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A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Neel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Neel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization vanishes this way, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single-particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and nonuniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling), which is exclusively Neel ordered, with zero local magnetization everywhere in the system.
We represent the Z2 topological invariant characterizing a one-dimensional topological superconductor using a Wess–Zumino–Witten dimensional extension. The invariant is formulated in terms of the single-particle Green’s function which allows us to classify interacting systems. Employing a recently proposed generalized Berry curvature method, the topological invariant is represented independent of the extra dimension requiring only the single-particle Green’s function at zero frequency of the interacting system. Furthermore, a modified twisted boundary conditions approach is used to rigorously define the topological invariant for disordered interacting systems.
Im Rahmen dieser Arbeit wurden Effekte der Paarbildung durch Wechselwirkung von hochenergetischer Gammastrahlung mit dem metagalaktischen FIR-UV Strahlungsfeld (MRF) untersucht. Einerseits hat die Paarbildung Folgen f"ur die beobachteten Spektren aktiver Galaxienkerne, andererseits hat sie auch einen gro"sen Einflu"s auf den extragalaktischen Gammastrahlungshintergrund. Es wurde ein verbesserte Version f"ur das Modell des FIR-UV Strahlungsfelds vorgestellt, mit dessen Hilfe aus beobachteten Daten intrinsische Blazarspektren ermittelt wurden. Im weiteren wurde ein auf EGRET-Blazaren basierendes Modell f"ur den Gammastrahlungshintergrund berechnet, in dem besonderer Wert auf die korrekte Beschreibung der Absorption prim"arer und der daraus resultierenden sekund"aren Gammastrahlung gelegt wurde. Schlie"slich wurde gezeigt, da"s der Beitrag von BL Lac Objekten zum Gammahintergrund nicht nur der fehlende Flu"s, sondern auch die spektrale Form der aus EGRET Beobachtungen gewonnenen Daten erkl"art werden kann, ohne den gegenw"artigen TeV-Daten zu widersprechen.
Chromium dioxide CrO\(_2\) belongs to a class of materials called ferromagnetic half-metals, whose peculiar aspect is that they act as a metal in one spin orientation and as a semiconductor or insulator in the opposite one. Despite numerous experimental and theoretical studies motivated by technologically important applications of this material in spintronics, its fundamental properties such as momentumresolved electron dispersions and the Fermi surface have so far remained experimentally inaccessible because of metastability of its surface, which instantly reduces to amorphous Cr\(_2\)O\(_3\). In this work, we demonstrate that direct access to the native electronic structure of CrO\(_2\) can be achieved with soft-x-ray angle-resolved photoemission spectroscopy whose large probing depth penetrates through the Cr\(_2\)O\(_3\) layer. For the first time, the electronic dispersions and Fermi surface of CrO\(_2\) are measured, which are fundamental prerequisites to solve the long debate on the nature of electronic correlations in this material. Since density functional theory augmented by a relatively weak local Coulomb repulsion gives an exhaustive description of our spectroscopic data, we rule out strong-coupling theories of CrO\(_2\). Crucial for the correct interpretation of our experimental data in terms of the valence-band dispersions is the understanding of a nontrivial spectral response of CrO\(_2\) caused by interference effects in the photoemission process originating from the nonsymmorphic space group of the rutile crystal structure of CrO\(_2\).
This work focuses on a fundamental problem in modern numerical rela- tivity: Extracting gravitational waves in a coordinate and gauge independent way to nourish a unique and physically meaningful expression. We adopt a new procedure to extract the physically relevant quantities from the numerically evolved space-time. We introduce a general canonical form for the Weyl scalars in terms of fundamental space-time invariants, and demonstrate how this ap- proach supersedes the explicit definition of a particular null tetrad. As a second objective, we further characterize a particular sub-class of tetrads in the Newman-Penrose formalism: the transverse frames. We establish a new connection between the two major frames for wave extraction: namely the Gram-Schmidt frame, and the quasi-Kinnersley frame. Finally, we study how the expressions for the Weyl scalars depend on the tetrad we choose, in a space-time containing distorted black holes. We apply our newly developed method and demonstrate the advantage of our approach, compared with methods commonly used in numerical relativity.
Vevacious: a tool for finding the global minima of one-loop effective potentials with many scalars
(2013)
Several extensions of the Standard Model of particle physics contain additional scalars implying a more complex scalar potential compared to that of the Standard Model. In general these potentials allow for charge- and/or color-breaking minima besides the desired one with correctly broken SU(2) L ×U(1) Y . Even if one assumes that a metastable local minimum is realized, one has to ensure that its lifetime exceeds that of our universe. We introduce a new program called Vevacious which takes a generic expression for a one-loop effective potential energy function and finds all the tree-level extrema, which are then used as the starting points for gradient-based minimization of the one-loop effective potential. The tunneling time from a given input vacuum to the deepest minimum, if different from the input vacuum, can be calculated. The parameter points are given as files in the SLHA format (though is not restricted to supersymmetric models), and new model files can be easily generated automatically by the Mathematica package SARAH. This code uses HOM4PS2 to find all the minima of the tree-level potential, PyMinuit to follow gradients to the minima of the one-loop potential, and CosmoTransitions to calculate tunneling times.
Die vorliegende Arbeit beschäftigt sich mit der Abstrahlung von Aktiven Galaxienkernen. Das erste Maximum der charakteristischen Doppelpeakstruktur des $\nu F_{\nu}$-Spektrums vom Blazaren ist zweifelsfrei Synchrotronstrahlung hochenergetischer Elektronen innerhalb des relativistischen Ausflusses des zugrundeliegenden Aktiven Galaxienkerns. Die zum zweiten (hochenergetischen) Maximum beitragenden Strahlungsprozesse und Teilchenspezies hingegen sind Gegenstand aktueller Diskussionen. In dieser Arbeit wir ein vollständig selbstkonsistentes und zeitabhängiges hybrides Emissionsmodell, welches auch Teilchenbeschleunigung berücksichtigt, entwickelt und auf verschiedene Blazar-Typen entlang der Blazar-Sequenz, von BL Lac Objekten mit verschiedenen Peakfrequenzen bis hin zu Flachspektrum-Radioquasaren, angewendet. Die spektrale Emission ersterer kann gut im rein leptonischen Grenzfall, d.h. der zweite $\nu F_{\nu}$-Peak kommt durch invers Compton-gestreute Synchrotronphotonen der abstrahlenden Elektronen selbst zustande, beschrieben werden. Zur Beschreibung letzterer muss man nicht-thermische Protonen innerhalb des Jets zulassen um die Dominanz des zweiten Maximums im Spektrum konsistent zu erklären. In diesem Fall besteht der zweite Peak aus Protonensynchrotronstrahlung und Kaskadenstrahlung der photohadronischen Prozesse. Mit dem entwickelten Modell ist es möglich auch die zeitliche Information, welche durch Ausbrüche von Blazaren bereitgestellt wird, auszunutzen um zum einen die freien Modellparameter weiter einzuschränken und -viel wichtiger- zum anderen leptonisch dominierte Blazare von hadronischen zu unterscheiden. Hierzu werden die typischen Zeitunterschiede in den Interbandlichtkurven als hadronischer Fingerabdruck benutzt.\\ Mit einer Stichprobe von 16 Spektren von zehn Blazaren entlang der Blazar-Sequenz, welche in unterschiedlichen Flusszuständen und mit starker Variabilität beobachtet wurden, ist es möglich die wichtigsten offenen Fragen der Physik relativistischer Ausbrüche in systematischer Art und Weise zu adressieren. Anhand der modellierten Ausbrüche kann man erkennen, dass sechs Quellen rein leptonisch dominiert sind, aber vier Protonen bis auf $\gamma \approx 10^{11}$ beschleunigen, was Auswirkungen auf die möglichen Quellen extragalaktischer kosmischer Strahlung unter den Blazaren hat. Darüber hinaus findet sich eine Abhängigkeit zwischen dem Magnetfeld der Emissionsregion und der injizierten Leuchtkraft, welche unabhängig von den zugrunde liegenden Teilchenpopulationen Gültigkeit besitzt. In diesem Zusammenhang lässt sich die Blazar-Sequenz als ein evolutionäres Szenario erklären: die Sequenz $FSRQ \rightarrow LBL/IBL \rightarrow HBL$ kommt aufgrund abnehmender Gasdichte der Hostgalaxie und damit einhergehender abnehmender Akkretionsrate zustande, dies wird durch weitere kosmologische Beobachtungen bestätigt. Eine abnehmende Materiedichte innerhalb des relativistischen Ausflusses wird von einem abnehmenden Magnetfeld begleitet, d.h. aber auch, dass Protonen weit vor den Elektronen nicht mehr im Strahlungsgebiet gehalten werden können. Die Blazar-Sequenz ist also ein Maß für die Hadronizität des Jets. Dies erklärt zudem die Dichotomie von FSRQs und BL Lac Objekten sowie die Zweiteilung in anderen Erscheinungsformen von AGN, z.B. FR-I und FR-II Radiogalaxien.\\ Während der Modellierung wird gezeigt, dass man Blazar-Spektren, speziell im hadronischen Fall, nicht mehr statisch betrachten kann, da es zu kumulierten Effekten aufgrund der langen Protonensynchrotronzeitskala kommt. Die niedrige Luminosität der Quellen und unterschiedlich lange Beobachtungszeiten verschiedener Experimente verlangen bei variablen Blazaren auch im leptonischen Fall eine zeitabhängige Betrachtung. Die Kurzzeitvariabilität scheint bei einzelnen Blazaren stets die selbe Ursache zu haben, unterscheidet sich aber bei der Betrachtung verschiedener Quellen. Zusätzlich wird für jeden Blazar, der in verschiedenen Flusszuständen beobachtet werden konnte, der Unterschied zwischen Lang- und Kurzzeitvariabilität, auch im Hinblick auf einen möglichen globalen Grundzustand hin, betrachtet.
It has been proposed that the observed diphoton excess at 750 GeV could be explained within the constrained minimal supersymmetric standard model via resonantly produced stop bound states. We reanalyze this scenario critically and extend previous work to include the constraints from the stability of the electroweak vacuum and from the decays of the stoponium into a pair of Higgs bosons. It is shown that the interesting regions of parameter space with a light stop and Higgs of the desired mass are ruled out by these constraints. This conclusion is not affected by the presence of the bound states because the binding energy is usually very small in the regions of parameter space which can explain the Higgs mass. Thus, this also leads to strong constraints on the diphoton production cross section which is in general too small.
One of the most popular extensions of the SM is Supersymmetry (SUSY). It is a symmetry relating fermions and bosons and also the only feasible extension to the symmetries of spacetime. With SUSY it is then possible to explain some of the open questions left by the SM while at the same time opening the possibility of gauge unification at a high scale. SUSY theories require the addition of new particles, in particular an extra Higgs doublet and at least as many new scalars as fermions in the SM. Much in the same way that the Higgs boson breaks SU (2)L symmetry, these new scalars can break any symmetry for which they carry a charge through spontaneous symmetry breaking.
Let us assume there is a local minimum of the potential that reproduces the correct phenomenol- ogy for a parameter point of a given model. By exploring whether there are other deeper minima with VEVs that break symmetries we want to conserve, like SU (3)C or U (1)EM , it is possible to exclude regions of parameter space where that happens. The local minimum with the correct phenomenology might still be metastable, so it is also necessary to calculate the probability of tunneling between minima.
In this work we propose and apply a framework to constrain the parameter space of models with many scalars through the minimization of the one-loop eff e potential and the calculation of tunneling times at zero and non zero temperature.After a brief discussion about the shortcomings of the SM and an introduction of the basics of SUSY, we introduce the theory and numerical methods needed for a successful vacuum stability analysis. We then present Vevacious, a public code where we have implemented our proposed framework. Afterwards we go on to analyze three interesting examples.
For the constrained MSSM (CMSSM) we explore the existence of charge- and color- breaking (CCB) minima and see how it constraints the phenomenological relevant region of its parameter space at T = 0. We show that the regions reproducing the correct Higgs mass and the correct relic density for dark matter all overlap with regions suffering from deeper CCB minima.
Inspired by the results for the CMSSM, we then consider the natural MSSM and check the region of parameter space consistent with the correct Higgs mass against CCB minima at T /= 0. We find that regions of parameter space with CCB minima overlap significantly with that reproducing the correct Higgs mass. When thermal eff are considered the majority of such points are then found to have a desired symmetry breaking minimum with very low survival probability. In both these studies we find that analytical conditions presented in the literature fail in dis- criminating regions of parameter space with CCB minima. We also present a way of adapting our framework so that it runs quickly enough for use with parameter fit studies.
Lastly we show a different example of using vacuum stability in a phenomenological study. For the BLSSM we investigate the violation of R-parity through sneutrino VEVs and where in parameter space does this happen. We find that previous analyses in literature fail to identify regions with R-parity conservation by comparing their results to our full numerical analysis.
A general theory for all classes of unconventional superconductors is still one of the unsolved key issues in condensed-matter physics. Actually, it is not yet fully settled if there is a common underlying pairing mechanism. Instead, it might be possible that several distinct sources for unconventional (not phonon-mediated) superconductivity have to be considered, or an electron-phonon interaction is not negligible. The focus of this thesis is on the most probable mechanism for the formation of Cooper pairs in unconventional superconductors, namely a strictly electronic one where spin fluctuations are the mediators. Studying different superconductors in this thesis, the emphasis is put on material-independent features of the pairing mechanism. In addition, the investigation of the phase diagrams enables a view on the vicinity of superconductivity. Thus, it is possible to clarify which competing quantum fluctuations enhance or weaken the propensity for a superconducting state. The broad range of superconducting materials requires the use of more than one numerical technique to study an appropriate microscopic description. This is not a problem but a big advantage because this facilitates the approach-independent description of common underlying physics. For this evaluation, the strongly correlated cuprates are simulated with the variational cluster approach. Especially the question of a pairing glue is taken into consideration. Furthermore, it is possible to distinguish between retarded and non-retarded contributions to the gap function. The cuprates are confronted with the cobaltate NaCoO and graphene. These weakly correlated materials are investigated with the functional renormalization group (fRG) and reveal a comprehensive phase diagram, including a d+id-wave superconductivity, which breaks time-reversal symmetry. The corresponding gap function is nodeless, but for NaCoO, it features a doping-dependent anisotropy. In addition, some general considerations on the kagome lattice are completing the discussion, where a sublattice interference dramatically affects the Fermi-surface instabilities, suppressing the usual spin-density wave and d+id-wave superconductivity. Thereby, some different fascinating charge and bond orders as well as a nematic are observable. In short, this thesis provides an insight to distinct classes of unconventional superconductors with appropriate simulation techniques. This facilitates to separate the material specific properties from the universal ones.