Electronic Structure of Novel Two-dimensional Materials and Graphene Heterostructures

Today a well-equipped library of two-dimensional materials can be synthesized or exfoliated, ranging from insulating hexagonal boron nitride, to semi-metallic graphene, and metallic as well as superconducting transition metal dichalcogenides and many others. Due to strong intra-layer covalent bondings, but weak inter-layer Van-der-Waals interactions, these layered materials can be stacked in a Lego-like fashion to artificial heterostructures which do not occur in nature. Thereby, these novel systems offer the possibility to combine specific properties of each of its constituents to tailor the heterostructure's properties on demand which might allow for completely new device classes. In fact, these kind of systems are already constructed and studied in labs around the world. In order to guide these efforts, we need an in-depth understanding of these complex heterostructures starting with its smallest components, namely the different two-dimensional materials and their mutual interactions. To this end, we study electronic and optical properties of novel two-dimensional materials in this thesis. In more detail, we here aim to investigate functionalized graphene, graphene heterostructures and doped or optically excited molybdenum disulfide (MoS$_2$) monolayers for which we combine \abinitio based models with many-body or multi-scale approaches. The first part is devoted to functionalized graphene and is subdivided into the investigation of disorder-induced optical effects of fluorographene and into a detailed study of the Coulomb interaction in graphene heterostructures in form of multilayer graphene, intercalated graphite and few-layer graphene within a dielectric environment. In the case of fluorographene we use a multi-scale approach to study the effects of realistic disorder patterns to the optical conductivity. Thereby, we provide important insights into the role of non-perfect fluorination of graphene. Regarding the graphene heterostructures we present a novel approach to easily and reliably derive Coulomb-interaction matrix elements in these structures. This method is used to study the robustness of bilayer graphene's ground state to changes in its dielectric surrounding. In the second part of the thesis we study a variety of many-body effects that arise in doped and optically excited MoS$_2$ monolayers. Once again, by deriving simplified yet accurate models from first-principles we are able to investigate many-body excitations like plasmons or excitons as well as many-body instabilities like superconductivity or charge-density wave phases. Regarding the latter, we are able to extend the electron-doping phase diagram of MoS$_2$ by the formation of a charge-density-wave phase and reveal its potential coexistence with the superconducting state. In the field of many-body excitations we study in detail excitonic line shifts upon optical excitations and we precisely describe different types of plasmonic excitations under electron or hole doping in MoS$_2$. Finally, we make use of the fundamental properties of the many-body interactions in layered materials in order to externally induce heterojunctions within homogeneous semiconducting monolayers by non-local manipulations of the Coulomb interaction

Coulomb-Engineered Heterojunctions and Dynamical Screening in Transition Metal Dichalcogenide Monolayers

The manipulation of two-dimensional materials via their dielectric environment offers novel opportunities to control electronic as well as optical properties and allows to imprint nanostructures in a non-invasive way. Here we asses the potential of monolayer semiconducting transition metal dichalcogenides (TMDCs) for Coulomb engineering in a material realistic and quantitative manner. We compare the response of different TMDC materials to modifications of their dielectric surrounding, analyze effects of dynamic substrate screening, i.e. frequency dependencies in the dielectric functions, and discuss inherent length scales of Coulomb-engineered heterojunctions. We find symmetric and rigid-shift-like quasi-particle band-gap modulations for both, instantaneous and dynamic substrate screening. From this we derive short-ranged self energies for an effective multi-scale modeling of Coulomb engineered heterojunctions composed of an homogeneous monolayer placed on a spatially structured substrate. For these heterojunctions, we show that band gap modulations on the length scale of a few lattice constants are possible rendering external limitations of the substrate structuring more important than internal effects. We find that all semiconducting TMDCs are similarly well suited for these external and non-invasive modifications.Comment: 10 pages, 7 figure

Dynamical correlations in single-layer CrI3_3

Chromium triiodide is a magnetic van-der-Waals material with weak inter-layer interactions. It is one of the first materials for which intrinsic magnetism was observed down to the single-layer limit. This remarkable discovery fostered a whole new field of 2D magnetism and magnetic layered heterostructure research holding high promisses for spintronic applications. First-principles electronic structure calculations have an outstanding role in this field not only to describe the properties of existing 2D magnets, but also to predict new materials, and thus to guide the experimental progress. So far the most 2D magnet studies are based on standard density functional theory (DFT), which poorly addresses the effects of strong electron correlations. Here, we provide a first-principles description of finite-temperature magnetic and spectral properties of monolayer CrI$_3$ based on fully charge self-consistent DFT combined with dynamical mean field theory (DFT+DMFT), revealing a formation of local moments on Cr from strong local Coulomb interactions. We show that local dynamical correlations play an important role in the electronic structure of CrI$_3$. In contrast to conventional DFT+$U$ calculations, we find that the top of the valence band in monolayer CrI$_3$ demonstrates essentially different orbital character for minority and majority spin states. This results in a strong spin-polarization of the optical conductivity upon hole doping, which could be verified experimentally.Comment: 13 pages, 4 figure

Charge transfer-induced Lifshitz transition and magnetic symmetry breaking in ultrathin CrSBr crystals

Ultrathin CrSBr flakes are exfoliated \emph{in situ} on Au(111) and Ag(111) and their electronic structure is studied by angle-resolved photoemission spectroscopy. The thin flakes' electronic properties are drastically different from those of the bulk material and also substrate-dependent. For both substrates, a strong charge transfer to the flakes is observed, partly populating the conduction band and giving rise to a highly anisotropic Fermi contour with an Ohmic contact to the substrate. The fundamental CrSBr band gap is strongly renormalized compared to the bulk. The charge transfer to the CrSBr flake is substantially larger for Ag(111) than for Au(111), but a rigid energy shift of the chemical potential is insufficient to describe the observed band structure modifications. In particular, the Fermi contour shows a Lifshitz transition, the fundamental band gap undergoes a transition from direct on Au(111) to indirect on Ag(111) and a doping-induced symmetry breaking between the intra-layer Cr magnetic moments further modifies the band structure. Electronic structure calculations can account for non-rigid Lifshitz-type band structure changes in thin CrSBr as a function of doping and strain. In contrast to undoped bulk band structure calculations that require self-consistent $GW$ theory, the doped thin film properties are well-approximated by density functional theory if local Coulomb interactions are taken into account on the mean-field level and the charge transfer is considered

Downfolding from Ab Initio to Interacting Model Hamiltonians: Comprehensive Analysis and Benchmarking

Model Hamiltonians are regularly derived from first-principles data to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare standard downfolding techniques with the best-possible ground-truth estimates for charge-neutral excited state energies and charge densities using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double counting correction diminishes the quality. Background screening to the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.Comment: 15 pages (+8 pages Supplemental Material), 8 figure