arXiv subjects

Francesco Sottile

Publications and source records attributed to Francesco Sottile.

At least 19 recordsLinked to original sources

arXiv2026

Unbiased Diffusion Monte Carlo for non local operators

We propose a new mathematically exact method for computing unbiased Diffusion Monte Carlo (DMC) estimates of non-local operators. We demonstrate that the current state-of- the-art technique, Forward Walking, is only exact for local quantities and fails to yield unbiased results for the non-local components of reduced density matrices (RDMs). Our method significantly outperforms Forward Walking, as shown in two systems: in the symmetric Hubbard dimer it yields a pure 1RDM; while in the Helium atom it will give an unbiased 1RDM in the limits of zero time step and infinite walkers.

cond-mat.mtrl-sci↗

arXiv2025

Trends in the electronic structure of borophene polymorphs

Borophene is a two-dimensional material made out of boron atoms only. It exhibits polymorphism and different allotropes can be studied in terms of a rigid electronic structure, where only the occupation of the states change with the respect to the number of electrons available in the system (self-doping). In this work we selected a set of representative borophene polymorphs ($δ_3$, $δ_5$, $δ_6$, $β_{12}$ $α_1$, $α'$, $α'$-Bilayer) and studied the shared features of their electronic structures and the limitations of this model. Our work revealed the appearance of defect-like states in some polymorphs when related to a parent rigid electronic structure, and bonding/antibonding monolayer-like states in the $α'$-Bilayer. Moreover, we show how the buckling of $δ_6$ and $α'$ can act as a tuning parameter, enabling semimetallicity, Dirac cones, and nesting of the Fermi surface. In light of their promises for exotic but also useful behavior, we expect our work to foster the interest in larger and more complex borophene structures.

cond-mat.mtrl-sci↗

arXiv2024

K-edge XANES of octahedral aluminum compounds: similarities and differences via the analysis of excitonic properties

This study presents an \textit{ab initio} investigation of the XANES spectra at the aluminum K edge for three compounds: Al$_2$O$_3$, AlF$_3$ and AlCl$_3$, where the Al atoms share the same oxidation state~(III) and are coordinated in an octahedral symmetry. The XANES spectra calculated within the independent-particle approximation reveal significant differences, including shifts in the spectrum onset, variations in the spectral shapes, and the presence of a pre-peak in the case of AlCl$_3$, all in correspondence with the behavior of the PDOS of the absorbing atom in the different materials. The origin of the features stems from the specific band structure of each compound. When electron--hole interactions are taken into account through the solution of the Bethe-Salpeter equation, a series of dark and bright excitons with large binding energies and Frenkel character is obtained. The strong excitonic effects lead to the suppression of the pre-peak in AlCl$_3$ and further accentuate the differences among the three Al K-edge spectra.

cond-mat.mtrl-sci↗

arXiv2024

Connections between resonant inelastic x-ray scattering and complementary x-ray spectroscopies: probing excitons at Al K and L$_1$ edges of $α$-Al$_2$O$_3$

We present an ab initio study of neutral core and valence electronic excitations in α-Al2O3 by solving the Bethe-Salpeter equation (BSE) of many-body perturbation theory within an all-electron framework. Calculated spectra at the Al K and L1 edges are in remarkable agreement with available experiments from X-ray absorption (XAS) and X-ray Raman spectroscopy once excitonic effects are taken into account. The combination of the BSE spectra for the two techniques confirms the dipole-forbidden nature of the exciton prepeak as suggested by recent calculations based on density-functional theory. Moreover, we make predictions for resonant inelastic X-ray scattering (RIXS) spectra at K and L1 edges, which strikingly fully overlap also beyond an independent-particle picture. The RIXS calculations reveal two distinct regimes as a function of incoming photon energy. Below and at the XAS threshold, we observe Raman-like features, characterised by strong excitonic effects, which we directly compare to peaks in the loss function. Above the XAS threshold, instead, fluorescence features become predominant: RIXS spectra can be well described and analyzed within an independent-particle approximation showing similarity with the X-ray emission spectrum.

cond-mat.mtrl-sci↗

arXiv2023

Total energy beyond GW : exact results and guidelines for approximations

The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body perturbation theory, we derive different expressions that are based on an approximate self-energy, but that yield nevertheless in principle the exact exchange-correlation contribution to the total energy for any interaction strength. Response functions play a crucial role, which explains why, for example, ingredients from time-dependent density functional theory can be used to build these approximate self-energies. We show that the key requirement for obtaining exact results is the consistent combination of ingredients. Also when further approximations are made, as it is necessary in practice, this consistency remains the key to obtain good results. All findings are illustrated using the exactly solvable symmetric Hubbard dimer.

cond-mat.str-el↗

arXiv2023

Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures: excitonic effects in Al2O3

We present an ab initio description of optical and shallow-core x-ray absorption spectroscopies in a unified formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter equation (BSE) within Green's functions theory. We show that norm-conserving pseudopotentials are reliable and accurate not only for valence, but also for semicore electron excitations. In order to validate our approach, we compare BSE absorption spectra obtained with two different codes: the pseudopotential-based code EXC and the all-electron full-potential code Exciting. We take corundum $α$-Al$_2$O$_3$ as an example, being a prototypical material that presents strong electron-hole interactions for both valence and core electron excitations. We analyze in detail the optical absorption spectrum as well as the Al L$_1$ and L$_{2,3}$ edges in terms of anisotropy, crystal local fields, interference and excitonic effects. We perform a thorough inspection of the origin and localization of the lowest-energy excitons, and conclude highlighting the purely electronic character off the pre-edge of L$_1$ and the dichroic nature of the optical and L$_{23}$ spectra.

cond-mat.mtrl-sci↗

arXiv2022

All-electron many-body approach to resonant inelastic x-ray scattering

We present a formalism for the resonant inelastic x-ray scattering (RIXS) cross section. The resulting compact expression in terms of polarizability matrix elements, particularly lends itself to the implementation in an all-electron many-body perturbation theory (MBPT) framework, which is realized in the full-potential package exciting. With the carbon K edge RIXS of diamond and the oxygen K edge RIXS of $β-\mathrm{Ga_2 O_3}$, respectively, we demonstrate the importance of electron-hole correlation and atomic coherence in the RIXS spectra.

cond-mat.mtrl-sci↗

arXiv2020

First-principles study of excitons in the optical spectra of silver chloride

Silver chloride is a material that has been investigated and used for many decades. Of particular interest are its optical properties, but only few fundamental theoretical studies exist. We present first-principles results for the optical properties of AgCl, obtained using time-dependent density functional theory and many-body perturbation theory. We show that optical properties exhibit strong excitonic effects, which are correctly captured only by solving the Bethe-Salpeter equation starting from quasiparticle self-consistent GW results. Numerical simulations are made feasible by using a model screening for the electron-hole interaction in a way that avoids the calculation of the static dielectric constant. A thorough analysis permits us to discuss localization in bright and dark excitons of silver chloride.

cond-mat.mtrl-sci↗

arXiv2020

Excitation Pathways in Resonant Inelastic X-Ray Scattering of Solids

We present a novel derivation of resonant inelastic x-ray scattering (RIXS) which yields an expression for the RIXS cross section in terms of emission pathways between intermediate and final many-body states. Thereby electron-hole interactions are accounted for, as obtained from full diagonalization of the Bethe-Salpeter equation within an all-electron first-principles framework. We demonstrate our approach with the emission spectra of the fluorine K edge in LiF, and provide an in-depth analysis of the pathways that determine the spectral shape. Excitoninc effects are shown to play a crucial role in both the valence and core regime.

cond-mat.mtrl-sci↗

arXiv2016

Excitons in van der Waals materials: from monolayer to bulk hexagonal boron nitride

We present a general picture of the exciton properties of layered materials in terms of the excitations of their single-layer building blocks. To this end, we derive a model excitonic hamiltonian by drawing an analogy with molecular crystals, which are other prototypical van der Waals materials. We employ this simplified model to analyse in detail the excitation spectrum of hexagonal boron nitride (hBN) that we have obtained from the {\it ab initio} solution of the many-body Bethe-Salpeter equation as a function of momentum. In this way we identify the character of the lowest-energy excitons in hBN, discuss the effects of the interlayer hopping and the electron-hole exchange interaction on the exciton dispersion, and illustrate the relation between exciton and plasmon excitations in layered materials.

cond-mat.mtrl-sci↗

arXiv2016

Interpretation of monoclinic hafnia valence electron energy loss spectra by TDDFT

We present the valence electron energy-loss spectrum and the dielectric function of monoclinic hafnia (m-HfO$_2$) obtained from time-dependent density-functional theory (TDDFT) predictions and compared to energy-filtered spectroscopic imaging measurements in a high-resolution transmission-electron microscope. Fermi's Golden Rule density-functional theory (DFT) calculations can capture the qualitative features of the energy-loss spectrum, but we find that TDDFT, which accounts for local-field effects, provides nearly quantitative agreement with experiment. Using the DFT density of states and TDDFT dielectric functions, we characterize the excitations that result in the m-HfO$_2$ energy loss spectrum. The sole plasmon occurs between 13-16 eV, although the peaks $\sim$28 and above 40 eV are also due to collective excitations. We furthermore elaborate on the first-principles techniques used, their accuracy, and remaining discrepancies among spectra. More specifically, we assess the influence of Hf semicore electrons (5$p$ and 4$f$) on the energy-loss spectrum, and find that the inclusion of transitions from the 4$f$ band damps the energy-loss intensity in the region above 13 eV. We study the impact of many-body effects in a DFT framework using the adiabatic local-density approximation (ALDA) exchange-correlation kernel, as well as from a many-body perspective using a $GW$-derived electronic structure to account for self-energy corrections. These results demonstrate some cancellation of errors between self-energy and excitonic effects, even for excitations from the Hf $4f$ shell. We also simulate the dispersion with increasing momentum transfer for plasmon and collective excitation peaks.

cond-mat.mtrl-sci↗

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

Exciton energy-momentum map of hexagonal boron nitride

Understanding and controlling the way excitons propagate in solids is a key for tailoring materials with improved optoelectronic properties. A fundamental step in this direction is the determination of the exciton energy-momentum dispersion. Here, thanks to the solution of the parameter-free Bethe- Salpeter equation (BSE), we draw and explain the exciton energy-momentum map of hexagonal boron nitride (h-BN) in the first three Brillouin zones. We show that h-BN displays strong excitonic effects not only in the optical spectra at vanishing momentum $\mathbf{q}$, as previously reported, but also at large $\mathbf{q}$. We validate our theoretical predictions by assessing the calculated exciton map by means of an inelastic x-ray scattering (IXS) experiment. Moreover, we solve the discrepancies between previous experimental data and calculations, proving then that the BSE is highly accurate through the whole momentum range. Therefore, these results put forward the combination BSE and IXS as the tool of choice for addressing the exciton dynamics in complex materials.

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

A simple screened exact-exchange approach for excitonic properties in solids

We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of the optical properties of solids, where the screening is achieved through the zero-wavevector limit of the inverse dielectric function. The SXX approach can be viewed as a simplification of the Bethe-Salpeter equation (BSE) or, in the context of time-dependent density-functional theory, as a first step towards a new class of hybrid functionals for the optical properties of solids. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of the BSE.

cond-mat.mtrl-sci↗

arXiv2014

Evidence for anisotropic dielectric properties of monoclinic hafnia using high-resolution TEM valence electron energy-loss spectroscopy and ab initio time-dependent density-functional theory

The effect of nanocrystal orientation on the energy loss spectra of monoclinic hafnia (m-HfO$_2$) is measured by high resolution transmission electron microscopy (HRTEM) and valence energy loss spectroscopy (VEELS) on high quality samples. For the same momentum-transfer directions, the dielectric properties are also calculated ab initio by time-dependent density-functional theory (TDDFT). Experiments and simulations evidence anisotropy in the dielectric properties of m-HfO$_2$, most notably with the direction-dependent oscillator strength of the main bulk plasmon. The anisotropic nature of m-HfO$_2$ may contribute to the differences among VEELS spectra reported in literature. The good agreement between the complex dielectric permittivity extracted from VEELS with nanometer spatial resolution, TDDFT modeling, and past literature demonstrates that the present HRTEM-VEELS device-oriented methodology is a possible solution to the difficult nanocharacterization challenges given in the International Technology Roadmap for Semiconductors.

cond-mat.mtrl-sci↗

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↗

arXiv2007

Efficient ab initio calculations of bound and continuum excitons

We present calculations of the absorption spectrum of semiconductors and insulators comparing various approaches: (i) the two-particle Bethe-Salpeter equation of Many-Body Perturbation Theory; (ii) time-dependent density-functional theory using a recently developed kernel that was derived from the Bethe-Salpeter equation; (iii) a scheme that we propose in the present work and that allows one to derive different parameter-free approximations to (ii). We show that all methods reproduce the series of bound excitons in the gap of solid argon, as well as continuum excitons in semiconductors. This is even true for the simplest static approximation, which allows us to reformulate the equations in a way such that the scaling of the calculations with number of atoms equals the one of the Random Phase Approximation.

cond-mat.other↗