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Nicola Marzari

Publications and source records attributed to Nicola Marzari.

At least 91 records · Page 5Linked to original sources
arXiv2024

On-site and inter-site Hubbard corrections in magnetic monolayers: The case of FePS$_3$ and CrI$_3$

Hubbard-corrected density-functional theory has proven to be successful in addressing self-interaction errors in 3D magnetic materials. However, the effectiveness of this approach for 2D magnetic materials has not been extensively explored. Here, we use PBEsol+$\textit{U}$ and its extensions PBEsol+$\textit{U}$+$\textit{V}$ to investigate the electronic, structural, and vibrational properties of 2D antiferromagnetic FePS$_3$ and ferromagnetic CrI$_3$, and compare the monolayers with their bulk counterparts. Hubbard parameters (on-site $\textit{U}$ and inter-site $\textit{V}$) are computed self-consistently using density-functional perturbation theory, thus avoiding any empirical assumptions. We show that for FePS$_3$ the Hubbard corrections are crucial in obtaining the experimentally observed insulating state with the correct crystal symmetry, providing also vibrational frequencies in good agreement with Raman experiments. For ferromagnetic CrI$_3$, we discuss how a straightforward application of Hubbard corrections worsens the results and introduces a spurious separation between spin-majority and minority conduction bands. Promoting the Hubbard $\textit{U}$ to be a spin-resolved parameter - that is, applying different (first-principles) values to the spin-up and spin-down manifolds - recovers a more physical picture of the electronic bands and delivers the best comparison with experiments.

cond-mat.mtrl-sci↗
arXiv2024

Magnetostriction-Driven Muon Localization in an Antiferromagnetic Oxide

Magnetostriction drives a rhombohedral distortion in the cubic rock salt antiferromagnet MnO at the Néel temperature $T_{N}=118$ K. As an unexpected consequence we show that this distortion acts to localize the site of an implanted muon due to the accompanying redistribution of electron density. This lifts the degeneracy between equivalent sites, resulting in a single observed muon precession frequency. Above $T_{N}$, the muon instead becomes delocalized around a network of equivalent sites. Our first-principles simulations based on Hubbard-corrected density-functional theory and molecular dynamics are consistent with our experimental data and help to resolve a long-standing puzzle regarding muon data on MnO, as well as having wider applicability to other magnetic oxides.

cond-mat.str-el↗
arXiv2024

First-Principles Electron-Phonon Interactions and Polarons in the Parent Cuprate La$_2$CuO$_4$

Understanding electronic interactions in high-temperature superconductors is an outstanding challenge. In the widely studied cuprate materials, experimental evidence points to strong electron-phonon ($e$-ph) coupling and broad photoemission spectra. Yet, the microscopic origin of this behavior is not fully understood. Here we study $e$-ph interactions and polarons in a prototypical parent (undoped) cuprate, La$_2$CuO$_4$ (LCO), by means of first-principles calculations. Leveraging parameter-free Hubbard-corrected density functional theory, we obtain a ground state with band gap and Cu magnetic moment in nearly exact agreement with experiments. This enables a quantitative characterization of $e$-ph interactions. Our calculations reveal two classes of longitudinal optical (LO) phonons with strong $e$-ph coupling to hole states. These modes consist of Cu-O plane bond-stretching and bond-bending as well as vibrations of apical O atoms. The hole spectral functions, obtained with a cumulant method that can capture strong $e$-ph coupling, exhibit broad quasiparticle peaks with a small spectral weight ($Z\approx0.25$) and pronounced LO-phonon sidebands characteristic of polaron effects. Our calculations predict features observed in photoemission spectra, including a 40-meV peak in the $e$-ph coupling distribution function not explained by existing models. These results show that the universal strong $e$-ph coupling found experimentally in lanthanum cuprates is an intrinsic feature of the parent compound, and elucidates its microscopic origin.

cond-mat.mtrl-sci↗
arXiv2023

Understanding the role of Hubbard corrections in the rhombohedral phase of BaTiO$_3$

We present a first-principles study of the low-temperature rhombohedral phase of BaTiO$_3$ using Hubbard-corrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard $U$ for Ti($3d$) states and the intersite Hubbard $V$ between Ti($3d$) and O($2p$) states. We show that applying the onsite Hubbard $U$ correction alone to Ti($3d$) states proves detrimental, as it suppresses the Ti($3d$)-O($2p$) hybridization and drives the system towards a cubic phase. Conversely, when both onsite $U$ and intersite $V$ are considered, the localized character of the Ti($3d$) states is maintained, while also preserving the Ti($3d$)-O($2p$) hybridization, restoring the rhombohedral phase of BaTiO$_3$. The generalized PBEsol+$U$+$V$ functional yields good agreement with experimental results for the band gap and dielectric constant, while the optimized geometry is slightly less accurate compared to PBEsol. Zone-center phonon frequencies and Raman spectra are found to be significantly influenced by the underlying geometry. PBEsol and PBEsol+$U$+$V$ provide satisfactory agreement with the experimental Raman spectrum when the PBEsol geometry is used, while PBEsol+$U$ Raman spectrum diverges strongly from experimental data highlighting the adverse impact of the $U$ correction alone in BaTiO$_3$. Our findings underscore the promise of the extended Hubbard PBEsol+$U$+$V$ functional with first-principles $U$ and $V$ for the investigation of other ferroelectric perovskites with mixed ionic-covalent interactions.

cond-mat.mtrl-sci↗
arXiv2023

Orbital-resolved DFT+U for molecules and solids

We present an orbital-resolved extension of the Hubbard $U$ correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS$_2$) and pyrolusite ($β$-MnO$_2$), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+$U$ beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

cond-mat.mtrl-sci↗
arXiv2023

The type-I antiferromagnetic Weyl semimetal InMnTi$_2$

Topological materials have been a main focus of studies in the past decade due to their protected properties that can be exploited for the fabrication of new devices. Among them, Weyl semimetals are a class of topological semimetals with non-trivial linear band crossing close to the Fermi level. The existence of such crossings requires the breaking of either time-reversal or inversion symmetry and is responsible for the exotic physical properties. In this work we identify the full-Heusler compound InMnTi$_2$, as a promising, easy to synthesize, $T$- and $I$-breaking Weyl semimetal. To correctly capture the nature of the magnetic state, we employed a novel $\mathrm{DFT}+U$ computational setup where all the Hubbard parameters are evaluated from first-principles; thus preserving a genuinely predictive \textit{ab initio} character of the theory. We demonstrate that this material exhibits several features that are comparatively more intriguing with respect to other known Weyl semimetals: the distance between two neighboring nodes is large enough to observe a wide range of linear dispersions in the bands, and only one kind of such node's pairs is present in the Brillouin zone. We also show the presence of Fermi arcs stable across a wide range of chemical potentials. Finally, the lack of contributions from trivial points to the low-energy properties makes the materials a promising candidate for practical devices.

cond-mat.mtrl-sci↗
arXiv2023

Phonon Self-Energy Corrections: To Screen, or Not to Screen

First-principles calculations of phonons are often based on the adiabatic approximation and on Brillouin-zone samplings that might not always be sufficient to capture the subtleties of Kohn anomalies. These shortcomings can be addressed through corrections to the phonon self-energy arising from the low-energy electrons. The exact self-energy involves a product of a bare and a screened electron-phonon vertex [Rev. Mod. Phys. 89, 015003 (2017)]; still, calculations often employ two adiabatically screened vertices, which have been proposed as a reliable approximation for self-energy differences [Phys. Rev. B 82, 165111 (2010)]. We assess the accuracy of both approaches in estimating the phonon spectral functions of model Hamiltonians and the adiabatic low-temperature phonon dispersions of monolayer TaS$_2$ and doped MoS$_2$. We find that the approximate method yields excellent corrections at low computational cost, due to its designed error cancellation to first order, while using a bare vertex could in principle improve these results but is challenging in practice. We offer an alternative strategy based on downfolding to partially screened phonons and interactions [Phys. Rev. B 92, 245108 (2015)]. This is a natural scheme to include electron-electron interactions and tackle phonons in strongly correlated materials and the frequency dependence of the electron-phonon vertex.

cond-mat.mtrl-sci↗
arXiv2023

Crossover from Boltzmann to Wigner thermal transport in thermoelectric skutterudites

Skutterudites are crystals with a cage-like structure that can be augmented with filler atoms ("rattlers"), usually leading to a reduction in thermal conductivity that can be exploited for thermoelectric applications. Here, we leverage the recently introduced Wigner formulation of thermal transport to elucidate the microscopic physics underlying heat conduction in skutterudites, showing that filler atoms can drive a crossover from the Boltzmann to the Wigner regimes of thermal transport, i.e., from particle-like conduction to wave-like tunnelling. At temperatures where the thermoelectric efficiency of skutterudites is largest, wave-like tunneling can become comparable to particle-like propagation. We define a Boltzmann deviation descriptor able to differentiate the two regimes and relate the competition between the two mechanisms to the materials' chemistry, providing a design strategy to select rattlers and identify optimal compositions for thermoelectric applications.

cond-mat.mtrl-sci↗
arXiv2023

Density-functional perturbation theory for one-dimensional systems: implementation and relevance for phonons and electron-phonon interactions

The electronic and vibrational properties and electron-phonon couplings of one-dimensional materials will be key to many prospective applications in nanotechnology. Dimensionality strongly affects these properties and has to be correctly accounted for in first-principles calculations. Here we develop and implement a formulation of density-functional and density-functional perturbation theory that is tailored for one-dimensional systems. A key ingredient is the inclusion of a Coulomb cutoff, a reciprocal-space technique designed to correct for the spurious interactions between periodic images in periodic-boundary conditions. This restores the proper one-dimensional open-boundary conditions, letting the true response of the isolated one-dimensional system emerge. In addition to total energies, forces and stress tensors, phonons and electron-phonon interactions are also properly accounted for. We demonstrate the relevance of the present method on a portfolio of realistic systems: BN atomic chains, BN armchair nanotubes, and GaAs nanowires. Notably, we highlight the critical role of the Coulomb cutoff by studying previously inaccessible polar-optical phonons and Frohlich electron-phonon couplings. We also develop and apply analytical models to support the physical insights derived from the calculations and we discuss their consequences on electronic lifetimes. The present work unlocks the possibility to accurately simulate the linear response properties of one-dimensional systems, sheds light on the transition between dimensionalities and paves the way for further studies in several fields, including charge transport, optical coupling and polaritronics.

cond-mat.mtrl-sci↗
arXiv2023

Towards a minimal description of dynamical correlation in metals

Dynamical correlations and non-local contributions beyond static mean-field theories are of fundamental importance for describing the electronic structure of correlated metals. Their effects are usually described with many-body approaches and non-local dynamical self-energies. We suggest here a class of simple model self-energies that are a generalization of the static DFT + Hubbard approach. This formulation, for simplicity called DFT+U(ω)+V, provides an intuitive physical picture, a lightweight implementation, and displays very good agreement with experimental data.

cond-mat.str-el↗
arXiv2023

On Green's function embedding using sum-over-pole representations

In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the interacting system is embedded into a bath. This latter can then act as a dynamical (i.e., frequency-dependent) potential, providing a more general framework than that of conventional static external potentials. Notably, the Klein functional includes a term of the form $\text{Tr}_ω\text{Ln}\left\{G_0^{-1}G\right\}$, where $\text{Tr}_ω$ is the frequency integration of the trace operator. Here, we show that using a sum-over-pole representation for the Green's functions and the algorithmic-inversion method one can obtain in full generality an explicit analytical expression for $\text{Tr}_ω\text{Ln}\left\{G_0^{-1}G\right\}$. This allows one, e.g., to derive a variational expression for the Klein functional in the presence of an embedding bath, or to provide an explicit expression of the RPA correlation energy in the framework of the optimized effective potential.

cond-mat.mtrl-sci↗
arXiv2023

A complementary screening for quantum spin Hall insulators in 2D exfoliable materials

Quantum spin Hall insulators are a class of topological materials that has been extensively studied during the past decade. One of their distinctive features is the presence of a finite band gap in the bulk and gapless, topologically protected edge states that are spin-momentum locked. These materials are characterized by a $\mathbb{Z}_2$ topological order where, in the 2D case, a single topological invariant can be even or odd for a trivial or a topological material, respectively. Thanks to their interesting properties, such as the realization of dissipationless spin currents, spin pumping and spin filtering, they are of great interest in the field of electronics, spintronics and quantum computing. In this work we perform an high-throughput screening of Quantum spin Hall insulators starting from a set of 783 2D exfoliable materials, recently identified from a systematic screening of the ICSD, COD, and MPDS databases. We find a new $\mathbb{Z}_2$ topological insulator (HgNS) as well as 3 already known ones and 7 direect gap metals that have the potential of becoming Quantum spin Hall insulators under a reasonably weak external perturbation.

cond-mat.mes-hall↗
arXiv2023

Automated all-functionals infrared and Raman spectra

Infrared and Raman spectroscopies are ubiquitous techniques employed in many experimental laboratories, thanks to their fast and non-destructive nature able to capture materials' features as spectroscopic fingerprints. Nevertheless, these measurements frequently need theoretical support in order to unambiguously decipher and assign complex spectra. Linear-response theory provides an effective way to obtain the higher-order derivatives needed, but its applicability to modern exchange-correlation functionals remains limited. Here, we devise an automated, open-source, user-friendly approach based on ground-state density-functional theory and the electric enthalpy functional to allow seamless calculations of first-principles infrared and Raman spectra. By employing a finite-displacement and finite-field approach, we allow for the use of any functional, as well as an efficient treatment of large low-symmetry structures. Additionally, we propose a simple scheme for efficiently sampling the Brillouin zone with different electric fields. To demonstrate the capabilities of our approach, we provide illustrations using the ferroelectric LiNbO$_3$ crystal as a paradigmatic example. We predict infrared and Raman spectra using various (semi)local, Hubbard corrected, and hybrid functionals. Our results also show how PBE0 and extended Hubbard functionals yield in this case the best match in term of peak positions and intensities, respectively.

cond-mat.mtrl-sci↗
arXiv2023

koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals

Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise linearity condition to the entire electronic manifold, ensuring that orbital energies match the corresponding electron removal/addition energy differences (in contrast to semi-local DFT, where a mismatch between the two lies at the heart of the band gap problem and, more generally, the unreliability of Kohn-Sham orbital energies). This strategy has proven to be very powerful, yielding molecular orbital energies and solid-state band structures with comparable accuracy to many-body perturbation theory but at greatly reduced computational cost while preserving a functional formulation. This paper reviews the theory of Koopmans functionals, discusses the algorithms necessary for their implementation, and introduces koopmans, an open-source package that contains all of the code and workflows needed to perform Koopmans functional calculations and obtain reliable spectral properties of molecules and materials.

cond-mat.mtrl-sci↗
arXiv2023

High-throughput screening of Weyl semimetals

Topological Weyl semimetals represent a novel class of non-trivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low-energy properties akin to those of Weyl fermions, and are responsible for several exotic phenomena. Up to this day, only a handful of Weyl semimetals have been discovered, and the search for new ones remains a very active area. The main challenge on the computational side arises from the fact that many of the tools used to identify the topological class of a material do not provide a complete picture in the case of Weyl semimetals. In this work, we propose an alternative and inexpensive, criterion to screen for possible Weyl fermions, based on the analysis of the band structure along high-symmetry directions in the absence of spin-orbit coupling. We test the method by running a high-throughput screening on a set of 5455 inorganic bulk materials and identify 49 possible candidates for topological properties. A further analysis, carried out by identifying and characterizing the crossings in the Brillouin zone, shows us that 3 of these candidates are Weyl semimetals. Interestingly, while these 3 materials underwent other high-throughput screenings, none had revealed their topological behavior before.

cond-mat.mtrl-sci↗
arXiv2023

The rule of four: anomalous stoichiometries of inorganic compounds

Why are materials with specific characteristics more abundant than others? This is a fundamental question in materials science and one that is traditionally difficult to tackle, given the vastness of compositional and configurational space. We highlight here the anomalous abundance of inorganic compounds whose primitive unit cell contains a number of atoms that is a multiple of four. This occurrence - named here the 'rule of four' - has to our knowledge not previously been reported or studied. Here, we first highlight the rule's existence, especially notable when restricting oneself to experimentally known compounds, and explore its possible relationship with established descriptors of crystal structures, from symmetries to energies. We then investigate this relative abundance by looking at structural descriptors, both of global (packing configurations) and local (the smooth overlap of atomic positions) nature. Contrary to intuition, the overabundance does not correlate with low-energy or high-symmetry structures; in fact, structures which obey the 'rule of four' are characterized by low symmetries and loosely packed arrangements maximizing the free volume. We are able to correlate this abundance with local structural symmetries, and visualize the results using a hybrid supervised-unsupervised machine learning method.

cond-mat.mtrl-sci↗
arXiv2023

Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Maximally-localized Wannier functions (MLWFs) are a powerful and broadly used tool to characterize the electronic structure of materials, from chemical bonding to dielectric response to topological properties. Most generally, one can construct MLWFs that describe isolated band manifolds, e.g. for the valence bands of insulators, or entangled band manifolds, e.g. in metals or describing both the valence and the conduction manifolds in insulators. Obtaining MLWFs that describe a target manifold accurately and with the most compact representation often requires chemical intuition and trial and error, a challenging step even for experienced researchers and a roadblock for automated high-throughput calculations. Here, we present a powerful approach that automatically provides MLWFs spanning the occupied bands and their natural complement for the empty states, resulting in Wannier Hamiltonian models that provide a tight-binding picture of optimized atomic orbitals in crystals. Key to the success of the algorithm is the introduction of a projectability measure for each Bloch state onto atomic orbitals (here, chosen from the pseudopotential projectors) that determines if that state should be kept identically, discarded, or mixed into a disentangling algorithm. We showcase the accuracy of our method by comparing a reference test set of 200 materials against the selected-columns-of-the-density-matrix algorithm, and its reliability by constructing Wannier Hamiltonians for 21737 materials from the Materials Cloud.

physics.comp-ph↗
arXiv2023

Fermi energy determination for advanced smearing techniques

Smearing techniques are widely used in first-principles calculations of metallic and magnetic materials, where they improve the accuracy of Brillouin zone sampling and lessen the impact of level-crossing instabilities. Smearing introduces a fictitious electronic temperature that smooths the discontinuities of the integrands; consequently, a corresponding fictitious entropic term arises, and needs to be considered in the total free energy functional. Advanced smearing techniques -- such as Methfessel-Paxton and cold smearing -- have been introduced to guarantee that the system's total free energy remains independent of the smearing temperature at least up to the second order. In doing so, they give rise to non-monotonic occupation functions (and, for Methfessel-Paxton, non-positive definite), which can result in the chemical potential not being uniquely defined. We explore this shortcoming in detail and introduce a numerical protocol utilizing Newton's minimization method that is able to identify the desired Fermi energy. We validate the method by calculating the Fermi energy of $\sim$20,000 materials and comparing it with the results of standard bisection approaches. In passing, we also highlight how traditional approaches, based on Fermi-Dirac or Gaussian smearing, are actually equivalent for all practical purposes, provided the smearing width is appropriately renormalized by a factor $\sim$2.565.

cond-mat.mtrl-sci↗