A first-principles DFT+GW study of spin-filter and spin-gapless semiconducting Heusler compounds

Among Heusler compounds, the ones being magnetic semiconductors (also known as spin-filter materials) are widely studied as they offer novel functionalities in spintronic/magnetoelectronic devices. The spin-gapless semiconductors are a special case. They possess a zero or almost-zero energy gap in one of the two spin channels. We employ the $GW$ approximation, which allows an elaborate treatment of the electronic correlations, to simulate the electronic band structure of these materials. Our results suggest that in most cases the use of $GW$ self energy instead of the usual density functionals is important to accurately determine the electronic properties of magnetic semiconductors.Comment: Final version as publishe

On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2

Tomographic readout of an opto-mechanical interferometer

The quantum state of light changes its nature when being reflected off a mechanical oscillator due to the latter's susceptibility to radiation pressure. As a result, a coherent state can transform into a squeezed state and can get entangled with the motion of the oscillator. The complete tomographic reconstruction of the state of light requires the ability to readout arbitrary quadratures. Here we demonstrate such a readout by applying a balanced homodyne detector to an interferometric position measurement of a thermally excited high-Q silicon nitride membrane in a Michelson-Sagnac interferometer. A readout noise of \unit{1.9 \cdot 10^{-16}}{\metre/\sqrt{\hertz}} around the membrane's fundamental oscillation mode at \unit{133}{\kilo\hertz} has been achieved, going below the peak value of the standard quantum limit by a factor of 8.2 (9 dB). The readout noise was entirely dominated by shot noise in a rather broad frequency range around the mechanical resonance.Comment: 7 pages, 5 figure

Quasiparticle band structure of the almost-gapless transition-metal-based Heusler semiconductors

Transition-metal-based Heusler semiconductors are promising materials for a variety of applications ranging from spintronics to thermoelectricity. Employing the $GW$ approximation within the framework of the FLAPW method, we study the quasi-particle band structure of a number of such compounds being almost gapless semiconductors. We find that in contrast to the \textit{sp}-electron based semiconductors such as Si and GaAs, in these systems the many-body corrections have a minimal effect on the electronic band structure and the energy band gap increases by less than 0.2~eV, which makes the starting point density functional theory (DFT) a good approximation for the description of electronic and optical properties of these materials. Furthermore, the band gap can be tuned either by the variation of the lattice parameter or by the substitution of the \emph{sp}-chemical element

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form \T as well as a flux 4-form \F. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We investigate the constraint \T \cdot \Psi = 0, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

Wannier Function Approach to Realistic Coulomb Interactions in Layered Materials and Heterostructures

We introduce an approach to derive realistic Coulomb interaction terms in free standing layered materials and vertical heterostructures from ab-initio modelling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random phase approximation, Wannier function representation of Coulomb matrix elements within some low energy Hilbert space and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab-initio calculations of the Coulomb matrix elements within an accuracy of $0.2$eV or better. We show that realistic Coulomb interactions in bilayer graphene can be manipulated on the eV scale by different dielectric and metallic environments. A comparison to electronic phase diagrams derived in [M. M. Scherer et al., Phys. Rev. B 85, 235408 (2012)] suggests that the electronic ground state of bilayer graphene is a layered antiferromagnet and remains surprisingly unaffected by these strong changes in the Coulomb interaction.Comment: 12 pages, 8 figure

Shape mode analysis exposes movement patterns in biology: flagella and flatworms as case studies

We illustrate shape mode analysis as a simple, yet powerful technique to concisely describe complex biological shapes and their dynamics. We characterize undulatory bending waves of beating flagella and reconstruct a limit cycle of flagellar oscillations, paying particular attention to the periodicity of angular data. As a second example, we analyze non-convex boundary outlines of gliding flatworms, which allows us to expose stereotypic body postures that can be related to two different locomotion mechanisms. Further, shape mode analysis based on principal component analysis allows to discriminate different flatworm species, despite large motion-associated shape variability. Thus, complex shape dynamics is characterized by a small number of shape scores that change in time. We present this method using descriptive examples, explaining abstract mathematics in a graphic way.Comment: 20 pages, 6 figures, accepted for publication in PLoS On