Exchange and Correlation effects in the electronic properties of transition metal oxides: the example of NiO (thesis)

Contents 

1 Introduction 1
2 eoretical framework 5
2.1 e many-body electron problem . . . . . . . . . . . . . . . . . . 5
2.2 Density-Functional eory . . . . . . . . . . . . . . . . . . . . . 6
2.3 Green’s functions theory . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Lehmann’s representation and the spectral function . . . . 10
2.3.2 G’s equation of motion and the self-energy . . . . . . . . . 12
2.3.3 Hedin’s equations . . . . . . . . . . . . . . . . . . . . . . 13
2.3.4 e GW approximation . . . . . . . . . . . . . . . . . . . 16
2.3.5 Hartree-Fock self energy . . . . . . . . . . . . . . . . . . 17
2.3.6 Plasmon-pole model . . . . . . . . . . . . . . . . . . . . 18
2.3.7 COHSEX approximation for the self-energy . . . . . . . . 18
2.3.8 Self-energy beyond GW: vertex corrections . . . . . . . . 20
2.4 e concept of quasiparticle in photoemission . . . . . . . . . . . 21
3 Exchange and spin in NiO 23
3.1 NiO: a strongly-correlated material . . . . . . . . . . . . . . . . . 23
3.2 Lattice and magnetic structure . . . . . . . . . . . . . . . . . . . . 27
3.3 Pseudopotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 e Ground State . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5 A Hartree-Fock study of NiO . . . . . . . . . . . . . . . . . . . . 40
3.5.1 Paramagnetic phase . . . . . . . . . . . . . . . . . . . . . 40
3.5.2 Anti-ferromagnetic phase . . . . . . . . . . . . . . . . . . 41
4 GW study of NiO 43 4.1 Perturbative GW . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 Self-consistency and alternative approaches . . . . . . . . . . . . 45
4.2.1 Self-consistent COHSEX in practice . . . . . . . . . . . . 47
 4.2.2 Hybridization in COHSEX band structure: PDOS . . . . . 49
4.3 LDA vs COHSEX wavefunctions . . . . . . . . . . . . . . . . . . 5
4.4 GW on top of COHSEX . . . . . . . . . . . . . . . . . . . . . . . 57
4.5 Vertex corrections to the self-energy . . . . . . . . . . . . . . . . 59
5 Conclusion 61
A Special points in reciprocal space 65
Acknowledgements/Ringraziamenti 73

Bibliography 77


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