Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.Comment: 16 pages, 3 figure

Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling

I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. OutlookComment: review article, 26 pages, 13 figures; V2: added three appendices, and provided code for the various implementation

Magnetic breakdown spectrum of a Kramers-Weyl semimetal

We calculate the Landau levels of a Kramers-Weyl semimetal thin slab in a perpendicular magnetic field $B$. The coupling of Fermi arcs on opposite surfaces broadens the Landau levels with a band width that oscillates periodically in $1/B$. We interpret the spectrum in terms of a one-dimensional superlattice induced by magnetic breakdown at Weyl points. The band width oscillations may be observed as $1/B$-periodic magnetoconductance oscillations, at weaker fields and higher temperatures than the Shubnikov-de Haas oscillations due to Landau level quantization. No such spectrum appears in a generic Weyl semimetal, the Kramers degeneracy at time-reversally invariant momenta is essential.Comment: 13 pages, 18 figure

Localization landscape for Dirac fermions

In the theory of Anderson localization, a landscape function predicts where wave functions localize in a disordered medium, without requiring the solution of an eigenvalue problem. It is known how to construct the localization landscape for the scalar wave equation in a random potential, or equivalently for the Schr\"{o}dinger equation of spinless electrons. Here we generalize the concept to the Dirac equation, which includes the effects of spin-orbit coupling and allows to study quantum localization in graphene or in topological insulators and superconductors. The landscape function $u(r)$ is defined on a lattice as a solution of the differential equation $\overline{{H}}u(r)=1$, where $\overline{{H}}$ is the Ostrowsky comparison matrix of the Dirac Hamiltonian. Random Hamiltonians with the same (positive definite) comparison matrix have localized states at the same positions, defining an equivalence class for Anderson localization. This provides for a mapping between the Hermitian and non-Hermitian Anderson model.Comment: 6 pages, 6 figure

Tractography-guided surgery of brain tumours: what is the best method to outline the corticospinal tract?

Background: Diffusion tensor imaging (DTI) is the imaging technique used in vivo to visualise white matter pathways. The cortico-spinal tract (CST) belongs to one of the most often delineated tracts preoperatively, although the optimal DTI method has not been established yet. Considering that various regions of interests (ROIs) could be selected, the reproducibility of CST tracking among different centres is low. We aimed to select the most reliable tractography method for outlining the CST for neurosurgeons. Materials and methods: Our prospective study consisted of 32 patients (11 males, 21 females) with a brain tumour of various locations. DTI and T1-weighed image series were acquired prior to the surgery. To draw the CST, the posterior limb of the internal capsule (PLIC) and the cerebral peduncle (CP) were defined as two main ROIs. Together with these main ROIs, another four cortical endpoints were selected: the frontal lobe (FL), the supplementary motor area (SMA), the precentral gyrus (PCG) and the postcentral gyrus (POCG). Based on these ROIs, we composed ten virtual CSTs in DSI Studio. The fractional anisotropy, the mean diffusivity, the tracts’ volume, the length and the number were compared between all the CSTs. The degree of the CST infiltration, tumour size, the patients’ sex and age were examined. Results: Significant differences in the number of tracts and their volume were observed when the PLIC or the CP stood as a single ROI comparing with the two- ROI method (all p < 0.05). The mean CST volume was 40054U (SD ± 12874) and the number of fibres was 259.3 (SD ± 87.3) when the PLIC was a single ROI. When the CP was a single ROI, almost a half of fibres (147.6; SD ± 64.0) and half of the CST volume (26664U; SD ± 10059U) was obtained (all p < 0.05). There were no differences between the various CSTs in terms of fractional anisotropy, mean diffusivity, the apparent diffusion coefficient, radial diffusivity and the tract length (p > 0.05). The CST was infiltrated by a growing tumour or oedema in 17 of 32 patients; in these cases, the mean and apparent diffusion of the infiltrated CST was significantly higher than in uncompromised CSTs (p = 0.04). CST infiltration did not alter the other analysed parameters (all p > 0.05). Conclusions: A universal method of DTI of the CST was not developed. However, we found that the CP or the PLIC (with or without FL as the second ROI) should be used to outline the CST

Experimental and theoretical investigation of ligand effects on the synthesis of ZnO nanoparticles

ZnO nanoparticles with highly controllable particle sizes(less than 10 nm) were synthesized using organic capping ligands in Zn(Ac)2 ethanolic solution. The molecular structure of the ligands was found to have significant influence on the particle size. The multi-functional molecule tris(hydroxymethyl)-aminomethane (THMA) favoured smaller particle distributions compared with ligands possessing long hydrocarbon chains that are more frequently employed. The adsorption of capping ligands on ZnnOn crystal nuclei (where n = 4 or 18 molecular clusters of(0001) ZnO surfaces) was modelled by ab initio methods at the density functional theory (DFT) level. For the molecules examined, chemisorption proceeded via the formation of Zn...O, Zn...N, or Zn...S chemical bonds between the ligands and active Zn2+ sites on ZnO surfaces. The DFT results indicated that THMA binds more strongly to the ZnO surface than other ligands, suggesting that this molecule is very effective at stabilizing ZnO nanoparticle surfaces. This study, therefore, provides new insight into the correlation between the molecular structure of capping ligands and the morphology of metal oxide nanostructures formed in their presence

Synthesis and characterization of hybrid nanostructures

There has been significant interest in the development of multicomponent nanocrystals formed by the assembly of two or more different materials with control over size, shape, composition, and spatial orientation. In particular, the selective growth of metals on the tips of semiconductor nanorods and wires can act to couple the electrical and optical properties of semiconductors with the unique properties of various metals. Here, we outline our progress on the solution-phase synthesis of metal-semiconductor heterojunctions formed by the growth of Au, Pt, or other binary catalytic metal systems on metal (Cd, Pb, Cu)-chalcogenide nanostructures. We show the ability to grow the metal on various shapes (spherical, rods, hexagonal prisms, and wires). Furthermore, manipulating the composition of the metal nanoparticles is also shown, where PtNi and PtCo alloys are our main focus. The magnetic and electrical properties of the developed hybrid nanostructures are shown

Insulin Glargine in the Intensive Care Unit: A Model-Based Clinical Trial Design

Online 4 Oct 2012Introduction: Current succesful AGC (Accurate Glycemic Control) protocols require extra clinical effort and are impractical in less acute wards where patients are still susceptible to stress-induced hyperglycemia. Long-acting insulin Glargine has the potential to be used in a low effort controller. However, potential variability in efficacy and length of action, prevent direct in-hospital use in an AGC framework for less acute wards. Method: Clinically validated virtual trials based on data from stable ICU patients from the SPRINT cohort who would be transferred to such an approach are used to develop a 24-hour AGC protocol robust to different Glargine potencies (1.0x, 1.5x and 2.0x regular insulin) and initial dose sizes (dose = total insulin over prior 12, 18 and 24 hours). Glycemic control in this period is provided only by varying nutritional inputs. Performance is assessed as %BG in the 4.0-8.0mmol/L band and safety by %BG<4.0mmol/L. Results: The final protocol consisted of Glargine bolus size equal to insulin over the previous 18 hours. Compared to SPRINT there was a 6.9% - 9.5% absolute decrease in mild hypoglycemia (%BG<4.0mmol/L) and up to a 6.2% increase in %BG between 4.0 and 8.0mmol/L. When the efficacy is known (1.5x assumed) there were reductions of: 27% BG measurements, 59% insulin boluses, 67% nutrition changes, and 6.3% absolute in mild hypoglycemia. Conclusion: A robust 24-48 clinical trial has been designed to safely investigate the efficacy and kinetics of Glargine as a first step towards developing a Glargine-based protocol for less acute wards. Ensuring robustness to variability in Glargine efficacy significantly affects the performance and safety that can be obtained