Two-dimensional (2D) topological insulators are a new class of materials with properties that are promising for potential future applications in quantum computers. For example, stanene represents a possible candidate for a topological insulator made of Sn atoms arranged in a hexagonal lattice. However, it has a relatively fragile low-energy spectrum and sensitive topology. Therefore, to experimentally realize stanene in the topologically non-trivial phase, a suitable substrate that accommodates stanene without compromising these topological properties must be found. A heterostructure consisting of a SiC substrate with a buffer layer of adsorbed group-III elements constitutes a possible solution for this problem. In this work, 2D adatom systems of Al and In were grown epitaxially on SiC(0001) and then investigated structurally and spectroscopically by scanning tunneling microscopy (STM) and photoelectron spectroscopy. Al films in the high coverage regime \( (\Theta_{ML}\approx2\) ML\( ) \) exhibit unusually large, triangular- and rectangular-shaped surface unit cells. Here, the low-energy electron diffraction (LEED) pattern is brought into accordance with the surface topography derived from STM. Another Al reconstruction, the quasi-one-dimensional (1D) Al phase, exhibits a striped surface corrugation, which could be the result of the strain imprinted by the overlayer-substrate lattice mismatch. It is suggested that Al atoms in different surface areas can occupy hexagonal close-packed and face-centered cubic lattice sites, respectively, which in turn lead to close-packed transition regions forming the stripe-like corrugations. On the basis of the well-known herringbone reconstruction from Au(111), a first structural model is proposed, which fits well to the structural data from STM. Ultimately, however, thermal treatments of the sample could not generate lower coverage phases, i.e. in particular, a buffer layer structure. Strong metallic signatures are found for In high coverage films \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) by scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES), which form a \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \) surface reconstruction. In all these In phases electrons follow the nearly-free electron model. Similar to the Al films, thermal treatments could not obtain the buffer layer system. Surprisingly, in the course of this investigation a triangular In lattice featuring a \( (1\times1) \) periodicity is observed to host massive Dirac-like bands at \( K/K^{\prime} \) in ARPES. Based on this strong electronic similarity with graphene at the Brillouin zone boundary, this new structure is referred to as \textit{indenene}. An extensive theoretical analysis uncovers the emergence of an electronic honeycomb network based on triangularly arranged In \textit{p} orbitals. Due to strong atomic spin-orbit coupling and a comparably small substrate-induced in-plane inversion symmetry breaking this material system is rendered topologically non-trivial. In indenene, the topology is intimately linked to a bulk observable, i.e., the energy-dependent charge accumulation sequence within the surface unit cell, which is experimentally exploited in STS to confirm the non-trivial topological character. The band gap at \( K/K^{\prime} \), a signature of massive Dirac fermions, is estimated by ARPES to approximately 125 meV. Further investigations by X-ray standing wave, STM, and LEED confirm the structural properties of indenene. Thus, this thesis presents the growth and characterization of the novel quantum spin Hall insulator material indenene.

Schon heute bilden Einzelphotonenquellen einen wichtigen Baustein in der Photonik und Quanteninformation. Der Fokus der Forschung liegt entsprechend auf dem Finden und Charakterisieren dafür geeigneter Materialsysteme. Konkret beschäftigt sich die vorliegende Arbeit vorwiegend mit dem Übergangsmetall-Dichalkogenid (TMDC1 ) Wolframdiselenid und seinen Eigenschaften. Diese Wahl ist durch den direkte Zugang zu Einzelphotonenquellen begründet, die sich in dessen Monolagen ausbilden können. Diese Lichtquellen können über eine Modulation der Verspannung der Monolage gezielt aktiviert werden. Durch die, verglichen mit ihrem Volumen, riesige Kontaktfläche lassen sich Monolagen zudem mit Hilfe des Substrats, auf das sie transferiert wurden, wesentlich beeinflussen. Im Rahmen dieser Arbeit wurden Monolagen von WSe2 in unterschiedlichen Bauteilen wie zirkulare Bragg-Gittern oder vorstrukturierten, metallischen Oberflächen implementiert und die Photolumineszenz des TMDCs untersucht. Diese Arbeit belegt die Möglichkeit, Einzelphotonenquellen basierend aufWSe2 -Monolagen auf verschiedenste Weise modulieren zu können. Dank ihrer zwei- dimensionalen Geometrie lassen sie sich einfach in bestehende Strukturen integrieren oder auch in der Zukunft mit weiteren 2D-Materialien kombinieren.

Ratios of top-quark pair to \(Z\)-boson cross sections measured from proton-proton collisions at the LHC centre-of-mass energies of \(\sqrt{s}\) = 13 TeV, 8 TeV, and 7 TeV are presented by the ATLAS Collaboration. Single ratios, at a given \(\sqrt{s}\) for the two processes and at different \(\sqrt{s}\) for each process, as well as double ratios of the two processes at different \(\sqrt{s}\), are evaluated. The ratios are constructed using previously published ATLAS measurements of the \({t\overline{t}}\) and \(Z\)-boson production cross sections, corrected to a common phase space where required, and a new analysis of \(Z\) → ℓ\(^+\)ℓ\(^-\) where ℓ = \(e, µ\) at \(\sqrt{s}\) = 13 TeV performed with data collected in 2015 with an integrated luminosity of 3.2 fb\(^−1\). Correlations of systematic uncertainties are taken into account when evaluating the uncertainties in the ratios. The correlation model is also used to evaluate the combined cross section of the \(Z\) → \(e\)\(^+\)\(e\)\(^−\) and the \(Z\) → \(µ\)\(^+\)\(µ\)\(^−\) channels for each \(\sqrt{s}\) value. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data demonstrate significant power to constrain the gluon distribution function for the Bjorken-\(x\) values near 0.1 and the light-quark sea for \(x\) < 0.02.

In this thesis, I study entanglement in quantum field theory, using methods from operator algebra theory. More precisely, the thesis covers original research on the entanglement properties of the free fermionic field. After giving a pedagogical introduction to algebraic methods in quantum field theory, as well as the modular theory of Tomita-Takesaki and its relation to entanglement, I present a coherent framework that allows to solve Tomita-Takesaki theory for free fermionic fields in any number of dimensions. Subsequently, I use the derived machinery on the free massless fermion in two dimensions, where the formulae can be evaluated analytically. In particular, this entails the derivation of the resolvent of restrictions of the propagator, by means of solving singular integral equations. In this way, I derive the modular flow, modular Hamiltonian, modular correlation function, R\'enyi entanglement entropy, von-Neumann entanglement entropy, relative entanglement entropy, and mutual information for multi-component regions. All of this is done for the vacuum and thermal states, both on the infinite line and the circle with (anti-)periodic boundary conditions. Some of these results confirm previous results from the literature, such as the modular Hamiltonian and entanglement entropy in the vacuum state. The non-universal solutions for modular flow, modular correlation function, and R\'enyi entropy, however are new, in particular at finite temperature on the circle. Additionally, I show how boundaries of spacetime affect entanglement, as well as how one can define relative (entanglement) entropy and mutual information in theories with superselection rules. The findings regarding modular flow in multi-component regions can be summarised as follows: In the non-degenerate vacuum state, modular flow is multi-local, in the sense that it mixes the field operators along multiple trajectories, with one trajectory per component. This was already known from previous literature but is presented here in a more explicit form. In particular, I present the exact solution for the dynamics of the mixing process. What was not previously known at all, is that the modular flow of the thermal state on the circle is infinitely multi-local even for a connected region, in the sense that it mixes the field along an infinite, discretely distributed set, of trajectories. In the limit of high temperatures, all trajectories but the local one are pushed towards the boundary of the region, where their amplitude is damped exponentially, leaving only the local result. At low temperatures, on the other hand, these trajectories distribute densely in the region to either---for anti-periodic boundary conditions---cancel, or---for periodic boundary conditions---recover the non-local contribution due to the degenerate vacuum state. Proceeding to spacetimes with boundaries, I show explicitly how the presence of a boundary implies entanglement between the two components of the Dirac spinor. By computing the mutual information between the components inside a connected region, I show quantitatively that this entanglement decreases as an inverse square law at large distances from the boundary. In addition, full conformal symmetry (which is explicitly broken due to the presence of a boundary) is recovered from the exact solution for modular flow, far away from the boundary. As far as I know, all of these results are new, although related results were published by another group during the final stage of this thesis. Finally, regarding relative entanglement entropy in theories with superselection sectors, I introduce charge and flux resolved relative entropies, which are novel measures for the distinguishability of states, incorporating a charge operator, central to the algebra of observables. While charge resolved relative entropy has the interpretation of being a ``distinguishability per charge sector'', I argue that it is physically meaningless without placing a cutoff, due to infinite short-distance entanglement. Flux resolved relative entropy, on the other hand, overcomes this problem by inserting an Aharonov-Bohm flux and thus passing to a variant of the grand canonical ensemble. It takes a well defined value, even without putting a cutoff, and I compute its value between various states of the free massless fermion on the line, the charge operator being the total fermion number.

A measurement of the \({t\overline{t}}Z\) and \({t\overline{t}}W\) production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton–proton collisions at \(\sqrt{s}\) = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb\(^{−1}\). The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in \(\sigma_{{t\overline{t}}Z}\) = 0.9 ± 0.3 pb and \(\sigma_{{t\overline{t}}W}\) = 1.5 ± 0.8 pb, in agreement with the Standard Model predictions.