Group theory of Wannier functions providing the basis for a deeper understanding of magnetism and superconductivity

The paper presents the group theory of best localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into best localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M, or to a subgroup of G or M. In this context, the paper considers usual as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the best localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly correlated localized electrons makes clear predictions whether or not the system can possess superconducting or magnetic eigenstates

The reason why doping causes superconductivity in LaFeAsO

The experimental observation of superconductivity in LaFeAsO appearing on doping is analyzed with the group-theoretical approach that evidently led in a foregoing paper (J. Supercond 24:2103, 2011) to an understanding of the cause of both the antiferromagnetic state and the accompanying structural distortion in this material. Doping, like the structural distortions, means also a reduction of the symmetry of the pure perfect crystal. In the present paper we show that this reduction modifies the correlated motion of the electrons in a special narrow half-filled band of LaFeAsO in such a way that these electrons produce a stable superconducting state

Galileo In-Situ Dust Measurements in Jupiter's Gossamer Rings

During its late orbital mission at Jupiter the Galileo spacecraft made two passages through the giant planet's gossamer ring system. The impact-ionization dust detector on board successfully recorded dust impacts during both ring passages and provided the first in-situ measurements from a dusty planetary ring. In all, a few thousand dust impacts were counted with the instrument accumulators during both ring passages, but only a total of 110 complete data sets of dust impacts were transmitted to Earth. Detected particle sizes range from about 0.2 to 5 micron, extending the known size distribution by an order of magnitude towards smaller particles than previously derived from optical imaging (Showalter et al. 2008). The grain size distribution increases towards smaller particles and shows an excess of these tiny motes in the Amalthea gossamer ring compared to the Thebe ring. The size distribution for the Amalthea ring derived from our in-situ measurements for the small grains agrees very well with the one obtained from images for large grains. Our analysis shows that particles contributing most to the optical cross-section are about 5 micron in radius, in agreement with imaging results. The measurements indicate a large drop in particle flux immediately interior to Thebe's orbit and some detected particles seem to be on highly-tilted orbits with inclinations up to 20 deg.Comment: 13 figures, 4 tables, submitted to Icaru

Density profiles of a colloidal liquid at a wall under shear flow

Using a dynamical density functional theory we analyze the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does not lead to a shear induced modification of the equilibrium density profile, which would be expected on physical grounds. By introducing a physically motivated dynamic mean field correction we incorporate the missing shear induced interparticle forces into the theory. We find that the shear flow tends to enhance the oscillations in the density profile of hard-spheres at a hard-wall and, at sufficiently high shear rates, induces a nonequilibrium transition to a steady state characterized by planes of particles parallel to the wall. Under gravity, we find that the center-of-mass of the density distribution increases with shear rate, i.e., shear increases the potential energy of the particles

The structural distortion in antiferromagnetic LaFeAsO investigated by a group-theoretical approach

As experimentally well established, undoped LaFeAsO is antiferromagnetic below 137K with the magnetic moments lying on the Fe sites. We determine the orthorhombic body-centered group Imma (74) as the space group of the experimentally observed magnetic structure in the undistorted lattice, i.e., in a lattice possessing no structural distortions in addition to the magnetostriction. We show that LaFeAsO possesses a partly filled "magnetic band" with Bloch functions that can be unitarily transformed into optimally localized Wannier functions adapted to the space group Imma. This finding is interpreted in the framework of a nonadiabatic extension of the Heisenberg model of magnetism, the nonadiabatic Heisenberg model. Within this model, however, the magnetic structure with the space group Imma is not stable but can be stabilized by a (slight) distortion of the crystal turning the space group Imma into the space group Pnn2 (34). This group-theoretical result is in accordance with the experimentally observed displacements of the Fe and O atoms in LaFeAsO as reported by Clarina de la Cruz et al. [nature 453, 899 (2008)]

One-Nucleon Effective Generators of the Poincare Group derived from a Field Theory: Mass Renormalization

We start from a Lagrangian describing scalar "nucleons" and mesons which interact through a simple vertex. Okubo's method of unitary transformation is used to describe a single nucleon dressed by its meson cloud. We find an expression for the physical mass of the nucleon being correct up to second order in the coupling constant. It is then verified that this result is the same as the corresponding expression found by Feynman techniques. Finally we also express the three boost operators in terms of the physical nucleon mass. Doing so we find expressions for all the ten generators of Poincar\'e transformations for the system of one single dressed nucleon.Comment: 19 pages, no figure