arXiv subjects

Xavier Gonze

Publications and source records attributed to Xavier Gonze.

At least 19 recordsLinked to original sources

arXiv2026

Optimal transition states for polaron hopping transport without supercells

Polaron formation localizes charge carriers and drives a crossover from band-like to hopping transport in materials. Hopping dynamics can be obtained from DFT supercell calculations of transition states, but these suffer from polaron self-interaction, spurious electrostatics, and poor scaling with polaron size. We introduce a supercell-free framework for ab initio polaron hopping transport based on the ab initio polaron equations formalism, its variational formulation, and the string method. The approach optimizes transition states between self-trapped polaron states directly in reciprocal space and provides the polaron configurations along the path, enabling evaluation of adiabatic hopping rates and mobilities. We apply the method to LiF and rutile TiO$_2$, revealing multi-step and anisotropic hopping mechanisms. In rutile TiO$_2$, the computed electron-polaron mobility agrees with experiment, whereas band-like Boltzmann transport substantially overestimates the mobility. Our results establish a scalable route to first-principles polaron-hopping dynamics in materials in which charge motion is governed by self-trapping.

cond-mat.mtrl-sci↗

arXiv2026

Implementation of rotational invariance for first-principles phonons and application to low-dimensional materials

The acoustic flexural (phonon) modes of low-dimensional materials should show a quadratic dispersion close to the Brillouin zone center. Any departure from this behavior in Density Functional Theory calculations is typically associated with a breaking of the rotational invariance, with few methods available to correct it. In this work, we reexamine this issue based on a reciprocal-space imposition of this condition, with corrections on the zone-center IFCs and their first and second derivatives with respect to the phonon wavevector. We propose two correction schemes for the short-range part of the interatomic force constants, one based on the Moore-Penrose pseudoinverse, that we implement in the ABINIT software package, and one based on the straight modification of the on-site antisymmetric part of the first-order derivative of the dynamical matrix with respect to the wavevector. We investigate the impact of imposing rotational invariance for different system dimensionalities and pseudopotentials. Finally, we discuss rotational invariance in the context of long-range electrostatics contribution to the IFCs. We observe that the usual treatment of electrostatics is by construction not rotationally invariant. This is found especially critical when correcting the second derivatives of the IFCs.

cond-mat.mtrl-sci↗

arXiv2026

Micro-environment of the Eu interstitial in $\beta$-SiAlON:Eu$^{2+}$ green phosphor

The precise atomic-scale structure around Eu$^{2+}$ activators in the $\beta$-Si$_{6-z}$Al$_z$O$_z$N$_{8-z}$:Eu$^{2+}$ commercial green phosphor remains elusive. We use the first-principles $\Delta$SCF excited-state method, embedding of the interatomic force constants for supercells up to 3501 atoms, and Huang-Rhys theory to clarify this issue. Monte Carlo exploration is used to identify representative low-energy structural models spanning different levels of Al/O concentration $z$. For the lowest-energy structure at low $z$, our computed photoluminescence spectrum reproduces the experimental vibronic peaks at 6~K with excellent agreement in peak positions and intensities, validating the Eu-N$_9$ coordination model with Al, O, and Eu confined to the same crystallographic plane. Analysis of the low-energy structures reveals that the electron-phonon coupling is weak ($S \approx 2.15$) with a robust characteristic phonon signature across different Al/O arrangements, explaining the surprising persistence of resolved phonon replicas with increasing $z$. We explain the experimentally observed red-shift of emission with increasing $z$ through systematic trends in zero-phonon line energies, modest increases in Huang-Rhys factors, and larger configurational diversity at higher compositions.

cond-mat.mtrl-sci↗

arXiv2025

Low-temperature behavior of density-functional theory for metals based on density-functional perturbation theory and Sommerfeld expansion

The temperature dependence of most solid-state properties is dominated by lattice vibrations, but metals display notable purely electronic effects at low temperature, such as the linear specific heat and the linear entropy, that were derived by Sommerfeld for the non-interacting electron gas via the low-temperature expansion of Fermi-Dirac integrals. Here we treat temperature as a perturbation within density-functional perturbation theory (DFPT). For finite temperature, we show how self-consistency screens the bare, temperature-induced density change obtained in the non-interacting picture: the inverse transpose of the electronic dielectric operator, that includes Adler-Wiser and a term related to the shift in Fermi level, links the self-consistent density response to the bare thermal density change. This approach is implemented in DFTK, and demonstrated by the computation of the second-order derivative of the free energy, and the first-order derivative of entropy for aluminum. Then, we examine the $T\!\to\!0$ limit. The finite temperature formalism contains divergences, that we cure using the Sommerfeld expansion to analyze metallic systems at 0 K. The electronic free energy is quadratic in $T$ provided the Fermi level is not at a Van Hove singularity of the density of states. If the latter happens, another temperature behavior might appear, depending on the type of Van Hove singularity, that we analyze. Our formulation applies to systems periodic in one, two, or three dimensions, and provides a basis for studying temperature-dependent electronic instabilities (e.g., charge-density waves) within density-functional theory and DFPT.

cond-mat.mtrl-sci↗

arXiv2025

In search of the electron-phonon contribution to total energy

The total energy is a fundamental characteristic of solids, molecules, and nanostructures. In most first-principles calculations of the total energy, the nuclear kinetic operator is decoupled from the many-body electronic Hamiltonian and nuclear potential, and the dynamics of the nuclei is reintroduced afterward. This two-step procedure introduced by Born and Oppenheimer (BO) is approximate. Energies beyond the electronic and vibrational (or phononic) main contributions might be relevant when small energy differences are important, such as when predicting stable polymorphs or describing magnetic energy landscape. We clarify the different flavors of BO decoupling and give an exact formulation for the total energy in the basis of BO electronic wavefunctions. Then, we list contributions, beyond the main ones, that appear in a perturbative expansion in powers of $M_0^{-1/4}$, where $M_0$ is a typical nuclear mass, up to sixth order. Some of these might be grouped and denoted the electron-phonon contribution to total energy, $E^{\textrm{elph}}$, that first appears at fourth order. The electronic inertial mass contributes at sixth order. We clarify that the sum of the Allen-Heine-Cardona zero-point renormalization of eigenvalues over occupied states is not the electron-phonon contribution to the total energy but a part of the phononic contribution. The computation of the lowest-order $E^{\textrm{elph}}$ is implemented and shown to be small but non-negligible (3.8~meV per atom) in the case of diamond and its hexagonal polymorph. We also estimate the electronic inertial mass contribution and the quasi-harmonic one. We confirm the size consistency of all computed terms.

cond-mat.mtrl-sci↗

arXiv2025

Abinit 2025: New Capabilities for the Predictive Modeling of Solids and Nanomaterials

Abinit is a widely used scientific software package implementing density functional theory and many related functionalities for excited states and response properties. This paper presents the novel features and capabilities, both technical and scientific, which have been implemented over the past 5 years. This evolution occurred in the context of evolving hardware platforms, high-throughput calculation campaigns, and the growing use of machine learning to predict properties based on databases of first principles results. We present new methodologies for ground states with constrained charge, spin or temperature; for density functional perturbation theory extensions to flexoelectricity and polarons; and for excited states in many-body frameworks including GW, dynamical mean field theory, and coupled cluster. Technical advances have extended abinit high-performance execution to graphical processing units and intensive parallelism. Second principles methods build effective models on top of first principles results to scale up in length and time scales. Finally, workflows have been developed in different community frameworks to automate \abinit calculations and enable users to simulate hundreds or thousands of materials in controlled and reproducible conditions.

cond-mat.mtrl-sci↗

arXiv2025

Variational first-principles approach to self-trapped polarons

The behavior of charge carriers in polar materials is governed by electron-phonon interactions, which affect their mobilities via phonon scattering and may localize carriers into self-induced deformation fields, forming self-trapped polarons. We present a first-principles study of self-trapped polaron formation in paradigmatic polar semiconductors and insulators using the variational polaron equations framework and self-consistent gradient optimization. Our method incorporates long-range corrections to the electron-phonon interaction, essential for finite-size systems. We demonstrate how the variational approach enables the identification of multiple polaronic states and supports the analysis of polarons with arbitrarily large spatial extent via energy filtering. The potential energy surfaces of the resulting polarons exhibit multiple local minima, reflecting distinct, symmetry-broken polaronic configurations in systems with degenerate band edges. Our findings align with previous theoretical studies and establish a robust foundation for future ab initio studies of polarons, especially those employing variational methods.

cond-mat.mtrl-sci↗

arXiv2025

Anisotropic temperature-dependent lattice parameters and elastic constants from first principles

The Quasi-harmonic Approximation (QHA) is a widely used method for calculating the temperature dependence of lattice parameters and the thermal expansion coefficients from first principles. However, applying QHA to anisotropic systems typically requires several dozens or even hundreds of phonon band structure calculations, leading to high computational costs. The Zero Static Internal Stress Approximation (ZSISA) QHA method partly addresses such caveat, but the computational load of its implementation remains high, so that its volumetric-only counterpart v-ZSISA-QHA is preferred. In this work, we present an efficient implementation of the ZSISA-QHA, enabling its application across a wide range of crystal structures under varying temperature (T) and pressure (P) conditions. By incorporating second-order derivatives of the vibrational free energy with respect to lattice degrees of freedom, we significantly reduce the number of required phonon band structure calculations for the determination of all lattice parameters and angles. For hexagonal, trigonal, and tetragonal systems, only six phonon band structure calculations are needed, while 10, 15, and 28 calculations suffice for orthorhombic, monoclinic, and triclinic systems, respectively. This method is tested for a variety of non-cubic materials, from uniaxial ones like ZnO and CaCO3 to monoclinic or triclinic materials such as ZrO2, HfO2, and Al2SiO5, demonstrating a significant reduction in computational effort while maintaining accuracy in modeling anisotropic thermal expansion, unlike the v-ZSISA-QHA. The method is also applied to the first-principles calculation of temperature-dependent elastic constants, with only up to six more phonon band structure calculations, depending on the crystallographic system.

cond-mat.mtrl-sci↗

arXiv2024

Surface-plasmon polaritons in multilayer jellium systems: dispersion and spatial description

Surface-plasmon polaritons (SPPs) are electromagnetic waves that propagate along metal-dielectric interfaces, with important applications in sensing, energy, and nanotechnology. While the behavior of SPPs in single metal slabs is well understood, the coupling between plasmon modes in multilayer systems has received less attention. In this paper, we explore the response functions of SPPs in single-slab, double-slab, and two-different-slab systems using the jellium model. Thanks to a comparison with classical models, our study reveals how quantum effects influence the resonance frequencies of these modes. It also details the spatial description of the different SPP modes and unveils how their coupling occurs in two-different-slab systems. These findings provide new insights into the behavior of SPPs, especially in complex nanostructures.

physics.optics↗

arXiv2024

Precision benchmarks for solids: G0W0 calculations with different basis sets

The GW approximation within many-body perturbation theory is the state of the art for computing quasiparticle energies in solids. Typically, Kohn-Sham (KS) eigenvalues and eigenfunctions, obtained from a Density Functional Theory (DFT) calculation are used as a starting point to build the Green's function G and the screened Coulomb interaction W, yielding the one-shot G0W0 selfenergy if no further update of these quantities are made. Multiple implementations exist for both the DFT and the subsequent G0W0 calculation, leading to possible differences in quasiparticle energies. In the present work, the G0W0 quasiparticle energies for states close to the band gap are calculated for six crystalline solids, using four different codes: Abinit, exciting, FHI-aims, and GPAW. This comparison helps to assess the impact of basis-set types (planewaves versus localized orbitals) and the treatment of core and valence electrons (all-electron full potentials versus pseudopotentials). The impact of unoccupied states as well as the algorithms for solving the quasiparticle equation are also briefly discussed. For the KS-DFT band gaps, we observe good agreement between all codes, with differences not exceeding 0.1 eV, while the G0W0 results deviate on the order of 0.1-0.3 eV. Between all-electron codes (FHI-aims and exciting), the agreement is better than 15 meV for KS-DFT and, with one exception, about 0.1 eV for G0W0 band gaps.

cond-mat.mtrl-sci↗

arXiv2024

Approximations in first-principles volumetric thermal expansion determination

In the realm of thermal expansion determination, the quasiharmonic approximation (QHA) stands as a widely embraced method for discerning minima of free energies across diverse temperatures such that the temperature dependence of lattice parameters as well as internal atomic positions can be determined. However, this methodology often imposes substantial computational demand, necessitating numerous costly calculations of full phonon spectra in a possibly many-dimensional geometry parameter space. Focusing on the volumetric thermal expansion only, the volume-constrained zero static internal stress approximation (v-ZSISA) within QHA allows one to limit significantly the number of phonon spectra determinations to typically less than 10. The linear Gruneisen approach goes even further with only two phonon spectra determinations to find the volumetric thermal expansion, but a deterioration of the accuracy of the computed thermal expansion is observed, except at low temperatures. We streamline this process by introducing further intermediate approximations between the linear Gruneisen and the v-ZSISA-QHA, corresponding to different orders of the Taylor expansion. The minimal number of phonon spectra calculations that is needed to maintain precise outcomes is investigated. The different approximations are tested on a representative set of 12 materials. For the majority of materials, three full phonon spectra, corresponding to quadratic order, is enough to determine the thermal expansion in reasonable agreement with the v-ZSISA-QHA method up to 800 K. Near perfect agreement is obtained with five phonon spectra. This study paves the way to multidimensional generalizations, beyond the volumetric case, with the expectation of much bigger benefits.

cond-mat.mtrl-sci↗

arXiv2024

Polarons in the Cubic Generalized Fröhlich Model: Spontaneous Symmetry Breaking

Within the variational polaron equation framework, the Fröhlich model for cubic systems with three-fold degenerate electronic bands is numerically solved in the strong coupling regime, for a wide range of its input parameters. By comparing the results to the previously reported ones obtained with the Gaussian Ansatz approach, the inadequacy of the latter is uncovered, especially when degenerate bands are present in a system. Moreover, the symmetry groups of polaronic solutions in the cubic generalized Fröhlich model without spin-orbit coupling are investigated: we provide and discuss a phase diagram of symmetry groups of ground-state polarons, showing spontaneous symmetry breaking. While the cubic symmetry of the three-band degenerate model Hamiltonian corresponds to the full octahedral group $O_h$, lowest-energy polarons possess either $D_{4h}$ or $D_{3d}$ point groups. This phase diagram bears some similarities but differs nevertheless from the one that is obtained by the straight analysis of the band effective masses. The obtained results will provide a firm ground for further exploration of the generalized Fröhlich model and will likely be applicable beyond the model's inherent approximations.

cond-mat.mtrl-sci↗

arXiv2024

Validation of the GreenX library time-frequency component for efficient GW and RPA calculations

Electronic structure calculations based on many-body perturbation theory (e.g. GW or the random-phase approximation (RPA)) require function evaluations in the complex time and frequency domain, for example inhomogeneous Fourier transforms or analytic continuation from the imaginary axis to the real axis. For inhomogeneous Fourier transforms, the time-frequency component of the GreenX library provides time-frequency grids that can be utilized in low-scaling RPA and GW implementations. In addition, the adoption of the compact frequency grids provided by our library also reduces the computational overhead in RPA implementations with conventional scaling. In this work, we present low-scaling GW and conventional RPA benchmark calculations using the GreenX grids with different codes (FHI-aims, CP2K and ABINIT) for molecules, two-dimensional materials and solids. Very small integration errors are observed when using 30 time-frequency points for our test cases, namely $<10^{-8}$ eV/electron for the RPA correlation energies, and 10 meV for the GW quasiparticle energies.

physics.comp-ph↗

arXiv2024

Variational Density Functional Perturbation Theory for Metals

Density functional perturbation theory is a well-established method to study responses of molecules and solids, especially responses to atomic displacements or to different perturbing fields (electric, magnetic). Like for density functional theory, the treatment of metals is delicate, due to the Fermi-Dirac statistics and electronic bands crossing the Fermi energy. At zero temperature, there is an abrupt transition from occupied states to unoccupied ones, usually addressed with smearing schemes. Also, at finite temperature, fractional occupations are present, and the occupation numbers may vary in response to the perturbation. The present work establishes the characteristics of density functional perturbation theory stemming from the underlying variational principle, in the case of metals. After briefly reviewing variational density functional theory for metals, the convexity of the entropy function of the occupation number is analyzed, and, at finite temperature, the benefit of resmearing the Fermi-Dirac broadening with the Methfessel-Paxton one is highlighted. Then the variational expressions for the second-order derivative of the free energy are detailed, exposing the different possible gauge choices. The influence of the inaccuracies in the unperturbed wavefunctions from the prior density functional theory calculation is studied. The whole formalism is implemented in the ABINIT software package.

cond-mat.mtrl-sci↗

arXiv2023

Generating and grading 34 Optimized Norm-Conserving Vanderbilt Pseudopotentials for Actinides and Super Heavy Elements in the PseudoDojo

In the last decades, material discovery has been a very active research field driven by the need to find new materials for many different applications. This has also included materials with heavy elements, beyond the stable isotopes of lead, as most actinides exhibit unique properties that make them useful in various applications. Furthermore, new heavy elements beyond actinides, collectively referred to as super-heavy elements (SHEs), have been synthesized, filling previously empty space of Mendeleev periodic table. Their chemical bonding behavior, of academic interest at present, would also benefit of state-of-the-art modeling approaches. In particular, in order to perform first-principles calculations with planewave basis sets, one needs corresponding pseudopotentials. In this work, we present a series of scalar- and fully-relativistic optimized norm-conserving Vanderbilt pseudopotentials (ONCVPs) for thirty-four actinides and super-heavy elements, for three different exchange-correlation functionals (PBE, PBEsol and LDA). The scalar-relativistic version of these ONCVPs is tested by comparing equations of states for crystals, obtained with \textsc{abinit} 9.6, with those obtained by all-electron zeroth-order regular approximation (ZORA) calculations, without spin-orbit coupling, performed with the Amsterdam Modeling Suite \textsc{band} code. $Δ$-Gauge and $Δ_1$-Gauge indicators are used to validate these pseudopotentials. This work is a contribution to the PseudoDojo project, in which pseudopotentials for the whole periodic table are developed and systematically tested. The pseudopotential files are available on the PseudoDojo web-interface pseudo-dojo.org in psp8 and UPF2 formats, both suitable for \textsc{abinit}, the latter being also suitable for Quantum ESPRESSO.

cond-mat.mtrl-sci↗

arXiv2023

Surface Enhanced Infrared Absorption mechanism and modification of the plasmonic response

Surface Enhanced Infrared Absorption (SEIRA) is an experimental method where trace amount of a compound can be detected with high sensibility. This high detection sensibility is the result of the interaction of the molecules with a localized plasmon, usually from a metallic nano-particle. In this study we numerically investigate by discrete dipole approximation the origin of the Fano-like response of the system, including the induced transparency when the plasmon resonance and the molecular vibrational mode coincide. The detailed analysis of the localization of the absorption show that the modification of the absorption cross-section when the molecule is present comes from a change of the plasmonic resonance, not from the direct molecular response which is negligible. This sheds a new light on the SEIRA mechanism. In particular, it demonstrates that the sensibility is associated with the influence of the molecule on the plasmon resonance rather than with the local field enhancement itself.

physics.optics↗

arXiv2023

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fröhlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $Γ$ point. We also incorporate SOC into a generalized Fröhlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fröhlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation within the physically relevant energy range of the Fröhlich interaction for materials with high phonon frequencies treated with SOC.

cond-mat.mtrl-sci↗

arXiv2023

A First-Principles Explanation of the Luminescent Line Shape of SrLiAl$_3$N$_4$:Eu$^{2+}$ Phosphor for Light-Emitting Diode Applications

White light-emitting diodes are gaining popularity and are set to become the most common light source in the U.S. by 2025. However, their performance is still limited by the lack of an efficient red-emitting component with a narrow band emission. The red phosphor SrLiAl$_3$N$_4$:Eu$^{2+}$ is among the first promising phosphors with a small bandwidth for next-generation lighting, but the microscopic origin of this narrow emission remains elusive. In the present work, density functional theory, the $Δ$SCF-constrained occupation method, and a generalized Huang-Rhys theory are used to provide an accurate description of the vibronic processes occurring at the two Sr$^{2+}$ sites that the Eu$^{2+}$ activator can occupy. The emission band shape of Eu(Sr1), with a zero-phonon line at 1.906 eV and a high luminescence intensity, is shown to be controlled by the coupling between the 5d$_{z^2}$-4f electronic transition and the low-frequency phonon modes associated with the Sr and Eu displacements along the Sr channel. The good agreement between our computations and experimental results allows us to provide a structural assignment of the observed total spectrum. By computing explicitly the effect of the thermal expansion on zero-phonon line energies, the agreement is extended to the temperature-dependent spectrum. These results provide insight into the electron-phonon coupling that accompanies the 5d-4f transition in similar UCr$_4$C$_4$-type phosphors. Furthermore, these results highlight the importance of the Sr channel in shaping the narrow emission of SrLiAl$_3$N$_4$:Eu$^{2+}$, and they shed new light on the structure-property relations of such phosphors.

cond-mat.mtrl-sci↗