Showing 1–30 of 30 results for author: Brouder, C

Representations of the symmetry groups of infinite crystals

Authors: Bachir Bekka, Christian Brouder

Abstract: We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a finite set of points. However, to deal with the continuous crystal momentum $\mathbf{k}$ required to discuss the continuity, singularity or analyticity of band e… ▽ More We investigate the representations of the symmetry groups of infinite crystals. Crystal symmetries are usually described as the finite symmetry group of a finite crystal with periodic boundary conditions, for which the Brillouin zone is a finite set of points. However, to deal with the continuous crystal momentum $\mathbf{k}$ required to discuss the continuity, singularity or analyticity of band energies $ε_n(\mathbf{k})$ and Bloch states $ψ_{\mathbf{k}}$, we need to consider infinite crystals. The symmetry groups of infinite crystals belong to the category of infinite non-compact groups, for which many standard tools of group theory break down. For example, character theory is no longer available for these groups and we use harmonic analysis to build the group algebra, the regular representation, the induction of irreducible representations of the crystallographic group from projective representations of the point groups and the decomposition of a representation into its irreducible parts. We deal with magnetic and non-magnetic groups in arbitrary dimensions. In the last part of the paper, we discuss Mackey's restriction of an induced representation to a subgroup, the tensor product of induced representations and the symmetric and antisymmetric squares of induced representations. △ Less

Submitted 24 December, 2025; originally announced December 2025.

Comments: 27 pages

Angular dependence and powder average of resonant inelastic X-ray scattering

Authors: Myrtille O. J. Y Hunault, Timothy G. Burrow, Fabien Besnard, Amélie Juhin, Christian Brouder

Abstract: Resonant Inelastic X-ray scattering (RIXS) is a synchrotron-based spectroscopy that has seen growing interest across a range of scientific disciplines beyond fundamental physics. The interpretation of experimental RIXS data requires theoretical calculations based on the Kramers-Heisenberg formula. However, due to the dependence of RIXS on both the incident and scattered photon properties, a tracta… ▽ More Resonant Inelastic X-ray scattering (RIXS) is a synchrotron-based spectroscopy that has seen growing interest across a range of scientific disciplines beyond fundamental physics. The interpretation of experimental RIXS data requires theoretical calculations based on the Kramers-Heisenberg formula. However, due to the dependence of RIXS on both the incident and scattered photon properties, a tractable treatment of the angular dependence in this formula has been lacking. In this work, within the electric dipole approximation, we determine the number of fundamental spectra contributing to the RIXS cross-section for all crystallographic point groups. We then derive a general expression for the RIXS cross-section of isotropic samples such as un-textured powders, homogeneous glasses or liquids, explicitly accounting for the polarization and propagation directions of both the incident and scattered photons. Simplified forms of the RIXS expressions are subsequently obtained for most common point groups. Finally, we demonstrate the applicability of our formalism through a case study of uranium 3d4f RIXS. △ Less

Submitted 23 October, 2025; originally announced October 2025.

Comments: 22 pages

Parametrization of the Coulomb interaction matrix with point-group symmetry

Authors: Coraline Letouzé, Guillaume Radtke, Benjamin Lenz, Christian Brouder

Abstract: Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure of strongly correlated materials. In this paper, Coulomb integrals are analyzed by considering both the point group symmetry of the site occupied by the atom in… ▽ More Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure of strongly correlated materials. In this paper, Coulomb integrals are analyzed by considering both the point group symmetry of the site occupied by the atom in the crystal or molecule and the permutation symmetries of the orbitals in the integrals. In particular, the case where one-electron orbitals form the basis of a general (i.e. a real, complex or pseudo-complex) irreducible representation is considered. Explicit formulas are provided to calculate all integrals of the interaction tensor in terms of a minimum set of independent ones. The effect of a symmetry breaking is also investigated by describing Coulomb integrals of a group in terms of those of one of its subgroups. We develope the specific example of O(3) as the larger group which can therefore be used to quantify the deviation of a specific system from the spherical symmetry. Possible applications of the presented framework include the calculation of solid-state and molecular spectroscopies via multiplet techniques, dynamical mean-field theory or the GW approximation. △ Less

Submitted 16 June, 2023; originally announced June 2023.

Comments: 14 pages, 1 figure

Fermi resonance in the Raman spectrum of graphene

Authors: Dipankar Kalita, Michele Amato, Alexandre Artaud, Laëtitia Marty, Vincent Bouchiat, Johann Coraux, Christian Brouder, Michele Lazzeri, Nedjma Bendiab

Abstract: We report the observation of an intense anomalous peak at 1608 cm$^{-1}$ in the Raman spectrum of graphene associated to the presence of chromium nanoparticles in contact with graphene. Bombardment with an electron beam demonstrates that this peak is distinct from the well studied D$'$ peak appearing as defects are created in graphene; the new peak is found non dispersive. We argue that the bondin… ▽ More We report the observation of an intense anomalous peak at 1608 cm$^{-1}$ in the Raman spectrum of graphene associated to the presence of chromium nanoparticles in contact with graphene. Bombardment with an electron beam demonstrates that this peak is distinct from the well studied D$'$ peak appearing as defects are created in graphene; the new peak is found non dispersive. We argue that the bonding of chromium atoms with carbon atoms softens the out-of-plane optical (ZO) phonon mode, in such a way that the frequency of its overtone decreases to $2ω_{\rm ZO}\simω_{\rm G}$, where $ω_{\rm G}$=1585~cm$^{-1}$ is the frequency of the Raman-active E$_{\rm 2g}$ mode. Thus, the observed new peak is attributed to the 2ZO mode which becomes Raman-active following a mechanism known as Fermi resonance. First-principles calculations on vibrational and anharmonic properties of the graphene/Cr interface support this scenario. △ Less

Submitted 18 November, 2020; originally announced November 2020.

Comments: 12 pages, 10 figures

Journal ref: Phys. Rev. B 102, 075436 (2020)

X-ray Magnetic and Natural Circular Dichroism from first principles: Calculation of K- and L1-edge spectra

Authors: N. Bouldi, N. J. Vollmers, C. G. Delpy-Laplanche, Y. Joly, A. Juhin, Ph. Sainctavit, Ch. Brouder, M. Calandra, L. Paulatto, F. Mauri, U. Gerstmann

Abstract: An efficient first principles approach to calculate X-ray magnetic circular dichroism (XMCD) and X-ray natural circular dichroism (XNCD) is developed and applied in the near edge region at the K-and L1-edges in solids. Computation of circular dichroism requires precise calculations of X-ray absorption spectra (XAS) for circularly polarized light. For the derivation of the XAS cross section, we use… ▽ More An efficient first principles approach to calculate X-ray magnetic circular dichroism (XMCD) and X-ray natural circular dichroism (XNCD) is developed and applied in the near edge region at the K-and L1-edges in solids. Computation of circular dichroism requires precise calculations of X-ray absorption spectra (XAS) for circularly polarized light. For the derivation of the XAS cross section, we used a relativistic description of the photon-electron interaction that results in an additional term in the cross-section that couples the electric dipole operator with an operator $\mathbfσ\cdot (\mathbfε \times \mathbf{r})$ that we name spin-position. The numerical method relies on pseudopotentials, on the gauge including projected augmented wave method and on a collinear spin relativistic description of the electronic structure. We apply the method to the calculations of K-edge XMCD spectra of ferromagnetic iron, cobalt and nickel and of I L1-edge XNCD spectra of $α$-LiIO3, a compound with broken inversion symmetry. For XMCD spectra we find that, even if the electric dipole term is the dominant one, the electric quadrupole term is not negligible (8% in amplitude in the case of iron). The term coupling the electric dipole operator with the spin-position operator is significant (28% in amplitude in the case of iron). We obtain a sum-rule relating this new term to the spin magnetic moment of the p-states. In $α$-LiIO3 we recover the expected angular dependence of the XNCD spectra. △ Less

Submitted 5 May, 2017; originally announced May 2017.

Journal ref: Phys. Rev. B 96, 085123 (2017)

Gauge invariance and relativistic effects in photon absorption and scattering by matter

Authors: Nadejda Bouldi, Christian Brouder

Abstract: There is an incompatibility between gauge invariance and the semi-classical time-dependent perturbation theory commonly used to calculate light absorption and scattering cross-sections. There is an additional incompatibility between perturbationtheory and the description of the electron dynamics by a semi-relativistic Hamiltonian.In this paper, the gauge-dependence problem of exact perturbation th… ▽ More There is an incompatibility between gauge invariance and the semi-classical time-dependent perturbation theory commonly used to calculate light absorption and scattering cross-sections. There is an additional incompatibility between perturbationtheory and the description of the electron dynamics by a semi-relativistic Hamiltonian.In this paper, the gauge-dependence problem of exact perturbation theory is described, the proposed solutions are reviewed and it is concluded that none of them seems fully satisfactory. The problem is finally solved by using the fully relativistic absorption and scattering cross-sections given by quantum electrodynamics. Then, a new many-body Foldy-Wouthuysen transformation is presented to obtain correct semi-relativistic transition operators.This transformation considerably simplifies the calculation of relativistic corrections. In the process, a new light-matter interaction term emerges, called the spin-position interaction, that contributes significantly to the magnetic x-ray circular dichroism of transition metals.We compare our result with the ones obtained by using several semi-relativistic time-dependent Hamiltonians. In the case of absorption, the final formula agrees with the result obtained from one of them. However, the correct scattering cross-section is not given by any of the semi-relativistic Hamiltonians. △ Less

Submitted 7 April, 2017; v1 submitted 19 October, 2016; originally announced October 2016.

Comments: The plan of the paper has been modified to make it more pedagogical

Phonon effects on x-ray absorption and nuclear magnetic resonance spectroscopies

Authors: Ruidy Nemausat, Delphine Cabaret, Christel Gervais, Christian Brouder, Nicolas Trcera, Amélie Bordage, Ion Errea, Francesco Mauri

Abstract: In material sciences, spectroscopic approaches combining ab initio calculations with experiments are commonly used to accurately analyze the experimental spectral data. Most state-of-the-art first-principle calculations are usually performed assuming an equilibrium static lattice. Yet, nuclear motion affects spectra even when reduced to the zero-point motion at 0 K. We propose a framework based on… ▽ More In material sciences, spectroscopic approaches combining ab initio calculations with experiments are commonly used to accurately analyze the experimental spectral data. Most state-of-the-art first-principle calculations are usually performed assuming an equilibrium static lattice. Yet, nuclear motion affects spectra even when reduced to the zero-point motion at 0 K. We propose a framework based on Density-Functional Theory that includes quantum thermal fluctuations in theoretical X- ray Absorption Near-Edge Structure (XANES) and solid-state Nuclear Magnetic Resonance (NMR) spectroscopies and allows to well describe temperature effects observed experimentally. Within the Born-Oppenheimer and quasi-harmonic approximations, we incorporate the nuclear motion by generating several non-equilibrium configurations from the dynamical matrix. The averaged calculated XANES and NMR spectral data have been compared to experiments in MgO, proof-of-principle compound. The good agreement obtained between experiments and calculations validates the developed approach, which suggests that calculating the XANES spectra at finite temperature by averaging individual non-equilibrium configurations is a suitable approximation. This study high- lights the relevance of phonon renormalization and the relative contributions of thermal expansion and nuclear dynamics on NMR and XANES spectra on a wide range of temperatures. △ Less

Submitted 17 September, 2015; originally announced September 2015.

Comments: 13 pages, 6 figures, 1 appendix

Journal ref: Phys. Rev. B 92, 144310 (2015)

Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

Authors: Amélie Juhin, Christian Brouder, Frank De Groot

Abstract: A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit… ▽ More A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected. △ Less

Submitted 19 May, 2014; v1 submitted 20 February, 2013; originally announced February 2013.

Journal ref: Central European Journal of Physics 12, 5 (2014) 323

K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects

Authors: M. Calandra, J. P. Rueff, C. Gougoussis, D. Ceolin, M. Gorgoi, S. Benedetti, P. Torelli, A. Shukla, D. Chandesris, Ch. Brouder

Abstract: The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS) is a widely used tool for studying electronic and local structure in materials. The precise interpretation of these spectra with the help of calculations is hence of prime importance, especially for the study of correlated materials which have a complicated electronic structure per se. The single particle approach, for e… ▽ More The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS) is a widely used tool for studying electronic and local structure in materials. The precise interpretation of these spectra with the help of calculations is hence of prime importance, especially for the study of correlated materials which have a complicated electronic structure per se. The single particle approach, for example, has generally limited itself to the dominant dipolar cross-section. It has long been known however that effects beyond this approach should be taken into account, both due to the inadequacy of such calculations when compared to experiment and the presence of shake-up many-body satellites in core-level photoemission spectra of correlated materials. This effect should manifest itself in XANES spectra and the question is firstly how to account for it theoretically and secondly how to verify it experimentally. By using state-of-the-art first principles electronic structure calculations and 1s photoemission measurements we demonstrate that shake-up many-body effects are present in K-edge XAS dipolar spectra of NiO, CoO and CuO at all energy scales. We show that shake-up effects can be included in K-edge XAS spectra in a simple way by convoluting the single-particle first-principles calculations including core-hole effects with the 1s photoemission spectra. We thus describe all features appearing in the XAS dipolar cross-section of NiO and CoO and obtain a dramatic improvement with respect to the single-particle calculation in CuO. These materials being prototype correlated magnetic oxides, our work points to the presence of shake-up effects in K-edge XANES of most correlated transition metal compounds and shows how to account for them, paving the way to a precise understanding of their electronic structure. △ Less

Submitted 19 June, 2012; originally announced June 2012.

Comments: 6 pages, 4 pictures

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

Authors: Damien Manuel, Delphine Cabaret, Christian Brouder, Philippe Sainctavit, Amélie Bordage, Nicolas Trcera

Abstract: After a review of temperature-dependent experimental x-ray absorption near-edge structure (XANES) and related theoretical developments, we present the Al K-edge XANES spectra of corundum and beryl for temperature ranging from 300K to 930K. These experimental results provide a first evidence of the role of thermal fluctuation in XANES at the Al K-edge especially in the pre-edge region. The study is… ▽ More After a review of temperature-dependent experimental x-ray absorption near-edge structure (XANES) and related theoretical developments, we present the Al K-edge XANES spectra of corundum and beryl for temperature ranging from 300K to 930K. These experimental results provide a first evidence of the role of thermal fluctuation in XANES at the Al K-edge especially in the pre-edge region. The study is carried out by polarized XANES measurements of single crystals. For any orientation of the sample with respect to the x-ray beam, the pre-edge peak grows and shifts to lower energy with temperature. In addition temperature induces modifications in the position and intensities of the main XANES features. First-principles DFT calculations are performed for both compounds. They show that the pre-edge peak originates from forbidden 1s to 3s transitions induced by vibrations. Three existing theoretical models are used to take vibrations into account in the absorption cross section calculations: i) an average of the XANES spectra over the thermal displacements of the absorbing atom around its equilibrium position, ii) a method based on the crude Born-Oppenheimer approximation where only the initial state is averaged over thermal displacements, iii) a convolution of the spectra obtained for the atoms at the equilibrium positions with an approximate phonon spectral function. The theoretical spectra so obtained permit to qualitatively understand the origin of the spectral modifications induced by temperature. However the correct treatment of thermal fluctuation in XANES spectroscopy requires more sophisticated theoretical tools. △ Less

Submitted 21 March, 2012; originally announced March 2012.

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

Authors: Amélie Juhin, Frank De Groot, György Vankó, Matteo Calandra, Christian Brouder

Abstract: 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 GGA+U calculations. The Co 1s core-hole on the absorber causes strong local attraction. The core-hole screening on the nearest neighbours cobalt induces a 2 eV shift in the density of states with respect to the on-site 1s-3d transit… ▽ More 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 GGA+U calculations. The Co 1s core-hole on the absorber causes strong local attraction. The core-hole screening on the nearest neighbours cobalt 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 DFT+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. △ Less

Submitted 15 December, 2009; originally announced December 2009.

Temperature dependence of the pre-edge structure in the Ti K-edge x-ray absorption spectrum of rutile

Authors: Olivier Durmeyer, Eric Beaurepaire, Jean-Paul Kappler, Christian Brouder, François Baudelet

Abstract: The temperature dependence of the pre-edge features in x-ray absorption spectroscopy is reviewed. Then, the temperature dependence of the pre-edge structure at the K-edge of titanium in rutile TiO2 is measured at low and room temperature. The first two peaks grow with temperature. The fact that these two peaks also correspond to electric quadrupole transitions is explained by a recently proposed… ▽ More The temperature dependence of the pre-edge features in x-ray absorption spectroscopy is reviewed. Then, the temperature dependence of the pre-edge structure at the K-edge of titanium in rutile TiO2 is measured at low and room temperature. The first two peaks grow with temperature. The fact that these two peaks also correspond to electric quadrupole transitions is explained by a recently proposed theory. △ Less

Submitted 12 December, 2009; originally announced December 2009.

Comments: 11 pages, 2 figures

Journal ref: Journal of Physics: Condensed Matter 22, 12 (2010) 125504

Effect of vibrations on the pre-edge features of x-ray absorption spectra

Authors: Christian Brouder, Delphine Cabaret, Amélie Juhin, Philippe Sainctavit

Abstract: The influence of atomic vibrations on x-ray absorption near edge structure (XANES) is calculated by assuming that vibrational energies are small with respect to the instrumental resolution. The resulting expression shows that, at the K-edge, vibrations enable electric dipole transitions to 3s and 3d final states. The theory is applied to the K-edge of Al in Al2O3 corundum and of Ti in TiO2 rutil… ▽ More The influence of atomic vibrations on x-ray absorption near edge structure (XANES) is calculated by assuming that vibrational energies are small with respect to the instrumental resolution. The resulting expression shows that, at the K-edge, vibrations enable electric dipole transitions to 3s and 3d final states. The theory is applied to the K-edge of Al in Al2O3 corundum and of Ti in TiO2 rutile and compared with experiment. At the Al K-edge, sizeable transitions towards 3s final states are obtained, leading to a clear improvement of the agreement with experimental spectra. At the Ti K-edge, electric dipole transitions towards 3d final states explain the temperature dependence of the pre-edge features. △ Less

Submitted 4 December, 2009; originally announced December 2009.

Comments: 4 pages, 2 figures

Journal ref: Physical Review B 81, 11 (2010) 115125

Tree expansion in time-dependent perturbation theory

Authors: Christian Brouder, Ângela Mestre, Frédéric Patras

Abstract: The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type diagrams...). We show that a very efficient perturbative expansion, both for theoretical and numerical purposes, can be obtained through an original parametrization by tr… ▽ More The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type diagrams...). We show that a very efficient perturbative expansion, both for theoretical and numerical purposes, can be obtained through an original parametrization by trees and generalized iterated integrals. We emphasize above all the simplicity and naturality of the new approach that links perturbation theory with classical and recent results in enumerative and algebraic combinatorics. These tools are applied to the adiabatic approximation and the effective Hamiltonian. We prove perturbatively and non-perturbatively the convergence of Morita's generalization of the Gell-Mann and Low wavefunction. We show that summing all the terms associated to the same tree leads to an utter simplification where the sum is simpler than any of its terms. Finally, we recover the time-independent equation for the wave operator and we give an explicit non-recursive expression for the term corresponding to an arbitrary tree. △ Less

Submitted 26 May, 2010; v1 submitted 27 November, 2009; originally announced November 2009.

Comments: 22 pages, 2 figures

Journal ref: Journal of Mathematical Physics 51, 7 (2010) 072104

The many-body Green function of degenerate systems

Authors: Christian Brouder, Gianluca Panati, Gabriel Stoltz

Abstract: A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0 V P0, where P0 is the projection onto a degenerate eigenspa… ▽ More A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0 leading to eigenstates of H0+V for degenerate systems. These initial states are eigenstates of P0 V P0, where P0 is the projection onto a degenerate eigenspace of H0. This result is used to give the proper definition of the Green function, the statistical Green function and the non-equilibrium Green function of degenerate systems. The convergence of these Green functions is established. △ Less

Submitted 31 October, 2009; v1 submitted 11 June, 2009; originally announced June 2009.

Comments: 4 pages, 1 figure

Journal ref: Physical Review Letters 103, 23 (2009) 230401

Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example

Authors: Christian Brouder, Gabriel Stoltz, Gianluca Panati

Abstract: We study a simple system described by a 2x2 Hamiltonian and the evolution of the quantum states under the influence of a perturbation. More precisely, when the initial Hamiltonian is not degenerate,we check analytically the validity of the adiabatic approximation and verify that, even if the evolution operator has no limit for adiabatic switchings, the Gell-Mann and Low formula allows to follow… ▽ More We study a simple system described by a 2x2 Hamiltonian and the evolution of the quantum states under the influence of a perturbation. More precisely, when the initial Hamiltonian is not degenerate,we check analytically the validity of the adiabatic approximation and verify that, even if the evolution operator has no limit for adiabatic switchings, the Gell-Mann and Low formula allows to follow the evolution of eigenstates. In the degenerate case, for generic initial eigenstates, the adiabatic approximation (obtained by two different limiting procedures) is either useless or wrong, and the Gell-Mann and Low formula does not hold. We show how to select initial states in order to avoid such failures. △ Less

Submitted 26 July, 2008; originally announced July 2008.

Comments: 6 pages, 2 figures

Journal ref: Phys.Rev.A78:042102,2008

Measuring the intrinsic charge transfer gap using K-edge X-ray absorption spectroscopy

Authors: C. Gougoussis, M. Calandra, A. Seitsonen, Ch. Brouder, A. Shukla, F. Mauri

Abstract: Pre-edge features in X-ray absorption spectroscopy contain key information about the lowest excited states and thus on the most interesting physical properties of the system. In transition metal oxides they are particularly structured but extracting physical parameters by comparison with a calculation is not easy due to several computational challenges. By combining core-hole attraction and corr… ▽ More Pre-edge features in X-ray absorption spectroscopy contain key information about the lowest excited states and thus on the most interesting physical properties of the system. In transition metal oxides they are particularly structured but extracting physical parameters by comparison with a calculation is not easy due to several computational challenges. By combining core-hole attraction and correlation effects in first principles approach, we calculate Ni K-edge X-ray absorption spectra in NiO. We obtain a striking, parameter-free agreement with experimental data and show that dipolar pre-edge features above the correlation gap are due to non-local excitations largely unaffected by the core-hole. We show that in charge transfer insulators, this property can be used to measure the correlation gap and probe the intrinsic position of the upper-Hubbard band. △ Less

Submitted 28 June, 2008; originally announced June 2008.

Comments: 4 pages, 3 figures

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

Authors: Amélie Juhin, Christian Brouder, Marie-Anne Arrio, Delphine Cabaret, Philippe Sainctavit, Etienne Balan, Amélie Bordage, Georges Calas, Sigrid G. Eeckhout, Pieter Glatzel

Abstract: The angular dependence (x-ray linear dichroism) of the Cr K pre-edge in MgAl2O4:Cr3+ spinel is measured by means of x-ray absorption near edge structure spectroscopy (XANES) and compared to calculations based on density functional theory (DFT) and ligand field multiplet theory (LFM). We also present an efficient method, based on symmetry considerations, to compute the dichroism of the cubic crys… ▽ More The angular dependence (x-ray linear dichroism) of the Cr K pre-edge in MgAl2O4:Cr3+ spinel is measured by means of x-ray absorption near edge structure spectroscopy (XANES) and compared to calculations based on density functional theory (DFT) and ligand field multiplet theory (LFM). We also present an efficient method, based on symmetry considerations, to compute the dichroism of the cubic crystal starting from the dichroism of a single substitutional site. DFT shows that the electric dipole transitions do not contribute to the features visible in the pre-edge and provides a clear vision of the assignment of the 1s-->3d transitions. However, DFT is unable to reproduce quantitatively the angular dependence of the pre-edge, which is, on the other side, well reproduced by LFM calculations. The most relevant factors determining the dichroism of Cr K pre-edge are identified as the site distortion and 3d-3d electronic repulsion. From this combined DFT, LFM approach is concluded that when the pre-edge features are more intense than 4 % of the edge jump, pure quadrupole transitions cannot explain alone the origin of the pre-edge. Finally, the shape of the dichroic signal is more sensitive than the isotropic spectrum to the trigonal distortion of the substitutional site. This suggests the possibility to obtain quantitative information on site distortion from the x-ray linear dichroism by performing angular dependent measurements on single crystals. △ Less

Submitted 10 June, 2008; originally announced June 2008.

Site symmetry and crystal symmetry: a spherical tensor analysis

Authors: Christian Brouder, Amélie Juhin, Amélie Bordage, Marie-Anne Arrio

Abstract: The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the… ▽ More The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet. △ Less

Submitted 3 June, 2008; originally announced June 2008.

Comments: 27 pages, 3 figures

Journal ref: Journal of Physics: Condensed Matter 20, 45 (2008) 455205

One-particle irreducibility with initial correlations

Authors: Christian Brouder, Frédéric Patras

Abstract: In quantum field theory (QFT), the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This simple property paves the way to the classical treatment of perturbative QFT. This is no longer the case in the presence of initial correlations, that is if the vacuum is replaced by a general state. As a consequence, the combinatorics of correlated systems su… ▽ More In quantum field theory (QFT), the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This simple property paves the way to the classical treatment of perturbative QFT. This is no longer the case in the presence of initial correlations, that is if the vacuum is replaced by a general state. As a consequence, the combinatorics of correlated systems such as the ones occurring in many-body physics is more complex than that of quantum field theory and the general theory has made very slow progress. Similar observations hold in statistical physics or quantum probability for the perturbation series arising from the study of non Gaussian measures. In this work, an analysis of the Hopf algebraic aspects of quantum field theory is used to derive the structure of Green functions in terms of connected and one-particle irreducible Greeen functions for perturbative QFT in the presence of initial correlations. △ Less

Submitted 7 January, 2011; v1 submitted 26 March, 2008; originally announced March 2008.

Comments: 22 pages, 2 figures, slightly edited version of the published paper

Exponential localization of Wannier functions in insulators

Authors: Christian Brouder, Gianluca Panati, Matteo Calandra, Christophe Mourougane, Nicola Marzari

Abstract: 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… ▽ More 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. △ Less

Submitted 7 March, 2007; v1 submitted 28 June, 2006; originally announced June 2006.

Comments: Four pages, two figures

Journal ref: Physical Review Letters 98 (01/2007) 046402

A differential identity for Green functions

Authors: Christian Brouder

Abstract: If P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a hierarchy of Green functions. The identity is first derived for scalar fields and the standard hierarchy is recovered. Then the case of fermions is considered an… ▽ More If P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a hierarchy of Green functions. The identity is first derived for scalar fields and the standard hierarchy is recovered. Then the case of fermions is considered and the identity is used to calculate the generating function for the Green functions of an electron system in a time-dependent external potential. △ Less

Submitted 15 February, 2006; originally announced February 2006.

Comments: 14 pages

Journal ref: Journal of Mathematical Chemistry 44, 4 (2008) 918-937

Boundary conditions for augmented plane wave methods

Authors: Christian Brouder

Abstract: The augmented plane wave method uses the Rayleigh-Ritz principle for basis functions that are continuous but with discontinuous derivatives and the kinetic energy is written as a pair of gradients rather than as a Laplacian. It is shown here that this procedure is fully justified from the mathematical point of view. The domain of the self-adjoint Hamiltonian, which does not contain functions wit… ▽ More The augmented plane wave method uses the Rayleigh-Ritz principle for basis functions that are continuous but with discontinuous derivatives and the kinetic energy is written as a pair of gradients rather than as a Laplacian. It is shown here that this procedure is fully justified from the mathematical point of view. The domain of the self-adjoint Hamiltonian, which does not contain functions with discontinuous derivatives, is extended to its form domain, which contains them, and this modifies the form of the kinetic energy. Moreover, it is argued that discontinuous basis functions should be avoided. △ Less

Submitted 21 March, 2005; originally announced March 2005.

Comments: 5 pages, no figure

Structural relaxations around Ti, Cr and Fe impurities in alpha-Al2O3 probed by x-ray absorption near edge structure combined with first-principles calculations

Authors: Emilie Gaudry, Delphine Cabaret, Philippe Sainctavit, Christian Brouder, Francesco Mauri, José Goulon, Andrei Rogalev

Abstract: We determine the structural relaxations around paramagnetic impurities (Ti, Cr, Fe) in corundum (alpha-Al2O3), by combining x-ray absorption near edge structure (XANES) experiments and ab initio calculations. The structural relaxations are found to be very local. We then show that XANES is sensitive to small variations in interatomic distances within the coordination shell of the absorbing atom.… ▽ More We determine the structural relaxations around paramagnetic impurities (Ti, Cr, Fe) in corundum (alpha-Al2O3), by combining x-ray absorption near edge structure (XANES) experiments and ab initio calculations. The structural relaxations are found to be very local. We then show that XANES is sensitive to small variations in interatomic distances within the coordination shell of the absorbing atom. The experiments were carried out on single crystals of ruby and sapphires. Linear dichroic signals are essential to characterize the geometry of the impurity site. The calculations were performed within a self-consistent ``non muffin-tin'' framework, that uses pseudopotentials, plane-wave basis set, and the continued fraction for the absorption cross section. △ Less

Submitted 12 January, 2005; originally announced January 2005.

Many-body theory of degenerate systems: A simple example

Authors: Christian Brouder

Abstract: The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy is derived explicitly, in terms of Green functions and of Feynman diagrams. The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy is derived explicitly, in terms of Green functions and of Feynman diagrams. △ Less

Submitted 5 December, 2003; originally announced December 2003.

Comments: 9 pages, 1 figure

Many-body theory of degenerate systems

Authors: Christian Brouder

Abstract: The many-body theory of degenerate systems is described in detail. More generally, this theory applies to systems with an initial state that cannot be described by a single Slater determinant. The double-source (or closed-time-path) formalism of nonequilibrium quantum field theory is used to derive an expression for the average value of a product of interacting fields when the initial state is n… ▽ More The many-body theory of degenerate systems is described in detail. More generally, this theory applies to systems with an initial state that cannot be described by a single Slater determinant. The double-source (or closed-time-path) formalism of nonequilibrium quantum field theory is used to derive an expression for the average value of a product of interacting fields when the initial state is not the vacuum or a Slater determinant. Quantum group techniques are applied to derive the hierarchy of unconnected Green functions and the hierarchy of connected ones. △ Less

Submitted 9 December, 2003; v1 submitted 24 September, 2003; originally announced September 2003.

Comments: 27 pages

A many-body approach to crystal field theory

Authors: Christian Brouder

Abstract: A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function of the density matrix of the noninteracting system. A variation of the energy with respect to the density matrix gives an effective Hamiltonian that is diago… ▽ More A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function of the density matrix of the noninteracting system. A variation of the energy with respect to the density matrix gives an effective Hamiltonian that is diagonalized to determine the density matrix providing the lowest energy. The equations are written in terms of the Hopf algebra of functional derivatives with respect to external fermionic sources. This approach contains the many-body theory of Green functions as a special case, and the usual crystal field theory as a first approximation. Therefore, it is expected to provide good results for strongly-interacting electron systems. △ Less

Submitted 3 October, 2003; v1 submitted 4 August, 2003; originally announced August 2003.

Comments: Equation (8) and references are corrected

Journal ref: physica status solidi (c) 2 (2005) 472-475

Multiple plasmon resonances in naturally-occurring multiwall nanotubes: infrared spectra of chrysotile asbestos

Authors: Etienne Balan, Francesco Mauri, Celine Lemaire, Christian Brouder, Francois Guyot, A. Marco Saitta, Bertrand Devouard

Abstract: Chrysotile asbestos is formed by densely packed bundles of multiwall hollow nanotubes. Each wall in the nanotubes is a cylindrically wrapped layer of $Mg_3 Si_2 O_5 (OH)_4$. We show by experiment and theory that the infrared spectrum of chrysotile presents multiple plasmon resonances in the Si-O stretching bands. These collective charge excitations are universal features of the nanotubes that ar… ▽ More Chrysotile asbestos is formed by densely packed bundles of multiwall hollow nanotubes. Each wall in the nanotubes is a cylindrically wrapped layer of $Mg_3 Si_2 O_5 (OH)_4$. We show by experiment and theory that the infrared spectrum of chrysotile presents multiple plasmon resonances in the Si-O stretching bands. These collective charge excitations are universal features of the nanotubes that are obtained by cylindrically wrapping an anisotropic material. The multiple plasmons can be observed if the width of the resonances is sufficiently small as in chrysotile. △ Less

Submitted 22 May, 2002; v1 submitted 21 May, 2002; originally announced May 2002.

Comments: 4 pages, 5 figures. Revtex4 compuscript. Misprint in Eq.(6) corrected

Rare earth contributions to the X-ray magnetic circular dichroism at the Co K edge in rare earth-cobalt compounds investigated by multiple-scattering calculations

Authors: J. P. Rueff, R. M. Galera, Ch. Giorgetti, E. Dartyge, Ch. Brouder, M. Alouani

Abstract: The X-ray magnetic circular dichroism (XMCD) has been measured at the Co K edge in Co-hcp and R-Co compounds (R=La, Tb, Dy). The structure of the experimental XMCD spectra in the near-edge region has been observed to be highly sensitive to the magnetic environment of the absorbing site. Calculations of the XMCD have been carried out at the Co K edge in Co metal, LaCo$_5$ and TbCo$_5$ within the… ▽ More The X-ray magnetic circular dichroism (XMCD) has been measured at the Co K edge in Co-hcp and R-Co compounds (R=La, Tb, Dy). The structure of the experimental XMCD spectra in the near-edge region has been observed to be highly sensitive to the magnetic environment of the absorbing site. Calculations of the XMCD have been carried out at the Co K edge in Co metal, LaCo$_5$ and TbCo$_5$ within the multiple-scattering framework including the spin-orbit coupling. In the three systems, the XMCD spectra in the near-edge region are well reproduced. The possibility to separate and quantitatively estimate the local effects from those due to the neighboring atoms in the XMCD cross section makes possible a more physical understanding of the spectra. The present results emphasize the major role played by the $d$ states of the Tb ions in the XMCD spectrum at the Co K edge in the TbCo$_5$ compound. △ Less

Submitted 10 July, 1998; v1 submitted 5 May, 1998; originally announced May 1998.

Comments: 34 pages, revtex, 10 eps figures included with epsf, after referee review

Multiple-Scattering Theory of X-Ray Magnetic Circular Dichroism: Implementation and Results for Iron K-edge

Authors: Ch. Brouder, M. Alouani, K. H. Bennemann

Abstract: An implementation of the multiple-scattering approach to x-ray magnetic circular dichroism (XMCD) in K-edge x-ray absorption spectroscopy is presented. The convergence problems due to the cluster size and the relativistic corrections are solved using an expansion of the Dirac Green function for complex energies up to the second order in 1/$c$. The Fermi energy is dealt with via a complex plane i… ▽ More An implementation of the multiple-scattering approach to x-ray magnetic circular dichroism (XMCD) in K-edge x-ray absorption spectroscopy is presented. The convergence problems due to the cluster size and the relativistic corrections are solved using an expansion of the Dirac Green function for complex energies up to the second order in 1/$c$. The Fermi energy is dealt with via a complex plane integration. Numerical methods used to obtain the semi-relativistic Green function in the whole complex plane are explained. We present a calculation of the magnetic circular dichroism at the K-edge of bcc-iron including the core hole effect. A good agreement is found at high energy. The physical origins of the XMCD spectrum near the edge and far from the edge are analyzed. The influence of the core hole, the possibility of a multiple-scattering expansion and the relation of XMCD with the spin-polarized density of states are discussed. A simple interpretation of XMCD at the K-edge is presented in terms of a rigid-band model. △ Less

Submitted 5 June, 1996; originally announced June 1996.

Comments: 38 RevTex pages and 18 figs in a compressed and uufiled tar file; Phys. Rev. B (in press)