Green Functions Approach to Graphene Nanostructures

Due to their fascinating optoelectronic properties, finite graphene nanostructures are expected to find use in a number of technological applications, ranging from field effect transistors and solar cells to quantum computers and even biomedical treatments. However, despite their small size, these systems can contain several hundred to thousands of electrons, unfortunately, making their theoretical modeling a major challenge. The main drawback of the established theoretical formalism, the nonequilibrium Green functions approach, is its high numerical effort, which scales cubically with the number of required time steps. Therefore, performing time-dependent simulations of the nonequilibrium dynamics of excited finite graphene nanostructures is not feasible, which makes further improvements urgently necessary. Such a feat was achieved by the author and coworkers during the work on this thesis by developing the G1–G2 scheme. It constitutes the first formulation of the nonequilibrium Green functions approach with linearly-scaling numerical effort with respect to the propagation time. Because of the great importance of this discovery, this thesis addresses two main topics. The first is the aforementioned theoretical framework in general and its application to finite graphene nanostructures. The focus is on special topologically protected states that can occur in these systems. Moreover, the G1–G2 scheme is used to study the ultrafast response of various graphene nanostructures to an external laser pulse. The second aspect includes a detailed discussion of the G1–G2 scheme. Many questions that have arisen in previous publications on the subject are answered. The central insight is that the derivation of the G1–G2 scheme holds many more advantages, besides the obvious numerical ones. These findings can contribute decisively to the further development of approximation methods in many-particle theory

Quantum Fluctuations Approach to the Nonequilibrium GWGW approximation

The quantum dynamics of fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGF) or reduced density matrix methods. Approximations are introduced via a proper choice of the selfenergy or decoupling of the BBGKY-hierarchy. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. Here we develop a different approach where, instead of equations of motion for the many-particle NEGF, equations for the correlation functions of fluctuations are analyzed. We present a derivation of the first two equations of the alternative hierarchy of fluctuations and discuss possible decoupling approximations. In particular, we derive the polarization approximation (PA) which is shown to be equivalent to the nonequilibrium $GW$ approximation with exchange effects of NEGF theory within the generalized Kadanoff-Baym ansatz for weak coupling. The main advantage of the quantum fluctuations approach is that the standard ensemble average can be replaced by a semiclassical average over different initial realizations, as was demonstrated before by Lacroix and co-workers. Here we introduce the stochastic $GW$ (SGW) approximation and the stochastic polarization approximation (SPA) which are demonstrated to be equivalent to the $GW$ approximation without and with exchange, respectively, in the weak coupling limit. In addition to the standard stochastic approach to sample initial configurations we also present an exact approach. Our numerical tests confirm that our approach has the same favorable linear scaling with the computation time as the recently developed G1--G2 scheme. At the same time the SPA and SGW approaches scale more favorably with the system size than the G1--G2 scheme, allowing to extend nonequilibrium $GW$ calculations to bigger systems

Correlated Topological States in Graphene Nanoribbon Heterostructures

Finite graphene nanoribbon (GNR) heterostructures host intriguing topological in-gap states (Rizzo, D. J. et al.~\textit{Nature} \textbf{2018}, \textit{560}, 204]). These states may be localized either at the bulk edges, or at the ends of the structure. Here we show that correlation effects (not included in previous density functional simulations) play a key role in these systems: they result in increased magnetic moments at the ribbon edges accompanied by a significant energy renormalization of the topological end states -- even in the presence of a metallic substrate. Our computed results are in excellent agreement with the experiments. Furthermore, we discover a striking, novel mechanism that causes an energy splitting of the non-zero-energy topological end states for a weakly screened system. We predict that similar effects should be observable in other GNR heterostructures as well

Quantum Fluctuations Approach to the Nonequilibrium GWGW-Approximation II: Density Correlations and Dynamic Structure Factor

The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGF) or reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle selfenergy or decoupling of the BBGKY-hierarchy, respectively. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. In a recent paper [E. Schroedter, J.-P. Joost, and M. Bonitz, Cond. Matt. Phys. \textbf{25}, 23401 (2022)] we have presented a different approach where, instead of equations of motion for the many-particle NEGF (or density operators), equations for the correlation functions of fluctuations are analyzed. In particular, we derived the stochastic GW and polarization approximations that are closely related to the nonequilibrium GW approximation. Here, we extend this approach to the computation of two-time observables depending on the specific ordering of the underlying operators. In particular, we apply this extension to the calculation of the density correlation function and dynamic structure factor of correlated Hubbard clusters in and out of equilbrium

Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond

The theory of Nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many-body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two-time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently we have introduced the G1-G2 scheme that exactly reformulates the Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA) into time-local equations, allowing for a dramatic reduction of the scaling to time-linear scaling [Schluenzen et al., Phys. Rev. Lett. \textbf{124}, 076601 (2020)]. Remarkably, this scaling is achieved quickly, and also for high-level selfenergies, including the nonequilibrium $GW$ and $T$-matrix approximations [Joost et al., Phys. Rev. B \textbf{101}, 245101 (2020)]. Even the dynamically screened ladder approximation is now feasible [Joost et al., Phys. Rev. B \textbf{105}, 165155 (2022)], and also applications to electron-boson systems were demonstrated. Here we present an overview on recent results that were achieved with the G1--G2 scheme. We discuss problems and open questions and present further ideas how to overcome the current limitations of the scheme.We illustrate the G1--G2 scheme by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials

Löwdin's symmetry dilemma within Green functions theory for the one‐dimensional Hubbard model

The energy gap of correlated Hubbard clusters is well studied for one-dimensional systems using analytical methods and density-matrix- renormalization-group (DMRG) simulations. Beyond 1D, however, exact results are available only for small systems by quantum Monte Carlo. For this reason and, due to the problems of DMRG in simulating 2D and 3D systems, alternative methods such as Green functions combined with many-body approximations (GFMBA), that do not have this restriction, are highly important. However, it has remained open whether the approximate character of GFMBA simulations prevents the computation of the Hubbard gap. Here we present new GFMBA results that demonstrate that GFMBA simulations are capable of producing reliable data for the gap which agrees well with the DMRG benchmarks in 1D. An interesting observation is that the accuracy of the gap can be significantly increased when the simulations give up certain symmetry restriction of the exact system, such as spin symmetry and spatial homogeneity. This is seen as manifestation and generalization of the “symmetry dilemma” introduced by Löwdin for Hartree–Fock wave function calculations

Poster: The Unknown Unknown: Cybersecurity Threats of Shadow IT in Higher Education

The growing number of employee-introduced IT solutions creates new attack vectors and challenges for cybersecurity management and IT administrators. These unauthorised hardware, software, or services are called shadow IT. In higher education, the diversity of the shadow IT landscape is even more prominent due to the flexible needs of researchers, educators, and students. We studied shadow IT and related cyber threats in higher education via interviews with 11 IT and security experts. Our results provide a comprehensive overview of observed shadow IT types and related cyber threats. The findings revealed prevalent cloud and self-acquired software use as common shadow IT, with cybersecurity risks resulting from outdated software and visibility gaps. Our findings led to advice for practitioners: manage shadow IT responsibly with cybersecurity best practices, consider stakeholder needs, support educators and researchers, and offer usable IT solutions