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

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)

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

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

Electron Doped HTSC e e Phase Diagram

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!

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, 147003 (2001); 88, 257001 (2002). T. Sato, Science 291, 1517 (2001); H. Matsui PRL 94, 047005 (2005); H. Matsui PRL 95, 017003 (2005)

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

Sign change in RH Y. Dagan, PRL, 92, 167001 (2004)

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)

Fermi Surface Suppression kx 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, 87,147003 (2001)

Doping Dependence Binding Energy (eV) N. P. Armitage, PRL 88, 257001 (2002).

Assuming Q=(p,p) scattering channel Theory I Assuming Q=(p,p) scattering channel t-t’-t”-U(x) C. Kusko, PRB 66, 140513 (2002) Theory Exp

More Theories (Hubbard or t-J models) PHYSICAL REVIEW B 72, 054504 (2005) Many-body calculations produce similar results : FS reconstruction, shadow FS & band folding. AF ordering is assumed PHYSICAL REVIEW B 66, 140513(R) (2002) PHYSICAL REVIEW LETTERS 91,186407 (2003) PHYSICAL REVIEW LETTERS 93,147004 (2004)

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

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

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

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, 047005 (2005)

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

Movie (Graphite) E M  K ky kx

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

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

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?

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

Fitting the Exp Data within the Model EF 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

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

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, 047005). 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)

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

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)

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, 047005 (2005)

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, 92,167001 (2004) Suggest quantum critical point at a critical doping near 0.165

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