Realistic Multi-Orbital Systems - Correlated Adatoms on Surfaces

Abstract

The most widely used experimental techniques in surface science, scanning tunnelling microscopy and spectroscopy, have attained at a degree of sophistication, that their findings demand the development of new theoretical approaches for their explanation. Nowadays the experimental precision allows for a detailed resolution of the physical and chemical composition of surfaces as well as of their spectral properties. While simplified models provide a first qualitative understanding of physical effects, the experimental resolution of orbital and spectral substructures call for a realistic theoretical representation of the physical systems under consideration and for a numerically exact solution of the associated models. The present thesis develops a combination of \textit{ab initio} density functional theory and the many-body Anderson impurity model to represent correlated adatoms, molecules, and nanosystems on substrate surfaces, and embeds both approaches and their combination into a wider theoretical and physics science context as well as into the current state of research. The development of the \textit{ab initio} many-body model and the numerical approach for its solution will be drawn around their application on three particular surface systems, of which two of them have been experimentally investigated beforehand.

The tantalum oxide surface Ta(001)-p(3$\times$3)-O is currently under consideration as regards the Kondo effect on superconducting surfaces, which result in the so-called Yu-Shiba-Rusinov states, and the geometric and quantum-chemical complexity of the substrate surface allows for the interplay of adsorbates at various locations, each being in a different Kondo state. The present thesis examines the Ta(001)-p(3$\times$3)-O surface by means of density functional theory, and identifies its electronic and quantum-chemical structure as well as its spectral properties. As its relevant adsorption mechanisms for single and several atoms is to date not well understood, the density functional analysis is extended as to account for van der Waals interactions, which have been observed to be important for the stability and for specific arrangements of adsorbates on several surfaces.

Due to the two-dimensional geometry of surface systems, symmetry breaking not only leads to a pronounced crystal field splitting and directionally dependent hybridization of adatom orbitals, but also leads to an anisotropic Coulomb interaction matrix. These become more important in pseudo-gapped substrates because the reduced density of states at the Fermi level renders the local interactions on the adatom dominating the low-energy physics. The present thesis considers Co adatoms on graphene and numerically solves the corresponding \textit{ab initio} Anderson impurity model by means of continuous-time quantum Monte Carlo and the recently developed stochastic optimization method. The Coulomb interaction anisotropy is determined within the constrained random phase approximation, which shows that also on pseudo-gapped substrates the local interactions may be not much stronger than the hybridization. Yet, their prevalence can be observed from the low-energy region of the self-energy, which reveals a restructuring of its orbital contributions due to symmetry breaking.

The system of a Co adatom on Cu(111) provides a benchmark for the multi-orbital Kondo effect of transition metal atoms on metallic surfaces. The spectral signature is a resonance feature at the Fermi level with a width determined by the Kondo temperature, which marks the middle of the cross-over scale of the effect and can be extracted either theoretically from numerical solutions, or experimentally by fitting with Fano or Frota lines. In multi-orbital systems the Kondo state is the result of a complicated superposition of spin and orbital contributions. Placing the Co adatom next to a symmetry-breaking Cu chain, additional crystal field splittings and hybridization anisotropies appear, which lead to a modified differential conductance spectrum. The present thesis analyses three specific CoCu$_n$/Cu(111) systems by means of solving their corresponding Anderson impurity models and of further deriving \textit{ab initio} differential conductance spectra, which can be directly compared to experimental results. The analysis not only leads to a quantitative agreement between theory and experiment, but can also identify the multi-orbital Kondo scenarios and extract Kondo temperatures, which was not possible by fitting to experimental data or within simplified single-orbital descriptions.