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

2. Contents Introduction Calculation method Results Discussion Summary
Material properties of La2-xSrxCuO4 (LSCO)
Purpose of my study
Calculation method
Local density approximation (LDA)
Self-Interaction Correction (SIC)
Results
Calculated electronic structure of LSCO
Stability of anti-ferromagnetic state
(The calculation code is MACHIKANEYAMA and the SIC program is developed by Toyoda.)
Discussion
Summary
Future work

3. Introduction La2CuO4 La Oz Oxy Cu Experiment Neel temperature TN
Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)
La2CuO4
AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic La
Experiment
Neel temperature TN
200～300 K
Local magnetic moment on Cu
0.3～0.5μB
Concentration x when the anti-ferromagnetism disappears.
x=0.02
Tc at the optimal doping
50 K
Concentration x at the optimal doping.
x=0.15 Oz
Oxy Cu

4. Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)
Introduction
Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)
La2CuO4
La2-xSrxCuO4
AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic
TN:200～300 K La
x=0.02
La2CuO4 is one of the transitional-metal oxides (TMO).
The electronic structure of the TMO is not well described by the band structure method based on the local density approximation (LDA)
The purpose of my study is to reproduce the magnetic phase diagram with the self-interaction correction (SIC) method in the first principle calculation. Oz
Oxy Cu

5. Kohn-Sham theory
We map a many body problem on one electron problem with effective potential.
Schrodinger equation
Kohn-Sham equation
veff(r) : effective potential
ψi(r) : wave function
ψi(r)
veff(r)
W. Kohn, L. J. Sham ; Phys. Rev. 140, A1133 (1965)

6. Local Density Approximation (LDA)
We do not know the μxc and 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.
External potential
Coulomb potential from electron density
effective potential
We call this “exchange correlation potential”.

7. 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.
...

8. Self-interaction correction (SIC)
External potential
Coulomb interaction between electrons
exchange correlation potential
effective potential
LDA
Self Coulomb interaction and self exchange correlation interaction don’t cancel each other perfectly.
We need self-interaction correction (SIC) .
J. P. Perdew, Alex Zunger; Phys. Rev. B23, 5048 (1981)
Alessio Filippetti and Nicola A. Spaldin; Phys. Rev. B67, (2003)

9. DOS of La2CuO4 by LDA and by SIC-LDA
LDA: non-magnetic and metallic.
SIC: anti-ferromagnetic and insulating:
local magnetic moment on Cu: 0.53 μB
band gap: about 0.8 eV
Exp: anti-ferromagnetic and insulating:
Cu local magnetic moment: 0.3 ～ 0.5 μB
band gap: about 0.9 eV
Cu 3d
O 2p
Cu 3d
anti-ferromagnetism with SIC-LDA
Cu 3d
O 2p
Cu 3d
Cu 3d
T. Takahashi et al ; Phys. Rev. B 37, 9788 (1988)

10. Type of the insulator of transition metal oxideUd
charge transfer insulator:
Ud > Δ
(La2CuO4) Δ
LH d state
p state
UH d state E Ud
Mott-Hubbard insulator:
Ud < Δ
LH d state
p state
UH d state E Δ

11. The experimental result Calculated by the SIC-LDA
LDA vs. SIC
For the La2CuO4
The experimental result
Calculated by the LDA
Calculated by the SIC-LDA
Magnetism
Anti-ferromagnetic
Nonmagnetic
(×)
(○)
Metal or insulator
Insulator
Metal
Local magnetic moment on Cu
0.3～0.5 μB
0.53 μB
position of Cu d state
About -8.0 eV
About -3.0 eV
About -7.0 eV
Band gap energy
About 0.9 eV
About 0.8 eV

12. The magnetic phase diagram
The stability of anti-ferromagnetic state
The energy difference between paramagnetic and anti-ferromagnetic state.
La2-xSrxCuO4
:Cu
The random system is calculated by Coherent Potential Approximation (CPA)
AFM ：anti-ferromagnetism, PM : paramagnetic, SG : spin glass, I : insulator, M : metal, N : normal conductivity, SC : superconductivity, T : tetragonal, O : orthorhombic
x=0.02
Warren E. Pickett ; Rev. Mod. Phys. 61, 433 (1989)

13. Stability of anti-ferromagnetic state
La2-xSrxCuO4
Experimental result of x
The anti-ferromagnetism becomes unstable by hole doping.

14. The doping dependence with Sr
anti-ferromagnetism (x=0)
anti-ferromagnetism (x=0.16)
Cu 3d
O 2p
Sr 5p
Cu 3d
O 2p
La2-xSrxCuO4
anti-ferromagnetism (x=0.06)
Holes are doped in O 2p state
→ Fermi level comes close to the valence band.
At x=0.16, the Fermi level comes into the valence band.
Sr 5p
Cu 3d
O 2p

15. Super exchange interactionEF
d state A E
A site
d state
anti-ferromagnetic A B
d state
B site E B
d state

16. p-d exchange interactionEF A B
d state
p state E
p state
d state
ferromagnetic.
The p-hole with up spin runs around in the crystal. EF
d state
p state E A B
p state
d state

17. Summary
The electronic structure is not reproduced by the LDA.
The anti-ferromagnetic state of La2CuO4 is well reproduced by the SIC method.
The trend of the stability of the anti-ferromagnetism has been reproduced by using the SIC method.
future work
I will estimate the Neel temperature with the Monte Carlo simulation.

18. Thank you for your attention.