Hubbard Model Approach to X-ray Spectroscopy

Thesis (Ph.D.)--University of Washington, 2012We have implemented a Hubbard model based first-principles approach for real-space calculations of x-ray spectroscopy, which allows one to study excited state electronic structure of correlated systems. Theoretical understanding of many electronic features in d and f electron systems remains beyond the scope of conventional density functional theory (DFT). In this work our main effort is to go beyond the local density approximation (LDA) by incorporating the Hubbard model within the real-space multiple-scattering Green's function (RSGF) formalism. Historically, the first theoretical description of correlated systems was published by Sir Neville Mott and others in 1937. They realized that the insulating gap and antiferromagnetism in the transition metal oxides are mainly caused by the strong on-site Coulomb interaction of the localized unfilled <italic>3d<\italic> orbitals. Even with the recent progress of first principles methods (e.g. DFT) and model Hamiltonian approaches (e.g., Hubbard-Anderson model), the electronic description of many of these systems remains a non-trivial combination of both. X-ray absorption near edge spectra (XANES) and x-ray emission spectra (XES) are very powerful spectroscopic probes for many electronic features near Fermi energy (EF), which are caused by the on-site Coulomb interaction of localized electrons. In this work we focus on three different cases of many-body effects due to the interaction of localized d electrons. Here, for the first time, we have applied the Hubbard model in the real-space multiple scattering (RSGF) formalism for the calculation of x-ray spectra of Mott insulators (e.g., NiO and MnO). Secondly, we have implemented in our RSGF approach a doping dependent self-energy that was constructed from a single-band Hubbard model for the over doped high-T<sub>c<\sub> cuprate La<sub>2−x<\sub>Sr<sub>x<\sub>CuO<sub>4<\sub>. Finally our RSGF calculation of XANES is calculated with the spectral function from Lee and Hedin's charge transfer satellite model. For all these cases our calculated x-ray spectra yield reasonable agreement with experiment. The above work has been implemented as an extension into the FEFF9 code, and we have also included notes for the new and modified key features of this development. Aside from the x-ray spectroscopy of correlated systems, we also present our calculation of the ground state local electronic structure of DNA nucleotides on graphene, and the transmission currents through graphene nanopores. Our calculation and analysis provide theoretical guidelines for developing DNA sequencing techniques using scanning tunneling spectroscopy (STS) and nanopore experiment. Evolved as a secondary focus of this thesis, we have added an additional chapter discussing our calculation of DNA-graphene hybrids