Yoshida Lab M1 Y oshitaka Mino

1. Electronic structure of La2-xSrxCuO4 calculated by self-interaction correction method Yoshida Lab M1 Yoshitaka Mino

2. Contents • Computational Materials Design • First-principles calculation • Local Density Approximation (LDA) • Self-Interaction Correction (SIC) • Previous study and my work • Summary

3. Computational Materials Design • Calculation & Simulation • Experiments • New ideas • Physical properties

4. First-principles calculation • Predict physical properties of materials ← Input parameters: Atomic Number and Atomic position ! • Advantage • Low costs • Extreme conditions • Ideal environment • … ・・・

5. Kohn-Sham theory We map a many body problem on one electron problem with effective potential. Kohn-Sham equation ψi(r) v(r)

6. Local Density Approximation (LDA) • We do not know the Exc and μxcand we need approximate expressions of them to perform electronic structure calculations. • For a realistic approximation, we refer homogeneous electron gas. Local Density Approximation (LDA) When the electron density changes in the space, we assume that the change is moderate and the electron density is locally homogeneous. Exchange correlation energy Exchange correlation energy of homogeneous electron gas with the density at that position.

7. Success of LDA • For almost of all materials, the LDA can describe electronic structures reasonably ! Calculated atomic volume (lattice constant) as a function of atomic number. Etotal Emin 笠井英明，赤井久純，吉田博　編 ; 「計算機マテリアルデザイン」（大阪大学出版会） r (lattice constant) a O

8. Systematic error of LDA LDA has some errors in predicting material properties. • Underestimation of lattice constant. • Overestimation of cohesion energy. • Overestimation of bulk modulus. • Underestimation of band gap energy. • Predicting occupied localize states (d states) at too high energy. • ...

9. Problem in LDA The picture on the left shows the distribution of exchange hole at distance R from an electron which is located at r from the Ne nucleus. The exchange hole is distributed around the electron in the LDA.But in reality, the exchange hole is distributed around the nucleus. +e electron -e electron -e r nuclear r nuclear +e J.P. Perdew, A. Zunger; Phys. Rev. B23 5048 (1981) exact LDA

10. Problem in LDA Exp. Zn d Calc. Zn d Exp. Zn d A. Filippetti, N.A. Spaldim ; Phys. Rev. B67, 125190 (2003) W. Gopel et al. : Phys. Rev. B26 3144 (1982) Band gap energy and the binding energy of Zn d state calculated by the LDA are much smaller than the experimental values. The calculated results by the LDA don’t reproduce the experimental results. band gap LDA : 0.9 eV Exp. : 3.2 eV

11. Self-interaction correction(SIC) Coulomb interaction between electrons. exchange correlation energy LDA Self Coulomb interaction and self exchange correlation interaction don’t cancel each other perfectly. We need self-interaction correction (SIC) !

12. Improvement by SIC The picture on the left shows the distribution of exchange hole located at R from an electron located at r from the nuclearabout Ne. The SIC can reproduce exact solution reasonably. electron electron -e -e r r nuclear nuclear +e +e exact SIC J.P. Perdew, A. Zunger; Phys. Rev. B23 5048 (1981)

13. Improvement by SIC A. Filippetti, N.A. Spaldim ; Phys. Rev. B67, 125190 (2003) A. Filippetti, N.A. Spaldim ; Phys. Rev. B67, 125190 (2003) Calc. Zn d Exp. Zn d Calc. Zn d Exp. Zn d band gap LDA : 0.9 eV SIC : 3.5 eV Exp. : 3.2 eV Exp. Zn d The result calculated by self-interaction correction (SIC) reproduces the experimental result of band gap and Zn d-state by photoemission spectroscopy much better than that of LDA. W. Gopel et al. : Phys. Rev. B26 3144 (1982)

14. previous study and my work The pictures on the right is the phase diagram and crystal structure of La2-xMxCuO4 which is produced experiments. La2CuO4 AFM ：antiferromagnetism, PM : paramagnetism, SG : spin glass, I : insulator,M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

15. Previous study and my work calculated results The LDA predicts nonmagnetic and metallic ground state for La2CuO4. metal … Not corresponding … Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989) experimental results Experimentally, La2CuO4 is antiferromagnetic and insulating. The local magnetic moment is from 0.3 to 0.5 μB. I will reproduce the phase diagram of La2CuO4 from first-principles, particularly AFM and insulating region, by introducing SIC.

16. Summary • We can calculate electronic structures of many materials from first-principles owing to the success of the local density approximation (LDA) • In general, the LDA is reasonable approximation for the exchange correlation potential. • The LDA results sometimes fails to reproduce experimental results, in particular when the system has moderately localized states due to the self-interaction. • So we introduce self-interaction correction (SIC) and the correction improve calculated results. • I will apply the SIC-LDA method to La2CuO4-based systems.

17. The end . . . thank you for your attention.