Georg Keller
Realistic Modeling of Strongly Correlated Electron Systems
Supervisor: Prof. Dr. Dieter Vollhardt [Theoretical physics III]
Date of oral examination: 06/10/2005
146 pages, english
The physics of materials with strongly correlated electrons is one of the most exciting topics of present-day theoretical and experimental solid-state research. A wide variety of interesting phenomena can be attributed to electronic correlations, among them metal-insulator transitions, the giant and colossal magnetoresistance effect and heavy-fermion behavior. One focus of experimental research is on transition metals and especially transition metal oxides. The electronic structure of such materials is mainly determined by the partially filled d-orbitals, which have only a small direct overlap. Furthermore, the crystal field splitting of the five d-orbitals due to the influence of the neighboring (oxygen) atoms, which is often of the same magnitude as the bandwidth, plays an important role for the physical properties of this class of systems.

A novel approach that was developed in the last few years and has already lead to impressive results is the LDA+DMFT method. It combines the advantages of the local density approximation (LDA), which provides a realistic ab initio description for many materials, with the correct treatment of the local correlations within dynamical mean-field theory (DMFT). A robust and numerically exact impurity solver for the effective quantum impurity problem encountered in DMFT is the quantum Monte Carlo (QMC) algorithm. It can be applied to multi-orbital systems like transition metal oxides with five 3d-orbitals or rare earth materials with seven 4f-orbitals for not too low temperatures. Thus, the LDA+DMFT method makes it possible for the first time to perform parameter-free, ab initio calculations for strongly correlated materials, and it gives new insight into long-debated problems like the metal-insulator transition in V2O3.

The main topic of this thesis is the investigation of strongly correlated transition metal oxide systems with the LDA+DMFT approach, where the self-consistent equations of the DMFT are solved with an auxiliary-field quantum Monte Carlo algorithm. In particular, the metallic and insulating phase of V2O3 and the peculiarities of its metal-insulator transition are explored. Furthermore, the strongly correlated metals SrVO3 and CaVO3 are studied, as well as LiV2O4, the first d-electron system that was found to exhibit heavy-fermion behavior. Where possible, the theoretical results are compared with recent experimental data.