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The subject of this thesis is the development and test of silicon strip detectors for the high luminosity upgrade of the tracking detector of the ATLAS experiment at the Large Hadron Collider. Special emphasis is devoted to the understanding of the impact of mechanical stress on the electrical properties and the particle detection performance of detector modules.
First simulations were done to estimate the maximum expected stress on a sensor when operated at -30 °C within the future silicon strip tracking detector ITk, at ATLAS. The maximum stress in a worst case scenario is expected to be 27 MPa. Tensile strength tests were done to estimate the maximum stress which can be applied to a silicon strip sensor. Silicon shards, with a thickness and dopand concentration corresponding to the ITk sensor specifications break at >23 MPa, wafers at >700 MPa and sensors at ~ 400 MPa. The huge variations lead to the assumption, that the tensile stregth, which is highly dependent on the quality of the crystal lattice, is due to different cutting technology. Wafers, irradiated with a fluence equivalent of a lifetime dose of an ITk sensor, show no stress dependency of the youngs modulus. The tensile strength of irradiated wafers is decreased by ~ 6,6 %. No damage on silicon sensors from mechanical stress is expected for sensor modules installed it the ITk.
The electrical properties of silicon strip sensors were studied for applied mechanical stress on ATLAS07 sensors up to 60 MPa. The specifications of the sensors are similar to the specification of strip sensors in the future silicon strip tracker barrel region of the ATLAS detector. The leakage current changes at 50 MPa by -1.7 %, the bias resistance by +0.8 % and the interstrip resistance by -25 %. The depletion voltage and the implant resistance are not affected by mechanical stress. Except for the interstrip resistance the results can be explained by piezoresistive effects.
Silicon strip modules were build and studied in particle test beams. These modules consists of an ATLAS07 or an ATLAS12 sensor and an analogue readout to study the influence of stress on the module performance. The sensor module noise is independent from the applied stress. An effect of stress on the signal strength was seen. The ATLAS07 sensor module signal strength was decreased and the ATLAS12 sensor module signal strength was increased with a slope of ~0,6 MPa^-1. The average cluster size of the ATLAS07 sensor module was increased by 0,25 % MPa^-1 and the average cluster size of the ATLAS12 sensor module was decreased by 0,06 % MPa^-1 with applied stress.
Luminosity is a key quantity of any collider, since it allows for the determination of the absolute cross sections from the observed rates in a detector. Since the Higgs boson discovery in 2012, the highest priority at the Large Hadron Collider (LHC) has been given to an accurate understanding of the electroweak scale and a search for new physics. Precise luminosity measurements in such conditions are of crucial importance, as they determine the precision of any physics cross section measurement.
To increase the production of particles of low cross section the LHC is running at the highest possible luminosity. After the first Long Shutdown (LS1) the original performance goal for the luminosity of was reached with 1011 protons per bunch and a bunch spacing of 25 ns. In such conditions radiation hard detectors with extremely fast response time are required, especially for instrumentation near the beam.
The Compact Muon Solenoid experiment is equipped with three online luminometers, which fulfill the listed requirements: the Fast Beam Conditions Monitor (BCM1F), the Pixel Luminosity Telescope (PLT) and the Forward Hadron calorimeter (HF).
The BCM1F was upgraded during LS1 from 8 to 24 diamond sensors and is read out by a dedicated fast ASIC. The back-end comprises a deadtime-less histogramming unit, with 6.25 ns bin width and analog-to-digital converters with 2 ns sampling time in the VME standard. A microTCA system with better time resolution is in development. Because of its excellent time resolution BCM1F measures separately both luminosity and machine induced background particles.
The performance of the detector in the first running period and radiation damage monitoring of the sensors and electronics chain form the first part of this thesis.
Calibration of the luminometers at the LHC is done using van der Meer (VdM) scans. The proton beams are scanned against each other. The effective width of the beams is measured and the visible cross section, the key quantity for the luminosity measurement, is determined.
The impact of detector instability, beam-beam effects, correlations of the particle density distributions in the X and Y planes, and satellite and ghost bunches are studied in detail and systematic uncertainties are derived. A comparison of the VdM scans of 2015 and 2016 completes the second part of the thesis.
As a contribution to the upgrade of the beam instrumentation for the high luminosity LHC, a novel single crystal sapphire detector was designed, built and studied in a test-beam. The detector comprises a stack of sapphire plates. The response depends on the direction of the incident particles. The performance of the detector is described in the third part of the thesis. It is demonstrated that this sapphire detector can be used for the detection of single relativistic particles. The results point to the dominant contribution of the electrons to the signal generation in sapphire.
We formulate a generalization of the time-dependent Gutzwiller theory for the application to multi-band Hubbard models. Our approach allows for the computation of general momentum- and frequency-dependent two-particle response functions. The in-depth knowledge of them is crucial for the understanding and interpretation of experiments in solid-state physics. In the calculation of ground-state properties of Hubbard models, the Gutzwiller approach is known to overcome the main shortcomings of the Hartree–Fock approximation, whose time-dependent generalization is the standard text-book method for the calculation of response functions. We therefore expect that the time-dependent Gutzwiller theory, that has been formulated only for the single-band Hubbard model so far, will offer a technique yielding new insight into the dynamics of strongly-correlated multi-orbital systems. In this thesis, we motivate the employment of multi-orbital Hubbard models and give an introduction to multi-band Hubbard models in Chapters 1 and 2. Their treatment within the Gutzwiller variational approach is subject of Chapter 3, where it is supplemented by investigations that connect our new approach to previous results. We derive the random-phase approximation as the time-dependent Hartree–Fock theory in Chapter 4, followed by the derivation of the corresponding time-dependent Gutzwiller theory in Chapter 5. We demonstrate the applicability of our new approach in Chapter 6, where we calculate the transversal spin susceptibility of a Hubbard model with two degenerate bands and present numerical results for systems in infinite and three spatial dimensions. A summary and conclusion is given in the final Chapter. Mathematical details of our derivations are presented in several appendices.
As a result of 20 years of experimental and theoretical investigations of high temperature superconductors (HTSC) one can draw a very complex and rich phase diagram that cannot be described completely yet. Numerous experimental findings give strong hints for an inhomogeneous distribution of spin and charge correlations in HTSC. Motivated by the experimental findings we try to answer the question whether pair correlations from broken symmetry states can be found in the framework of the Gutzwiller approximation of the Hubbard model.After an introductory discussion of selected experimental works and theoretical models we derive the charge-rotationally invariant Gutzwiller functional for the one-band Hubbard model. On this basis we calculate various states from the saddle point solution of functional in the attractive (U<0) regime. Starting with a second order expansion we investigate the instability of a normal system towards SC in the framework of the time dependent Gutzwiller approximation (TDGA). We derive criteria for a phase transition from the normal to the superconducting phase in the paramagnetic regime. We show results for an infinite dimensional lattice that are in good agreement with QMC data. In the next section of this work we present results for finite dimensional systems. We compare numerical results from the GA with the conventional Hartree-Fock approximation. As an example we discuss a homogeneously superconducting and a charge-ordered state. We show that the difference is mainly in the crossover from weak to strong coupling which is due to the renormalization in the Gutzwiller formalism. In a next step we derive an effective Hamiltonian on top of the saddle point solution. We compare the formalism analytically with the findings from the well known BCS theory. We verify our conclusions by numerical calculations. Motivated by different experimental works on d-wave symmetric k-dependent SC gaps we focus on the question whether states including non-local pair correlations can be a solution of the GA and how does this correlation lower the energy.We restrict to the repulsive regime (U>0) and discuss the formal requirements for a possible solution in view of a coexisting spin order and the interplay of local and non-local pair order. As a next application we prepare inhomogeneous solutions in the normal and in the extended Hubbard model where we include an additional inter-site interaction by the parameter V>0. We present inhomogeneous solutions that are characterized by stripe-shaped domains where the parameters for charge- and pair- ordering change their phases or their amplitude. We obtain results for the normal and the extended Hubbard model and we discuss the influence of the parameter V. We show that in case of V>0 a pair density wave (PDW) without stripes is the ground state. Another focus of the work is on point-like inhomogeneities namely polarons and (anti-)vortices in finite clusters. We present results that show a good agreement with the logarithmic dependence of the energy of the vortex state with respect to the vortex radius as well as possible attraction between vortex and anti-vortices. Finally in the last chapter we introduce the superfluid density in order to discuss the stability of our solutions in finite dimensional systems. We give a short overview on different analytical approaches to this quantity. We present an approach that is based on an energy expansion view of an angular distortion of the charge vector field. We discuss this approach by comparing the numerical GA results with exact QMC results where our approach turned out to be in good qualitative agreement.