meV)

N. P. Armitage

PRL (2001)Binding energy(eV)

• Spectral weight suppression near EF at the intersection of AF Billiouin Zone Boundary (AFBZ) and the underlying FS

• Coupling to a bosonicmode localized at Q=(π,π)?

kx

ky

Pseudo-gap effect

PG in electron doped cuprates

Static 2 x 2 order

(π, π) scattering from 2 x 2 order?

AFBZ

EF

Original Fermi surface

(π,0)

(π,π)

Γ

Band StructureAFBZ

2Vπ,π

EF

Reconstructed Fermi surface

EF

2Vπ,π

Inter-band transition

( π,0 )

Bind

ing

Ener

gy (e

V)EF

0.1

0.2

2Vππ

(π/2, π/2)

σ 1(Ω

-1 c

m-1

)

00

2

4

Photon Energy (eV)0.5

onset

x103

1.0

220K140K70K10K

300K

(0,π) (π,0)

EF

2Vππ

(π/2,π/2)

Bind

ing

Ener

gy

Momentum

Energy (eV)0 2 4 86 10 12 14

0.2

0.4

0.6

0.8

1.0

Refl

ecti

vity

DOS

0-2-4

-8-6

2 Energy (eV)

visible pwh

copper

S. R. ParkPRB 2007

Overshooting problemBi

ndin

g En

ergy

(eV)

EF

0.1

0.2

0.3

0.4

k parallel to (0,0)-(p,p) (1.41p/a)(π,0.3π)(π,0)

a)dcb

a (π,π)

Γ

S. R. Park et al., PRB® (2007)

(π,π)

Γ

H. Matsui et al., PRL (2005)

0.50.4 0.6

d)

0.4 0.5 0.6

c)

0.4 0.5 0.6

b)SCCO(x=0.15)

NCCO(x=0.13)AFBZ

2Vπ,π

EF

EF spectral weight at hot spot

kx (p/a)

k y(p

/a)

1-1

a)

b)1

B.E.

(eV)

0.0

0.2

0.4

PGa)

Momentum

B.E.

(eV)

0.0

0.2

0.4

Momentum

b)

Inte

nsit

y (a

rb.)

0.4 0.3 0.0Binding energy (eV)

0.2 0.1

NCCO

AF LRO

Hot spot

Hot spot

FS, Tem.=10KNd1.85Ce0.15CuO4

Two problems:1. Band overshoots across AFZB

2. Ef Spectral weight @ hot spot

In addition:

What is the origin of scattering?(Spin-fermion, localized moments, …)

Effect of short range order?Te

mpe

ratu

re (K

)

Cerium concentration, x

100

200

300

400

500

00 0.5 1.0 1.5

ξ/a2

400

50

5

10

20

100

200

Nd2-xCxCuO4

AF correlation length by INS

Cu

AF long range order

E. M. Motoyama et al., nature (2007)

2ξ

How to control the ordering length?

Rare earth element dependent AF: muon spin relaxation

2.0Time (ms)

0.0 0.5 1.0 1.5A

sym

met

ry

Nd2-xCexCuO4 T=10K

x=0.0

x=0.10

x=0.14

x=0.16

Doping concentration0.0 0.0

50.10 0.15 0.2

0

AFMSCTe

mpe

ratu

re (k

)

0

100

200

300Nd2-xCexCuO4

Time (ms)0 1 2 3 4

Asy

mm

etry

Sm1.95Ce0.05CuO4120K

110K

75K

100K

75K

Sm1.80Ce0.20CuO4

G. M. Luke et al., PRB, 1990 T. Sasakawa, unpublished

heavier rare-earth element, stronger AF

static AF cover all SC dome in SCCO

SCAFM

0.0 0.05 0.10 0.15 0.200

0.25

100

200

Doping concentration

Sm2-xCexCuO4

Tem

pera

ture

(k)

Pr1-xLaCexCuO4

Doping concentration0.0 0.10 0.2

0

Tem

pera

ture

(k)

100

200

M. Fujita et al., PRB, 2003

Samples

Nd1.85Ce0.15CuO4(Tc=23K)

Sm1.90Ce0.10CuO4(Tc=0K)

Sm1.85Ce0.15CuO4(Tc=17K)

Sm1.82Ce0.18CuO4(Tc=9K)

Eu1.85Ce0.15CuO4(Tc=0K)

Gd1.85Ce0.15CuO4(Tc=0K)

Rn2-xCexCuO4

Floating zone

SSRL, Stanford, USAB.L. 5-4 high resolution ARPES

ARPES Optical

Yonsei Univ.

Experiments

• ARPES experiments: Stanford Synchrotron Radiation Lab.

• Energy resolution : 15 meV

• Temperature : 15K

Rare-earth elements dependent

kx (p/a) 1 1

SCCO ECCO GCCO

kx (p/a) kx (p/a)0 1

k y(p

/a)

1 90

80

70

60

50

40

30

Nd Sm Eu GdIn

tens

ity(

arb.

)Ln1.85Ce0.15CuO4

Integrated Intensity from

-0.1 to EF

.0

.1

.2

.3

.4 NCCO SCCOECCO

SCCO

NCCO

Bin

ding

ene

rgy

(eV

)

0.00.10.20.3Binding Energy (eV)

Momentum ( (1/2,1/2) → (1,0) )

Tem. Dep. Spectral weight

kx (π/a)

k y(π

/a)

1-1

1FS, Tem.=10K

kx (π/a)

k y(π

/a)

1

1

-1

FS, Tem.=280K

A(k,w)/F.D.

105

95

10 30 80 130 180 230 280

Inte

nsit

y (a

rb.)

Temperature (K)

Integrated intensity from -0.1 to EF~1/correlation length(ξ)

Tem

pera

ture

(K)

Cerium concentration, x

100

200

300

400

500

00 0.5 1.0 1.5

ξ/a2

400

50

5

10

20

100200

Nd2-xCxCuO4

Intensity (arb. units)

0.00.10.20.3

10K80K130K180K230K280K

Previously also seen in NCCOH. Matsui et al., PRB (2007)

Doping dep. spectral weight

Sm2-xCexCuO4

0.00.10.20.3Binding Energy (eV)

0.10

0.15

0.18

Doping, temperature, rare earth dependences all show that:

1. Overall, gap size does not change much

2. Gap is filled up as AF ordering length

decreases

⇒Similar to pseudo-gap in hole doped & reminiscence of phase fluctuation.

Spin-fermion model

Coupling to spin excitations

χ”

U = 1.59 eV

ξ=4a

ξ=16

a

0.00.10.20.30.4

Binding Energy (eV)

0.00.10.20.3

Electron doped case

(0.5, 0.5)

Ene

rgy

(eV

)

0.1

0.3

0.0

0.2

Imχ(ω)

q=(0.5, 0.5)

FS Dispersion

Momentum

Wilson et al., PRL 96, 157001 (2006)

kx (p/a) 1

SCCO

0

k y(p

/a)

1

Optical conductivity

Experiment Simulation

σ1 (arb. unit)σ 1(Ω

-1 c

m-1

)

0

2

4

Photon Energy (eV)

x103

0.0

220K140K70K10K

300K

0.2 0.4 0.0 0.2 0.4

ξ=32aξ=16a

ξ=8a

ξ=4a

ξ=2a

AF phase fluctuation model

(“Yet another spin-fermion model”,A. Chubukov)

Subject to potential from AF order

mi = local magnetic momentSi = electron spinλ = coupling constant

<= AF phase fluctuation

with

and

Finally:

with∗ ξ = ordering length

AF phase fluctuation effect(averaging over different Q’s)

Γ (π,0)

(π,π)

Q0

∼1/ξ

Q0+δ

∼1/ξ

Γ (π,0)

(π,π)

Q0+δ

∼1/ξ

Γ (π,0)

(π,π)

Q0+δ

∼1/ξ

Γ (π,0

(π,π)

ξ~8a ξ~4a ξ~2aξ~16aξ~32a

0.0

0.1

0.2

0.3

0.4

1 2 1 2 1 2 1 2 1 2

1

2

1

2

1

2

1

2

1

2

Bind

ing

Ener

gy (e

V)

EF

0.1

0.2

0.3

0.4

0.50.4 0.6

c)

0.4 0.5 0.6

b)

cb

(π,π)

Γ

a

0.4 0.5 0.6

a)

Bind

ing

Ener

gy (e

V)

EF

0.1

0.2

0.3

0.4

a) b) c)

k parallel to (0,0)-(π,π) (1.41π/a)

Momentum

Sm1.85Ce0.15CuO4

Short Range Order(SRO) , ξ~4a Long Range order

Electron-AF SRO coupling

0.0

0.1

0.2

0.3

0.4Bind

ing

ener

gy (e

V)Momentum

Gap filling and EF weightBi

ndin

g En

ergy

(eV) EF

0.1

0.2

0.3

0.4Momentum Momentum Momentum Momentum Momentum

Fermi surfaceξ~8aξ~16aξ~32a ξ~4a ξ~2a

Binding Energy (eV)

A(k

,w)

Spectral weight near EF

ξ~32a, 16a

ξ~4aξ~2a

ξ~8aξ~16aξ~32a ξ~4a ξ~2a

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00

ξ~8a

Optical conductivity

Experiment Simulation

σ1 (arb. unit)σ 1(Ω

-1 c

m-1

)

0

2

4

Photon Energy (eV)

x103

0.0 0.2 0.4

ξ=32aξ=16aξ=8aξ=4aξ=2a

0.0

220K140K70K10K

300K

0.2 0.4

The model….

1. Not spin-boson but phase gradient ( φ) couples to electron.

2. Tc can be estimated based within the model.

3. The parameter λm can be obtained by fitting exp data.

Summary

1. Correlation between pseudo-gap behavior and AF ordering

2. Pseudo-gap does not close but fills up as AF ordering decreases

3. ARPES spectral function and optical conductivity are well explained within AF phase fluctuation model

Quasi-particle dynamics intopological insulator Bi2Se3

S. R. Park, W. S. Jung, Chul Kim, D. J. Song, C. Kim, S. Kimura, K. D. Lee and N. Hur

Importance

1. Long lifetime of surface metallic states due to helical spin structure

2. Protected surface metallic states• No Fermi surface instability

: TI

: normal

FS of surface state and spin structure

Γ

Dissipationless nano-device and spinstronics

Long lifetime?- ARPES studies

ARPES for lifetime measurement

22 ),(Im)),(Re(),(Im1),(

ωωεωω

πω

kkkkA

k Σ+Σ−−Σ

=

Spectral function

energy

AR

PES

inte

nsity

FWHM:2ImΣ ~ 1/τ

ARPES on TI “Bi2Se3”Crystal structure Surface states

Y. Xia et al., Nat. Phys. (2009)H. Zhang et al., Nat. Phys. (2009)

Bulk

Our ARPES data (15 K, 8eV P. E.)

Γ

Fermi surface

0.3

0.2

0.1

0.0

Bin

ding

ene

rgy

(eV

)

-0.1 0.0 0.1Momentum (Å-1)

Experimental Fermi level

K

H. Zhang et al., Nat. Phys. (2009)

• Transport measurements as a bulksensitive tool also report metallicbehavior

Bulk

Bulk

Time dependence

-0.1 0.0 0.1Momentum (Å-1)

-0.1 0.0 0.1 -0.1 0.0 0.1

0.3

0.2

0.1

0.0

Bin

ding

ene

rgy

(eV

)

0.4

0.5

8 eV 10 eV 17 eV

Momentum (Å-1)

0.3

0.2

0.1

0.0

Bin

ding

ene

rgy

(eV

)0.4

0.5

~ 0.1eV

Fresh surface 4 days later

Surface (electron) doping effect with time

8eV

10

15

17

19

21

0.2 0.1 0.0Binding energy (eV)

0.3-0.1 0.0 0.1Momentum (Å-1)

-0.1 0.0 0.1 -0.1 0.0 0.1

0.3

0.2

0.1

0.0

Bin

ding

ene

rgy

(eV

)

0.4

0.5

8 eV 10 eV 17 eV EDCs @Γ

• Bulk states taken with 8 eV are suppressed due to kz-selection rule.• B. E. of bulk conduction band (EBB) ~ 0.1eV

After 4days

After 4days

Photon energy dependence

Life time : kink in ImΣ at ~EBB

ImΣ

(meV

)

0.25 0.20 0.15 0.10 0.05

60

50

40

70

Binding energy (eV)

Fresh surface (EBB ~ 0.1 eV)

0.0

4 days later (EBB ~ 0.2 eV)

ImΣ

EF

EBB

e-h pair phonon impurity

Scattering channels

EF impurity

e

h

• Kink in ImΣ at around EBB is originated from scatteringdue to phonon or impurity

Surface electron lifetime

• Scattering to bulk states due to impurity is the mainscattering channel for TM states.

0.25 0.20 0.15 0.10 0.05Binding energy (eV)

0.0

60

50

40

30

20

10

0

ImΣ

(meV

)

total

e-h pairphonon + impurity

P. E. 8eV, 15KFresh surface

Mob

ile e

lect

rons

τ=40 fs

)(02.0)/(105)(1040 515 msmsl gm μυτ =⋅×⋅=×= −

. To appear in PRB(R)

Summary

Experimental observation• Kink in scattering rate at around bulk

conduction band bottom

Interpretation• Strong scattering between surface and

bulk electrons due to electron-phonon coupling or impurity near EF

• Carrier life time in TM states hardly affected by adsorbate created disorder potential