Christian Brouder

Angular dependence of X-ray absorption spectra

A detailed account of the dependence of X-ray absorption spectra (XAS) on polarisation and light beam directions is given. Anisotropic XAS measured on single crystals, layered compounds, polymers and oriented powders are tabulated. The X-ray absorption cross section by non-magnetic samples is derived, including electric dipole and quadrupole contributions. Orders of magnitude are found for magnetic dipole and electric dipole-octupole terms. Using a spherical tensor expansion of the absorption cross section, simple analytical formulae are given for the angular dependence of the electric dipole and quadrupole contributions to XAS for all crystal point groups. These formulae are valid down to the edge and include many-body effects. The are applied to two experimental examples, the iron K-edge in haematite and the copper K-edge in CuCl42-. For the latter case, spherical tensor components are interpreted in terms of molecular orbitals. The influence of unpolarised and circularly polarised X-rays is discussed, as well as various experimental problems met in angle-resolved XAS. In an appendix, the quadrupole contribution to angular XAS is derived within the multiple-scattering formalism, along with closed expressions for the dipole and quadrupole spherical tensor components.

Runge-Kutta methods and renormalization

Abstract. Rooted trees have been used to calculate the solution of nonlinear flow equations and Runge–Kutta methods. More recently, rooted trees have helped systematizing the algebra underlying renormalization in quantum field theories. The Butcher group and B-series establish a link between these two approaches to rooted trees. On the one hand, this link allows for an alternative representation of the algebra of renormalization, leading to nonperturbative results. On the other hand, it helps to renormalize singular flow equations. The usual approach is extended here to nonlinear partial differential equations. A nonlinear Born expansion is given, and renormalization is used to partly remove the secular terms of the perturbative expansion.

Exponential localization of Wannier functions in insulators

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.

Angular dependence of core hole screening in LiCoO2: A DFT + U calculation of the oxygen and cobalt K-edge x-ray absorption spectra

Angular-dependent core hole screening effects have been found in the cobalt K-edge x-ray absorption spectrum of LiCoO2, using high-resolution data and parameter-free general gradient approximation plus U calculations. The Co 1s core hole on the absorber causes strong local attraction. The core hole screening on the cobalt nearest-neighbors induces a 2 eV shift in the density of states with respect to the on-site 1s-3d transitions, as detected in the Co K pre-edge spectrum. Our density functional theory plus U calculations reveal that the off-site screening is different in the out-of-plane direction, where a 3 eV shift is visible in both calculations and experiment. The detailed analysis of the inclusion of the core hole potential and the Hubbard parameter U shows that the core hole is essential for the off-site screening while U improves the description of the angular-dependent screening effects. In the case of oxygen K edge, both the core hole potential and the Hubbard parameter improve the relative positions of the spectral features.

QED Hopf algebras on planar binary trees

Abstract In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some semi-direct coproduct of Hopf algebras.

X-ray natural circular dichroism in a uniaxial gyrotropic single crystal of LiIO3

We produce the first experimental evidence of x-ray natural circular dichroism (XNCD) in a uniaxial gyrotropic crystal of α-LiIO3 that is known to crystallize with space group P63 and to exhibit a very strong nonlinear susceptibility. For the sake of simplicity, the optical axis was set colinear to the direction of the exciting x-ray beam in order to get rid of undesirable birefringence and linear dichroism effects. The nicely structured XNCD spectra recorded at the LI, LII, and LIII edges of iodine are assigned to the electric dipole–electric quadrupole (E1.E2) interference terms which do not vanish in gyrotropic crystals but contribute to a second order polarizability. Our interpretation is consistent with a band structure calculation and is fully supported by ab initio multiple scattering simulations. The signatures recorded at the LII and LIII edges are similar and have the same sign. This is in contrast to x-ray magnetic circular dichroism (XMCD) spectra which usually exhibit opposite signs at the LI...

X-ray Linear Dichroism in cubic compounds: the case of Cr3+ in MgAl2O4

The angular dependence (x-ray linear dichroism) of the

Quantum field theory and Hopf algebra cohomology

\text{Cr}\text{ }K

Renormalization of QED with planar binary trees

pre-edge in

Experimental evidence of thermal fluctuations on the X-ray absorption near-edge structure at the aluminum K-edge

{\text{MgAl}}_{2}{\text{O}}_{4}:{\text{Cr}}^{3+}