Dark spinor inflation -- theory primer and dynamics

Inflation driven by a single dark spinor field is discussed. We define the notion of a dark spinor field and derive the cosmological field equations for such a matter source. The conditions for inflation are determined and an exactly solvable model is presented. We find the power spectrum of the quantum fluctuation of this field and compare the results with scalar field inflation.Comment: 13 pages; typo in Eq. (12) corrected, minor improvement

Electronic nematic susceptibility of iron-based superconductors

We review our recent experimental results on the electronic nematic phase in electron- and hole-doped BaFe$_2$As$_2$ and FeSe. The nematic susceptibility is extracted from shear-modulus data (obtained using a three-point-bending method in a capacitance dilatometer) using Landau theory and is compared to the nematic susceptibility obtained from elastoresistivity and Raman data. FeSe is particularly interesting in this context, because of a large nematic, i.e., a structurally distorted but paramagnetic, region in its phase diagram. Scaling of the nematic susceptibility with the spin lattice relaxation rate from NMR, as predicted by the spin-nematic theory, is found in both electron- and hole-doped BaFe$_2$As$_2$, but not in FeSe. The intricate relationship of the nematic susceptibility to spin and orbital degrees of freedom is discussed.Comment: Invited review article for a special issue on Fe-based superconductors in Comptes Rendus Physiqu

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Stable splitting of bivariate spline spaces by Bernstein-Bézier methods

We develop stable splitting of the minimal determining sets for the spaces of bivariate C1 splines on triangulations, including a modified Argyris space, Clough-Tocher, Powell-Sabin and quadrilateral macro-element spaces. This leads to the stable splitting of the corresponding bases as required in Böhmer's method for solving fully nonlinear elliptic PDEs on polygonal domains

Bounds on the basic physical parameters for anisotropic compact general relativistic objects

We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant. The values of these quantities are strongly dependent on the value of the anisotropy parameter (the difference between the tangential and radial pressure) at the surface of the star. In the presence of the cosmological constant, a minimum mass configuration with given anisotropy does exist. Anisotropic compact stellar type objects can be much more compact than the isotropic ones, and their radii may be close to their corresponding Schwarzschild radii. Upper bounds for the anisotropy parameter are also obtained from the analysis of the curvature invariants. General restrictions for the redshift and the total energy (including the gravitational contribution) for anisotropic stars are obtained in terms of the anisotropy parameter. Values of the surface redshift parameter greater than two could be the main observational signature for anisotropic stellar type objects.Comment: 18 pages, no figures, accepted for publication in CQ