arXiv subjects

Xavier Gonze

Publications and source records attributed to Xavier Gonze.

At least 37 records · Page 2Linked to original sources

arXiv2022

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

cond-mat.mtrl-sci↗

arXiv2022

Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

The zero-point lattice expansion (ZPLE) is a small variation of the lattice parameters induced by the presence of phonons in a material compared to the static lattice picture. It contributes significantly to the zero-point renormalization (ZPR) of the band gap energy, but its consequences have not been investigated as thoroughly as those stemming from electron-phonon interactions. In the usual first-principles approach, one evaluates the ZPLE by minimizing the $T=0$ K Helmholtz free energy. In this work, we show that the formalism based on the Grüneisen parameters, which commonly neglects zero-point effects, can be efficiently used to compute ZPLE for both isotropic and anisotropic materials at much lower computational cost. We systematically test this formalism on 22 cubic and wurtzite materials and obtain excellent agreement with free energy minimization results for both the ZPLE and the resulting band gap ZPR. We use our results to validate an empirical expression estimating the ZPLE-induced ZPR and unveil its sensitivity to the temperature range involved in estimating the ZPLE from experimental data. Our findings finally reveal that the ZPLE contribution to the band gap ZPR can reach 20% to more than 80% of the electron-phonon interaction contribution for heavier or more ionic materials, including materials containing light atoms. Considering both contributions on an equal footing is thus essential should one attempt to compare theoretical ZPR results with experimental data.

cond-mat.mtrl-sci↗

arXiv2022

High-throughput analysis of Fröhlich-type polaron models

The electronic structure of condensed matter can be significantly affected by the electron-phonon interaction, leading to important phenomena such as electrical resistance, superconductivity or the formation of polarons. This interaction is often neglected in band structure calculations but can have a strong impact on band gaps or optical spectra. Commonly used frameworks for electron-phonon energy corrections are the Allen-Heine-Cardona theory and the Fröhlich model. While the latter shows qualitative agreement with experiment for many polar materials, its simplicity should bring hard limits to its applicability in real materials. Improvements can be made by introducing a generalized version of the model, which considers anisotropic and degenerate electronic bands, and multiple phonon branches. In this work, we search for trends and outliers on over a thousand materials in existing databases of phonon and electron band structures. We use our results to identify the limits of applicability of the standard Frölich model by comparing to the generalized version, and by testing its basic hypothesis of a large radius for the polaronic wavefunction and the corresponding atomic displacement cloud. Among our extended set of materials, most exhibit large polaron behavior as well as validity of the perturbative treatment. For the valence band, there is also a significant fraction of the materials for which the perturbative treatment cannot be applied and/or for which the size of the self-trapping region is close to the atomic repetition distance. We find a large variety of behaviors, and employ much more accurate, fully ab initio Allen-Heine-Cardona calculations to understand extreme cases, where the Fröhlich model should fail and unusually large zero-point renormalization energies occur.

cond-mat.mtrl-sci↗

arXiv2022

Variational Polaron Equations Applied to the Anisotropic Fröhlich Model

Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fröhlich model with anisotropic non-degenerate electronic bands, both in two- and three-dimensional cases. The effect of the divergence of Fröhlich electron-phonon matrix elements at $Γ$-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fröhlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fröhlich model.

cond-mat.mtrl-sci↗

arXiv2022

Spectroscopic signatures of nonpolarons : the case of diamond

Polarons are quasi-particles made from electrons interacting with vibrations in crystal lattices. They derive their name from the strong electron-vibration polar interaction in ionic systems, that induces associated spectroscopic and optical signatures of such quasi-particles in these materials. In this paper, we focus on diamond, a non-polar crystal with inversion symmetry which nevertheless shows characteristic signatures of polarons, better denoted "nonpolarons" in this case. The polaronic effects are produced by short-range crystal fields with only a small influence of long-range quadrupoles. The many-body spectral function has a characteristic energy dependence, showing a plateau structure that is similar to but distinct from the satellites observed in the polar Fröhlich case. The temperature-dependent spectral function of diamond is determined by two methods: the standard Dyson-Migdal approach, which calculates electron-phonon interactions within the lowest-order expansion of the self-energy, and the cumulant expansion, which includes higher orders of electron-phonon interactions. The latter corrects the nonpolaron energies and broadening, providing a more realistic spectral function, which we examine in detail for both conduction and valence band edges.

cond-mat.mtrl-sci↗

arXiv2021

Sr-Doped Molecular Hydrogen: Synthesis and Properties of SrH$_{22}$

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Following the mainstream of extensive investigations of compressed polyhydrides, in this work we demonstrate that small (4 atom %) doping of molecular hydrogen by strontium leads to a dramatic reduction in the metallization pressure to about 200 GPa. Studying the high-pressure chemistry of the Sr-H system at 56-180 GPa, we observed the formation of several previously unknown compounds: C2/m-Sr$_3$H$_{13}$, pseudocubic SrH$_6$, SrH$_9$ with cubic F-43m Sr sublattice, and pseudotetragonal P1-SrH$_{22}$, the metal hydride with the highest hydrogen content discovered so far. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-Tc superconductors with an atomic H sublattice. The latter phase, SrH$_{22}$ or Sr$_{0.04}$H$_{0.96}$, may be considered as a convenient model of the consistent bandgap closure and metallization of hydrogen. Using the impedance measurements in diamond anvil cells at 300-440 K, we estimated the direct bandgap of the Pm-3n-like compound P1-SrH$_6$ to be 0.44-0.51 eV at 150 GPa, and its metallization pressure to be 220 GPa. Together with the machine learning interatomic potentials, the impedance spectroscopy allowed us to estimate the diffusion coefficients of hydrogen D$_H$ = 1.0-2.8 E-10 m$^2$/s in SrH$_6$ and 1.2-2.1 E-9 m$^2$/s in P1-SrH$_{22}$ at 500-600 K.

cond-mat.mtrl-sci↗

arXiv2021

Fröhlich polaron effective mass and localization length in cubic materials: degenerate and anisotropic electronic bands

Polarons, that is, charge carriers correlated with lattice deformations, are ubiquitous quasiparticles in semiconductors, and play an important role in electrical conductivity. To date most theoretical studies of so-called large polarons, in which the lattice can be considered as a continuum, have focused on the original Fröhlich model: a simple (non-degenerate) parabolic isotropic electronic band coupled to one dispersionless longitudinal optical phonon branch. The Fröhlich model allows one to understand characteristics such as polaron formation energy, radius, effective mass and mobility. Real cubic materials, instead, have electronic band extrema that are often degenerate or anisotropic and present several phonon modes. In the present work, we address such issues. We keep the continuum hypothesis inherent to the large polaron Fröhlich model, but waive the isotropic and non-degeneracy hypotheses, and also include multiple phonon branches. For polaron effective masses, working at the lowest order of perturbation theory, we provide analytical results for the case of anisotropic electronic energy dispersion, with two distinct effective masses (uniaxial) and numerical simulations for the degenerate 3-band case, typical of III-V and II-VI semiconductor valence bands. We also deal with the strong-coupling limit, using a variational treatment: we propose trial wavefunctions for the above-mentioned cases, providing polaron radii and energies. Then, we evaluate the polaron formation energies, effective masses and localisation lengths using parameters representative of a dozen II-VI, III-V and oxide semiconductors, for both electron and hole polarons...In the non-degenerate case, we compare the perturbative approach with the Feynman path integral approach in characterisizing polarons in the weak coupling limit...

cond-mat.mtrl-sci↗

arXiv2021

Design rule for the emission linewidth of Eu$^{2+}$-activated phosphors

We study from first principles the emission linewidth of Eu$^{2+}$-doped LED phosphors. Based on the one-dimensional configuration coordinate model, an analysis of first principles data obtained for fifteen compounds show that, at working temperature, the linewidth of Eu$^{2+}$ emission band in solids is negligibly affected by quantum effects, and can be extracted from the Franck-Condon energy shifts. For a fixed Stokes shift, the difference of Franck-Condon energy shifts in the excited and ground states is the key factor for the FWHM determination. Narrow emission Eu$^{2+}$-doped LED phosphors are expected for the case with large positive value of such difference.

cond-mat.mtrl-sci↗

arXiv2021

Importance of long-range channel Sr displacements for the narrow emission in Sr[Li$_2$Al$_2$O$_2$N$_2$]:Eu$^{2+}$ phosphor

The recently discovered Sr[Li$_2$Al$_2$O$_2$N$_2$]:Eu$^{2+}$ red phosphor, candidate for the next generation of eco-efficient white light-emitting diodes, exhibits excellent emission spectral position and exceptionally small linewidth. It belongs to the UCr$_4$C$_4$-structure family of phosphors, containing many potential candidates commercial phosphors, whose small linewidth, tentatively ascribed to the high-symmetry cuboid environment of the doping site, has drawn the attention of researchers in the last five years. We use density functional theory, $Δ$SCF method and configuration coordinate models (CCM) to provide a complete characterization of this material. Using a multi-dimensional CCM, an accurate description of the coupling of the vibronic structure with the electronic 5d$\rightarrow$4f transition is obtained, including the partial Huang-Rhys factors and frequency of the dominant modes. We show that, in addition to the first-coordination shell cuboid deformation mode, low-frequency phonon modes involving chains of strontium atoms along the tetragonal axis shape the emission linewidth in Sr[Li$_2$Al$_2$O$_2$N$_2$]:Eu$^{2+}$. This finding sheds new light on the emission properties of UCr$_4$C$_4$-structure phosphors, possessing similar Ca/Sr/Ba channel. Our approach provides a robust theoretical framework to systematically study the emission spectra of such Eu-doped phosphors, and predict candidates with expected similar or even sharper linewidth.

cond-mat.mtrl-sci↗

arXiv2020

Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

Electronic and optical properties of materials are affected by atomic motion through the electron-phonon interaction: not only band gaps change with temperature, but even at absolute zero temperature, zero-point motion causes band-gap renormalization. We present a large-scale first-principles evaluation of the zero-point renormalization of band edges beyond the adiabatic approximation. For materials with light elements, the band gap renormalization is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if accurate band gaps are sought. For infrared-active materials, global agreement with available experimental data is obtained only when non-adiabatic effects are taken into account. They even dominate zero-point renormalization for many materials, as shown by a generalized Fröhlich model that includes multiple phonon branches, anisotropic and degenerate electronic extrema, whose range of validity is established by comparison with first-principles results.

cond-mat.mtrl-sci↗

arXiv2020

Phonon-limited electron mobility in Si, GaAs and GaP with exact treatment of dynamical quadrupoles

We describe a new approach to compute the electron-phonon self-energy and carrier mobilities in semiconductors. Our implementation does not require a localized basis set to interpolate the electron-phonon matrix elements, with the advantage that computations can be easily automated. Scattering potentials are interpolated on dense $\mathbf{q}$ meshes using Fourier transforms and ab initio models to describe the long-range potentials generated by dipoles and quadrupoles. To reduce significantly the computational cost, we take advantage of crystal symmetries and employ the linear tetrahedron method and double-grid integration schemes, in conjunction with filtering techniques in the Brillouin zone. We report results for the electron mobility in Si, GaAs, and GaP obtained with this new methodology.

cond-mat.mtrl-sci↗

arXiv2020

Electron-Phonon Beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids

We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.

cond-mat.mtrl-sci↗

arXiv2020

Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene

Organic molecular crystals are expected to feature appreciable electron-phonon interactions that influence their electronic properties at zero and finite temperature. In this work, we report first-principles calculations and an analysis of the electron-phonon self-energy in naphthalene crystals. We compute the zero-point renormalization and temperature dependence of the fundamental band gap, and the resulting scattering lifetimes of electronic states near the valence- and conduction-band edges employing density functional theory. Further, our calculated phonon renormalization of the $GW$-corrected quasiparticle band structure predicts a fundamental band gap of 5 eV for naphthalene at room temperature, in good agreement with experiments. From our calculated phonon-induced electron lifetimes, we obtain the temperature-dependent mobilities of electrons and holes in good agreement with experimental measurements at room temperatures. Finally, we show that an approximate energy self-consistent computational scheme for the electron-phonon self-energy leads to the prediction of strong satellite bands in the electronic band structure. We find that a single calculation of the self-energy can reproduce the self-consistent results of the band gap renormalization and electrical mobilities for naphthalene, provided that the on-the-mass-shell approximation is used, i.e., if the self-energy is evaluated at the bare eigenvalues.

cond-mat.mtrl-sci↗

arXiv2019

First-principles prediction of lattice coherency in van der Waals heterostructures

The emergence of superconductivity in slightly-misaligned graphene bilayer [1] and moiré excitons in MoSe$_2$-WSe$_2$ van der Waals (vdW) heterostructures [2] is intimately related to the formation of a 2D superlattice in those systems. At variance, perfect primitive lattice matching of the constituent layers has also been reported in some vdW-heterostructures [3-5], highlighting the richness of interfaces in the 2D world. In this work, the determination of the nature of such interface, from first principles, is demonstrated. To do so, an extension of the Frenkel-Kontorova (FK) model [6] is presented, linked to first-principles calculations, and used to predict lattice coherency for a set of 56 vdW-heterostructures. Computational predictions agree with experiments, when available. New superlattices as well as perfectly-matching interfaces are predicted.

cond-mat.mtrl-sci↗

arXiv2019

Beyond the one-dimensional configuration coordinate model of photoluminescence

The one-dimensional configuration coordinate model (1D-CCM) is widely used for the analysis of photoluminescence in molecules and doped solids, and relies on a linear combination of the equilibrium nuclear configurations of ground and excited states. It delivers an estimation of the energy barrier at which ground and excited state curves cross, semi-classically linked to non-radiative transition rate and thermal quenching. To assess its predictive power for the latter properties, we propose a new \textit{optimized configuration path (OCP) method in which} the ground-state and excited-state forces are mixed instead of their configurations. We also define another one-parameter model thanks a double energy parabola hypothesis (DEPH). We compare the OCP method and the DEPH reference with the 1D-CCM for three paradigmatic 4f-5d phosphors Y$_3$Al$_5$O$_{12}$:Ce, Lu$_2$SiO$_5$:Ce, and YAlO$_3$:Ce. We find that the OCP and DEPH methods yield similar results with geometries that have significantly lower ground-state energies than the 1D-CCM for the same 4f-5d energy difference. However, the OCP method suffers from the appearance of multiple local minima, rendering the clear determination of the optimal geometry very difficult in practice. Still the OCP method allows one to quantify the deviations from the 1D-CCM, therefore increasing confidence in the lower bound obtained from the DEPH for the 4f-5d crossing barrier, and its comparison with the energy of the auto-ionization thermal quenching mechanism. We expect the OCP approach to be applicable to other luminescent materials or molecules.

cond-mat.mtrl-sci↗

arXiv2019

Vibrational and dielectric properties of monolayer transition metal dichalcogenides

First-principles studies of two-dimensional transition metal dichalcogenides have contributed considerably to the understanding of their dielectric, optical, elastic, and vibrational properties. The majority of works to date focus on a single material or physical property. Here we use a single first-principles methodology on the whole family of systems, to investigate in depth the relationships between different physical properties, the underlying symmetry and the composition of these materials, and observe trends. We compare to bulk counterparts to show strong interlayer effects in triclinic compounds. Previously unobserved relationships between these monolayer compounds become apparent. These trends can then be exploited by the materials science, nanoscience, and chemistry communities to better design devices and heterostructures for specific functionalities.

cond-mat.mtrl-sci↗

arXiv2018

Ab initio Study of Luminescence in Ce-doped Lu$_2$SiO$_5$: The Role of Oxygen Vacancies on Emission Color and Thermal Quenching Behavior

We study from first principles the luminescence of Lu$_2$SiO$_5$:Ce$^{3+}$ (LSO:Ce), a scintillator widely used in medical imaging applications, and establish the crucial role of oxygen vacancies (V$_O$) in the generated spectrum. The excitation energy, emission energy and Stokes shift of its luminescent centers are simulated through a constrained density-functional theory method coupled with a $Δ$SCF analysis of total energies, and compared with experimental spectra. We show that the high-energy emission band comes from a single Ce-based luminescent center, while the large experimental spread of the low-energy emission band originates from a whole set of different Ce-V$_O$ complexes together with the other Ce-based luminescent center. Further, the luminescence thermal quenching behavior is analyzed. The $4f-5d$ crossover mechanism is found to be very unlikely, with a large crossing energy barrier (E$_{fd}$) in the one-dimensional model. The alternative mechanism usually considered, namely the electron auto-ionization, is also shown to be unlikely. In this respect, we introduce a new methodology in which the time-consuming accurate computation of the band gap for such models is bypassed. We emphasize the usually overlooked role of the differing geometry relaxation in the excited neutral electronic state Ce$^{3+,*}$ and in the ionized electronic state Ce$^{4+}$. The results indicate that such electron auto-ionization cannot explain the thermal stability difference between the high- and low-energy emission bands. Finally, a hole auto-ionization process is proposed as a plausible alternative. With the already well-established excited state characterization methodology, the approach to color center identification and thermal quenching analysis proposed here can be applied to other luminescent materials in the presence of intrinsic defects.

cond-mat.mtrl-sci↗

arXiv2018

Vibrational and dielectric properties of the bulk transition metal dichalcogenides

Interest in the bulk transition metal dichalcogenides for their electronic, photovoltaic, and optical properties has grown and led to their use in many technological applications. We present a systematic investigation of their interlinked vibrational and dielectric properties, using density functional theory and density functional perturbation theory, studying the effects of the spin-orbit interaction and of the long-range e$^-$- e$^-$ correlation as part of our investigation. This study confirms that the spin-orbit interaction plays a small role in these physical properties, while the direct contribution of dispersion corrections is of crucial importance in the description of the interatomic force constants. Here, our analysis of the structural and vibrational properties, including the Raman spectra, compare well to experimental measurement. Three materials with different point groups are showcased and data trends on the full set of fifteen existing hexagonal, trigonal, and triclinic materials are demonstrated. This overall picture will enable the modeling of devices composed of these materials for novel applications.

cond-mat.mtrl-sci↗