arXiv subjects

Lucia Reining

Publications and source records attributed to Lucia Reining.

At least 37 records · Page 2Linked to original sources

arXiv2018

Spectroscopy of the Hubbard dimer: the spectral potential

The spectral potential is the dynamical generalization of the Kohn-Sham potential. It targets, in principle exactly, the spectral function in addition to the electronic density. Here we examine the spectral potential in one of the simplest solvable models exhibiting a non-trivial interplay between electron-electron interaction and inhomogeneity, namely the asymmetric Hubbard dimer. We discuss a general strategy to introduce approximations, which consists in calculating the spectral potential in the homogeneous limit (here represented by the symmetric Hubbard dimer) and importing it in the real inhomogeneous system through a suitable "connector". The comparison of different levels of approximation to the spectral potential with the exact solution of the asymmetric Hubbard dimer gives insights about the advantages and the difficulties of this connector strategy for applications in real materials.

cond-mat.str-el↗

arXiv2018

Cubic BN optical gap and intragap optically active defects

We report a comprehensive study on the optical properties of cubic boron nitride (c-BN) and its optically active defects. Using electron energy-loss spectroscopy (EELS) within a monochromated scanning transmission electron microscope (STEM) on the highest-quality crystals available, we demonstrate unequivocally that the optical-gap energy of c-BN slightly exceeds 10 eV. Further theoretical analysis in the framework of the Bethe-Salpeter equation of many-body perturbation theory supports this result. The spatial localization of defect-related emissions has been investigated using nanometric resolved cathodoluminescence (nano-CL) in a STEM. By high-temperature annealing a c-BN powder, we have promoted phase transitions in nanometric domains which have been detected by the appearance of specific hexagonal-phase signatures in both EELS and CL spectra. A high number of intragap optically active centers are known in c-BN, but the literature is rather scattered and hence has been summarized here. For several emission lines we have obtained nano-CL maps which show emission spot sizes as small as few tens of nanometers. Finally, by coupling nano-CL to a Hanbury-Brown-Twiss intensity interferometer, we have addressed individual spots in order to identify the possible presence of single-photon sources. The observed CL bunching effect is compatible with a limited set of single-photon emitters and it permits obtaining emission lifetimes of the order of the nanosecond.

cond-mat.mtrl-sci↗

arXiv2017

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fröhlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $ε_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,ω)=-{\Im m}G_R(k,ω) /π$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fröhlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fröhlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fröhlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.

cond-mat.mtrl-sci↗

arXiv2017

Many-body perturbation theory and non-perturbative approaches: the screened interaction as key ingredient

Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Green's function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called 'one-point model') that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff-Baym equation for the one-body Green's function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.

cond-mat.str-el↗

arXiv2017

Non-local Coulomb interactions on the triangular lattice in the high-doping regime: Spectra and charge dynamics from Extended Dynamical Mean Field Theory

We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field Theory. We compute the low-temperature phase diagram, displaying a metallic phase and a symmetry-broken phase for strong intersite repulsions. We describe the correlation effects on both single-particle and two-particle observables in the metallic phase. Whereas single-particle spectra feature a Hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non-interacting limit, even for large on-site repulsions. We argue that this behaviour is typical of the strongly doped case. We also report a region in parameter space with negative static local screening.

cond-mat.str-el↗

arXiv2017

Cumulant Green's function calculations of plasmon satellites in bulk sodium: influence of screening and the crystal environment

We present ab initio calculations of the photoemission spectra of bulk sodium using different flavors of the cumulant expansion approximation for the Green's function. In particular, we study the dispersion and intensity of the plasmon satellites. We show that the satellite spectrum is much more sensitive to many details than the quasi-particle (QP) spectrum, which suggests that the experimental investigation of satellites could yield additional information beyond the usual studies of the band structure. In particular, a comparison to the homogeneous electron gas (HEG) shows that the satellites are influenced by the crystal environment, although the crystal potential in sodium is weak. Moreover, the temperature dependence of the lattice constant is reflected in the position of the satellites. Details of the screening also play an important role; in particular, the contribution of transitions from 2s and 2p semi-core levels influence the satellites, but not the QP. Moreover, inclusion of contributions to the screening beyond the RPA has an effect on the satellites. Finally, we elucidate the importance of the coupling of electrons and holes by comparing the results of the time-ordered (TOC) and the retarded (RC) cumulant expansion approximations. Again, we find small but noticeable differences. Since all the small effects add up, our most advanced calculation yields a satellite position which is improved with respect to previous calculations by almost one eV. This stresses the fact that the calculation of satellites is much more delicate than the calculation of a QP band structure.

cond-mat.str-el↗

arXiv2017

Dynamical local connector approximation for electron addition and removal spectra

Realistic calculations of electron addition and removal spectra rely most often on Green's functions and complex, non-local self-energies. We introduce a shortcut to obtain the spectral function directly from a local and frequency-dependent, yet real, potential. We calculate this potential in the homogeneous electron gas (HEG), and we design a connector which prescribes the use of the HEG results to calculate spectral functions of real materials. Benchmark results for several solids demonstrate the potential of our approach.

cond-mat.mtrl-sci↗

arXiv2017

The self-consistent Dyson equation and self-energy functionals: failure or new opportunities?

Perturbation theory using self-consistent Green's functions is one of the most widely used approaches to study many-body effects in condensed matter. On the basis of general considerations and by performing analytical calculations for the specific example of the Hubbard atom, we discuss some key features of this approach. We show that when the domain of the functionals that are used to realize the map between the non-interacting and the interacting Green's functions is properly defined, there exists a class of self-energy functionals for which the self-consistent Dyson equation has only one solution, which is the physical one. We also show that manipulation of the perturbative expansion of the interacting Green's function may lead to a wrong self-energy as functional of the interacting Green's function, at least for some regions of the parameter space. These findings confirm and explain numerical results of Kozik et al. for the widely used skeleton series of Luttinger and Ward [Phys. Rev. Lett. 114, 156402]. Our study shows that it is important to distinguish between the maps between sets of functions and the functionals that realize those maps. We demonstrate that the self-consistent Green's functions approach itself is not problematic, whereas the functionals that are widely used may have a limited range of validity.

cond-mat.str-el↗

arXiv2016

Photoemission Spectra from Reduced Density Matrices: the Band Gap in Strongly Correlated Systems

We present a method for the calculation of photoemission spectra in terms of reduced density matrices. We start from the spectral representation of the one-body Green's function G, whose imaginary part is related to photoemission spectra, and we introduce a frequency-dependent effective energy that accounts for all the poles of G. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong correlation regime. In real systems reduced density matrices can be obtained from reduced density-matrix functional theory. Here we use this approach to calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and paramagnetic phases, contrary to mean-field methods, in which the paramagnet is a metal.

cond-mat.str-el↗

arXiv2015

Exciton band structure in two-dimensional materials

Low-dimensional materials differ from their bulk counterpart in many respects. In particular, the screening of the Coulomb interaction is strongly reduced, which can have important consequences such as the significant increase of exciton binding energies. In bulk materials the binding energy is used as an indicator in optical spectra to distinguish different kinds of excitons, but this is not possible in low-dimensional materials, where the binding energy is large and comparable in size for excitons of very different localization. Here we demonstrate that the exciton band structure, which can be accessed experimentally, instead provides a powerful way to identify the exciton character. By comparing the ab initio solution of the many-body Bethe-Salpeter equation for graphane and single-layer hexagonal BN, we draw a general picture of the exciton dispersion in two-dimensional materials, highlighting the different role played by the exchange electron-hole interaction and by the electronic band structure. Our interpretation is substantiated by a prediction for phosphorene.

cond-mat.mtrl-sci↗

arXiv2015

Unphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation

Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of non-linear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green's function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green's function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.

cond-mat.mtrl-sci↗

arXiv2015

Estimating Excitonic Effects in the Absorption Spectra of Solids: Problems and Insight from a Guided Iteration Scheme

A major obstacle for computing optical spectra of solids is the lack of reliable approximations for capturing excitonic effects within time-dependent density-functional theory. We show that the trustful prediction of strongly bound electron-hole pairs within this framework using simple approximations is still a challenge and that available promising results have to be revisited. Deriving a set of analytical formula we analyze and explain the difficulties. We deduce an alternative approximation from an iterative scheme guided by previously available knowledge, significantly improving the description of exciton binding energies. Finally, we show how one can "read" exciton binding energies from spectra determined in the random phase approximation, without any further calculation.

cond-mat.mtrl-sci↗

arXiv2015

Reduced Density-Matrix Functional Theory: correlation and spectroscopy

In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard molecule at 1/4 and 1/2 filling as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison we also report the results of the $GW$ approximation, where the self-energy functional is approximated, but no further hypothesis are made concerning the approximations of the observables. In particular we focus on the atomic limit, where the two sites of the molecule are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard molecule at 1/2 filling with or without a spin-symmetry-broken ground state, allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in $GW$ the signature of strong correlation are present in the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover we show how the spectroscopic properties change from one spin structure to the other. Our findings can be generalized to other situations, which allows us to make connections to real materials and experiment.

cond-mat.str-el↗

arXiv2014

Excitons and stacking order in h-BN

The strong excitonic emission at 5.75 eV of hexagonal boron nitride (h-BN) makes this material one of the most promising candidate for light emitting devices in the far ultraviolet (UV). However, single excitons occur only in perfect monocrystals that are extremely hard to synthesize, while regular h-BN samples present a complex emission spectrum with several additional peaks. The microscopic origin of these additional emissions has not yet been understood. In this work we address this problem using an experimental and theoretical approach that combines nanometric resolved cathodoluminescence, high resolution transmission electron microscopy and state of the art theoretical spectroscopy methods. We demonstrate that emission spectra are strongly inhomogeneus within individual flakes and that additional excitons occur at structural deformations, such as faceted plane folds, that lead to local changes of the h-BN stacking order.

cond-mat.mtrl-sci↗

arXiv2012

Beyond the GW approximation: combining correlation channels

In many-body perturbation theory (MBPT) the self-energy Σ=iGWΓplays the key role since it contains all the many body effects of the system. The exact self-energy is not known; as first approximation one can set the vertex function Γto unity which leads to the GW approximation. The latter properly describes the high-density regime, where screening is important; in the low-density regime, instead, other approximations are proposed, such as the T matrix, which describes multiple scattering between two particles. Here we combine the two approaches. Starting from the fundamental equations of MBPT we show how one can derive the T-matrix approximation to the self-energy in a common framework with GW. This allows us to elucidate several aspects of this formulation, including the origin of, and link between, the electron-hole and the particle-particle T matrix, the derivation of a screened T matrix, and the conversion of the T matrix into a vertex correction. The exactly solvable Hubbard molecule is used for illustration.

cond-mat.str-el↗

arXiv2012

Approximations for many-body Green's functions: insights from the fundamental equations

Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. In the present work we apply a linear response expansion in order to obtain insights in various approximations for Green's functions calculations. The expansion leads to an effective screening, while keeping the effects of the interaction to all orders. In order to study various aspects of the resulting equations we discretize them, and retain only one point in space, spin, and time for all variables. Within this one-point model we obtain an explicit solution for the Green's function, which allows us to explore the structure of the general family of solutions, and to determine the specific solution that corresponds to the physical one. Moreover we analyze the performances of established approaches like $GW$ over the whole range of interaction strength, and we explore alternative approximations. Finally we link certain approximations for the exact solution to the corresponding manipulations for the differential equation which produce them. This link is crucial in view of a generalization of our findings to the real (multidimensional functional) case where only the differential equation is known.

cond-mat.str-el↗

arXiv2011

The valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites

The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellites that cannot be described by the GW approximation for the self-energy in the framework of many-body perturbation theory. Taking silicon as a prototypical example, we compare experimental high energy photoemission spectra with GW calculations and analyze the origin of the GW failure. We then propose an approximation to the functional differential equation that determines the exact one-body Green's function, whose solution has an exponential form. This yields a calculated spectrum, including cross sections, secondary electrons, and an estimate for extrinsic and interference effects, in excellent agreement with experiment. Our result can be recast as a dynamical vertex correction beyond GW, giving hints for further developments.

cond-mat.str-el↗

arXiv2010

Density-based mixing parameter for hybrid functionals

A very popular ab-initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of Fock exchange with DFT functionals. In spite of their success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This method is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.

cond-mat.mtrl-sci↗