1. Dept. of Physics, Yonsei U
Electronic Structure of Electron Doped Superconductor Sm1.85Ce0.15CuO4: Quantitative Analysis Based on (p,p) Scattering Model
Chang Young Kim
Dept. of Physics, Yonsei U

2. Work done by… ARPES S. Park, H.S. Jin, C.S. Leem (Yonsei)
Peter Armitage (Geneva)
B.J. Kim (SNU)
H. Koh, Eli Rotenberg (ALS)
Donghui Lu (SSRL)
Sample
Hiroshi Eisaki (AIST)

3. Outline Past work Interpretation in (p,p) scattering model
New data and further understanding
Summary

4. Angle Resolved Photoemission Spectroscopy (ARPES)hv e - q Z X Y f
Detector
Electron Analyzer
EDCs at different angles
Photoelectron kinetic energy is measured
Emission angle of photo electron is measured
Energy and emission angle are transformed into
momentum
Angle (Momentum) Resolved PES

5. Electron Doped HTSC e e
Phase Diagram

6. Hole- vs Electron-doped (Structure)
Cu2+
Cu2+
La3+/Sr2+
Nd3+/Ce4+
O2-
O2-
O2- (Apical)
O2-
(La,Sr)
CuO
(Nd,Ce)
CuO 2 4 2 4
No apical oxygens!

7. ARPES on Electron Doped HTSC
Binding Energy (eV)
-0.8
-0.4
0.4
First ARPES work:
J. Allen et al. , PRL 70, 3155 (1993); D. M. King et al. , PRL 70, 3159 (1993).
(On low quality of the samples grown by flux method)
8 year gap!
Recent ARPES work:
N. P. Armitage, PRL 86, 1126 (2001); 87,
(2001); 88, (2002).
T. Sato, Science 291, 1517 (2001); H. Matsui
PRL 94, (2005); H. Matsui PRL 95,
(2005)

8. Fermi liquid? Pr2-xCexCuO4 thin film ARPES P. Fournier et. al.
* For hole-doped: rab ~ T ~ T2 depending on doping
P. Fournier et. al.

9. Sign change in RH
Y. Dagan, PRL, 92, (2004)

10. Main Valence Band hv = 16.5 eV T = 10 K Intensity (Arb. Unit)
0.6
0.4
0.2
0.0
Nd2-xCexCuO4 7 6 5 4 3 2 1
Binding
Energy (eV)

11. Fermi Surface Suppressionkx
FS suppression at the intersection of AF Billiouin Zone Boundary (AFBZ) with the underlying FS
Coupling to a bosonic mode localized at Q=(p,p)?
If it is due to low energy Q=(p,p) bosonic mode, suppression is expected to exist on at the Fermi energy. ky
Binding energy(eV)
N. P. Armitage, PRL, 87, (2001)

12. Doping Dependence Binding Energy (eV)
N. P. Armitage, PRL 88, (2002).

13. Assuming Q=(p,p) scattering channel
Theory I
Assuming Q=(p,p) scattering channel
t-t’-t”-U(x)
C. Kusko, PRB 66, (2002)
Theory
Exp

14. More Theories (Hubbard or t-J models)
PHYSICAL REVIEW B 72, (2005)
Many-body calculations produce similar results : FS reconstruction, shadow FS & band folding.
AF ordering is assumed
PHYSICAL REVIEW B 66, (R) (2002)
PHYSICAL REVIEW LETTERS 91, (2003)
PHYSICAL REVIEW LETTERS 93, (2004)

15. <Degenerate perturbation theory>
Effect of Ordering
<Degenerate perturbation theory>
New Bragg plane

16. ordering - (p, p) scattering
Fig. 1
(p,p)
With a static ordering.
FS (Fig 1).
Band structure along the blue arrow in Fig 1 (Fig 2).
Q=(p,p) G
(p,0)
Fermi surface
Fig.2 EF
AFBZ
Band Structure

17. New Band Structure Reconstructed FS (Fig 1).
No electronic states at the Fermi energy where FS intersects the AFBZ.
Band structure along the cut (a) in Fig 1 (Fig 2).
Band structure along the cut (b) in Fig 1 (along the AFBZ, Fig 3).
* Constant energy split (2Vpp)
(a)
Q=(p,p)
(b)
Fig. 2
Fig. 3 EF EF
2Vp,p
2Vp,p
AFBZ

18. Interpretation of Recent NCCO (x=0.13)
Binding energy(eV)
0.1
0.2
0.3
FS suppression and band splitting – Assigned to AF spin correlation
Difficult to understand band structures near (p.0) in the model
No quantitative analysis.
H. Matsui, PRL, 94, (2005)

19. Going to ALS ALS BL7 Sample : SCCO (Tc=13K) Sample preparation : FZ
in situ cleaving
Analyzer: Scienta 100
Temperature : 40 K
Total Energy Resolution: 40 meV
Angular Resolution: 0.25O
Photon energy : 85eV
Pass energy : 20eV
Manipulator: 6 axis motion,
completely Motorized
Automated data acquisition
ALS BL7

20. Movie (Graphite) E M  K ky kx

21. New Results from Sm1.85Ce0.15CuO4
0.0
1.0
0.5
1.5 1
0.0
1.0
0.5
1.5 ky G2 G -2 -1
kx (Å-1)
~1 eV total dispersion

22. Violation of Luttinger Theorem?
x=0.15
2*shaded/square=1.073
0.073 more than half filled
which is less than the doping
1.5
1.0
0.5
0.0 ky
-1.5
-1.0
-0.5 kx
2*(shaded+2*little square)/square=1.20 which is larger than 1.15

23. Two Component Interpretation?
this exists only near (p,0)
Fermi Arc from Na-CCOC
(hole-doped)
F. Ronning et al.,
(p,p)
(0,p) G
(p,0)
This never reaches EF near (p,0).
Signature of AF fluctuation?

24. Other Possibilities? - unreduced - hn=85eV - reduced - hn=85eV
FS suppression is a universal character of the electron doped HTSCs.

25. Fitting the Exp Data within the ModelEF
Along the AFBZ
2Vp,p E EF
200
400
2Vpp
300
100
Binding Energy (meV)`
(p/2,p/2)
(p,0)
(p,p) G
2Vp,p= 0.2eV ky kx

26. FS reconstruction & FS volume
Fig. 1
Yellow dashed lines near the (p,0) points are reconstructed FS segments.
Fig 2 illustrates measurements of the filling factor.
Filling factor for the original FS is about 1.07, but filling factor within the (p,p) scattering model is about 1.13.
We observe an energy gap of ~10 meV at (p/2,p/2). This will be discussed later. G
G ’
(p,p)
(p,0) 1
Fig. 2 2 G
(p,p)
Q=(p,p)
Fig. 3
(p,0.3p)
Binding Energy (meV)`
Intensity (arb. Units)
(p/2,p/2)
500
400
300
200
100 EF

27. High Resolution Data Faint shadow FS (red arrow in Fig 1)
(0,0)
(p,p)
Faint shadow FS (red arrow in Fig 1)
Also visible in the published data from NCCO (PRL 94, ).
E vs k plot along the white arrow in Fig 1, along the AFBZ.
Splitting of ~200 meV, consistent with high photon energy data from ALS
Fig. 2 EF
200
400
2Vpp
300
100
Binding Energy (meV)`
(p/2,p/2)
(p,0)

28. Band Folding and Gap at the (p,p) Crossing
Fig. 1 EF
200
400
Intensity (arb. Units)
Binding Energy (meV)
Fig. 2 EF
100
200
300
500
400
(0,0)
(p,p)
Binding Energy (meV)
(p,p)
(0,0)
Fig. 3
(p,p) cut.
Kink-like feature at about 50 meV.
Band folding
Gap due to band folding
(p,0.3p)
Binding Energy (meV)`
Intensity (arb. Units)
(p/2,p/2)
500
400
300
200
100 EF

29. Problems with the model : band structure near (p,0)
Fig. 1 EF
200
400
Binding Energy (meV) 32
Band splitting energy decreases as we approach the original Brilliouin zone boundary.
This was interpreted as anisotropic spin correlation gap in an earlier work (PRL94,047005).
Band folding is not centered at the AFBZ contrary to what anisotropic spin correlation gap would predict. Therefore, anisotropic gap interpretation can not be right.
AFBZ
AFBZ
AFBZ
Fig. 2
(0,0)
(p,p)

30. Interpretation of Recent NCCO (x=0.13)
Binding energy(eV)
0.1
0.2
0.3
FS suppression and band splitting : AF spin correlation
Hard to understand band structures near (p.0)
H. Matsui, PRL, 94, (2005)

31. Hall Measurements 1 Y. Dagan, PRL, 92,167001 (2004)
Pr2-xCexCuO4 G
G ’
(p,p)
(p,0) 1
Electron pocket
Increasing doping, reducing FS suppression
Y. Dagan, PRL, 92, (2004)
Suggest quantum critical point at a critical doping near 0.165

32. Summary Comprehensive analysis based on (p,p) scattering model
Band splitting due to (p,p) scattering appears to be robust.
Vpp = ~100 meV (no momentum dependent scattering needed)
Doping and temperature dependence should clarify the issue