Topological insulator on honeycomb lattices and ribbons without inversion symmetry

We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the $\mathbb{Z}_2$ invariant of the system as function of spin-orbit coupling, Hubbard interaction $U$, and inversion-symmetry-breaking on-site potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological non-trivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state, since for moderate values the transition from the non-trivial topological to the trivial Mott insulator is pushed to larger values of interaction $U$. This feature of an enhanced topological state is also found on honeycomb ribbons. With inversion symmetry, the edge of the zigzag ribbon is magnetic for any value of $U$. This magnetic moment destroys the gapless edge mode. Lifting inversion symmetry allows for a finite region in interaction strength $U$ below which gapless edge modes exist.Comment: 9 pages, 9 figure

“I am what I’m not”:A corpus-based study of negative self-identification in UK web forums

This thesis analyses a corpus of 936 instances of the structure “I + copula + NOT + indefinite noun phrase” and its variants, as used in UK web forums. Making assertions about one’s identity in the negative not only provides information about what one claims not to be, but also indexes various aspects of, and potentially modifies, the interpretation of the textual and non-textual context in which such assertions are used. The thesis develops a theoretical and methodological framework to qualitatively and quantitatively identify the multifunctional, context-dependent meaning potential of the structure in focus. The corpus was qualitatively analysed and tagged for conceptual categories of identifying NPs as well as for formal and functional features of the co-texts in which the structure appears. A conceptual profile of negative self-identifiers was developed, and the experiential meanings of the immediate context of the structure were examined, as were their relations of co-occurrence with particular conceptual categories of negative identifiers. By investigating whether users of English in particular co-texts negate self-identification with noun phrases from particular conceptual domains in patterned ways, the study identified certain conceptualisations that were implicitly acknowledged as relevant for people’s self-representation in these discourse contexts. Key findings include: (a) negative identification with expertise is a frequent linguistic choice in the context of presenting one’s knowledge; and (b) negative identification with preferences is a frequent linguistic choice in contexts describing one’s experience. These findings are discussed in light of the wider sociopolitical context, suggesting an ideological struggle around – and a possible reconceptualisation of – the notion of epistemic authority

Variational perspective photometric stereo

In this thesis we present a method to estimate the surface orientation of a 3D object. The general technique is called Photometric Stereo (PS) since we use several 2D images taken from the same location while the illumination changes for each image. Therefore, we use the varying intensities for each pixel to estimate the surface normal vector. In order to compute the estimation of the surface normals we used a variational approach and derived an energy functional depending on the Cartesian depth z. This energy functional is like a cost function that we want to minimise to obtain a good estimation of the shape of the test object. For the minimisation technique we used the method of Maurer et al. [MJBB15] to overcome the difficulties in the minimisation of the energy functional and efficiently reach a global minimum. Further, we present three variants of this model that use different illumination models and two model extensions. Finally, we compare the performances of all the variants of the PS model in different experiments

Investigation of Vector Discretization Schemes for Box Volume Methods

ABSTRACT The application of the box integration method in Technology CAD environments is investigated. A particular difficulty arises from physical models like the impact ionization rate or the high-field mobility within the drift-diffusion carrier transport equations which rely on vector quantities. We discuss different methods how generation rates can be approximated in the box scheme and how the requirements for the applied vector discretizations are. Simulation results of devices operated near break-down are presented using implementations of the presented schemes. Advantages and disadvantages in respect to implementation, to errors, and to convergence behavior are presented

Maximum entropy formalism for the analytic continuation of matrix-valued Green’s functions

We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO$_3$, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.Comment: 15 pages, 7 figure

Spin-orbit coupling and correlations in three-orbital systems

We investigate the influence of spin-orbit coupling $\lambda$ in strongly-correlated multiorbital systems that we describe by a three-orbital Hubbard-Kanamori model on a Bethe lattice. We solve the problem at all integer fillings $N$ with the dynamical mean-field theory using the continuous-time hybridization expansion Monte Carlo solver. We investigate how the quasiparticle renormalization $Z$ varies with the strength of spin-orbit coupling. The behavior can be understood for all fillings except $N=2$ in terms of the atomic Hamiltonian (the atomic charge gap) and the polarization in the $j$-basis due to spin-orbit induced changes of orbital degeneracies and the associated kinetic energy. At $N=2$, $\lambda$ increases $Z$ at small $U$ but suppresses it at large $U$, thus eliminating the characteristic Hund's metal tail in $Z(U)$. We also compare the effects of the spin-orbit coupling to the effects of a tetragonal crystal field. Although this crystal field also lifts the orbital degeneracy, its effects are different, which can be understood in terms of the different form of the interaction Hamiltonian expressed in the respective diagonal single-particle basis

Combining targeted and systematic prostate biopsy improves prostate cancer detection and correlation with the whole mount histopathology in biopsy naïve and previous negative biopsy patients

OBJECTIVE: Guidelines for previous negative biopsy (PNB) cohorts with a suspicion of prostate cancer (PCa) after positive multiparametric (mp) magnetic-resonance-imaging (MRI) often favour the fusion-guided targeted prostate-biopsy (TB) only approach for Prostate Imaging-Reporting and Data System (PI-RADS) ≥3 lesions. However, recommendations lack direct biopsy performance comparison within biopsy naïve (BN) vs. PNB patients and its prognostication of the whole mount pathology report (WMPR), respectively. We suppose, that the combination of TB and concomitant TRUS-systematic biopsy (SB) improves the PCa detection rate of PI-RADS 2, 3, 4 or 5 lesions and the International Society of Urological Pathology (ISUP)-grade predictability of the WMPR in BN- and PNB patients. METHODS: Patients with suspicious mpMRI, elevated prostate-specific-antigen and/or abnormal digital rectal examination were included. All PI-RADS reports were intramurally reviewed for biopsy planning. We compared the PI-RADS score substratified TB, SB or combined approach (TB/SB) associated BN- and PNB-PCa detection rate. Furthermore, we assessed the ISUP-grade variability between biopsy cores and the WMPR. RESULTS: According to BN (n = 499) vs. PNB (n = 314) patients, clinically significant (cs) PCa was detected more frequently by the TB/SB approach (62 vs. 43%) than with the TB (54 vs. 34%) or SB (57 vs. 34%) (all p < 0.0001) alone. Furthermore, we observed that the TB/SB strategy detects a significantly higher number of csPCa within PI-RADS 3, 4 or 5 reports, both in BN and PNB men. In contrast, applied biopsy techniques were equally effective to detect csPCa within PI-RADS 2 lesions. In case of csPCa diagnosis the TB approach was more often false-negative in PNB patients (BN 11% vs. PNB 19%; p = 0.02). The TB/SB technique showed in general significantly less upgrading, whereas a higher agreement was only observed for the total and BN patient cohort. CONCLUSION: Despite csPCa is more frequently found in BN patients, the TB/SB method always detected a significantly higher number of csPCa within PI-RADS 3, 4 or 5 reports of our BN and PNB group. The TB/SB strategy predicts the ISUP-grade best in the total and BN cohort and in general shows the lowest upgrading rates, emphasizing its value not only in BN but also PNB patients