arXiv subjects

Marco Bernardi

Publications and source records attributed to Marco Bernardi.

At least 55 records · Page 3Linked to original sources

arXiv2020

Physical Origin of the One-Quarter Exact Exchange in Density Functional Theory

Exchange interactions are a manifestation of the quantum mechanical nature of the electrons and play a key role in predicting the properties of materials from first principles. In density functional theory (DFT), a widely used approximation to the exchange energy combines fractions of density-based and Hartree-Fock (exact) exchange. This so-called hybrid DFT scheme is accurate in many materials, for reasons that are not fully understood. Here we show that a 1/4 fraction of exact exchange plus a 3/4 fraction of density-based exchange is compatible with a correct quantum mechanical treatment of the exchange energy of an electron pair in the unpolarized electron gas. We also show that the 1/4 exact-exchange fraction mimics a correlation interaction between doubly-excited electronic configurations. The relation between our results and trends observed in hybrid DFT calculations is discussed, along with other implications.

cond-mat.mtrl-sci↗

arXiv2020

Exciton-Phonon Interaction and Relaxation Times from First Principles

Electron-phonon ($e$-ph) interactions are key to understanding the dynamics of electrons in materials, and can be modeled accurately from first-principles. However, when electrons and holes form Coulomb-bound states (excitons), quantifying their interactions and scattering processes with phonons remains an open challenge. Here we show a rigorous approach for computing exciton-phonon (ex-ph) interactions and the associated exciton dynamical processes from first principles. Starting from the ab initio Bethe-Salpeter equation, we derive expressions for the ex-ph matrix elements and relaxation times. We apply our method to bulk hexagonal boron nitride, for which we map the ex-ph relaxation times as a function of exciton momentum and energy, analyze the temperature and phonon-mode dependence of the ex-ph scattering processes, and accurately predict the phonon-assisted photoluminescence. The approach introduced in this work is general and provides a framework for investigating exciton dynamics in a wide range of materials.

cond-mat.mtrl-sci↗

arXiv2020

Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN

First-principles calculations of $e$-ph interactions are becoming a pillar of electronic structure theory. However, the current approach is incomplete. The piezoelectric (PE) $e$-ph interaction, a long-range scattering mechanism due to acoustic phonons in non-centrosymmetric polar materials, is not accurately described at present. Current calculations include short-range $e$-ph interactions (obtained by interpolation) and the dipole-like Fröhlich long-range coupling in polar materials, but lack important quadrupole effects for acoustic modes and PE materials. Here we derive and compute the long-range $e$-ph interaction due to dynamical quadrupoles, and apply this framework to investigate $e$-ph interactions and the carrier mobility in the PE material wurtzite GaN. We show that the quadrupole contribution is essential to obtain accurate $e$-ph matrix elements for acoustic modes and to compute PE scattering. Our work resolves the outstanding problem of correctly computing $e$-ph interactions for acoustic modes from first principles, and enables studies of $e$-ph coupling and charge transport in PE materials.

cond-mat.mtrl-sci↗

arXiv2020

Perturbo: a software package for ab initio electron-phonon interactions, charge transport and ultrafast dynamics

Perturbo is a software package for first-principles calculations of charge transport and ultrafast carrier dynamics in materials. The current version focuses on electron-phonon interactions and can compute phonon-limited transport properties such as the conductivity, carrier mobility and Seebeck coefficient. It can also simulate the ultrafast nonequilibrium electron dynamics in the presence of electron-phonon scattering. Perturbo uses results from density functional theory and density functional perturbation theory calculations as input, and employs Wannier interpolation to reduce the computational cost. It supports norm-conserving and ultrasoft pseudopotentials, spin-orbit coupling, and polar electron-phonon corrections for bulk and 2D materials. Hybrid MPI plus OpenMP parallelization is implemented to enable efficient calculations on large systems (up to at least 50 atoms) using high-performance computing. Taken together, Perturbo provides efficient and broadly applicable ab initio tools to investigate electron-phonon interactions and carrier dynamics quantitatively in metals, semiconductors, insulators, and 2D materials.

cond-mat.mtrl-sci↗

arXiv2019

Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO$_{\mathrm{3}}$

In materials with strong electron-phonon ($e$-ph) interactions, the electrons carry a phonon cloud during their motion, forming quasiparticles known as polarons. Predicting charge transport and its temperature dependence in the polaron regime remains an open challenge. Here, we present first-principles calculations of charge transport in a prototypical material with large polarons, SrTiO$_{3}$. Using a cumulant diagram-resummation technique that can capture the strong $e$-ph interactions, our calculations can accurately predict the experimental electron mobility in SrTiO$_{3}$ between 150$-$300 K. They further reveal that for increasing temperature the charge transport mechanism transitions from band-like conduction, in which the scattering of renormalized quasiparticles is dominant, to a beyond-quasiparticle transport regime governed by incoherent contributions due to the interactions between the electrons and their phonon cloud. Our work reveals long-sought microscopic details of charge transport in SrTiO$_{3}$, and provides a broadly applicable method for predicting charge transport in materials with strong $e$-ph interactions and polarons.

cond-mat.mtrl-sci↗

arXiv2019

Ab initio electron-defect interactions using Wannier functions

Computing electron-defect (e-d) interactions from first principles has remained impractical due to computational cost. Here we develop an interpolation scheme based on maximally localized Wannier functions (WFs) to efficiently compute e-d interaction matrix elements. The interpolated matrix elements can accurately reproduce those computed directly without interpolation, and the approach can significantly speed up calculations of e-d relaxation times and defect-limited charge transport. We show example calculations of vacancy defects in silicon and copper, for which we compute the e-d relaxation times on fine uniform and random Brillouin zone grids (and for copper, directly on the Fermi surface) as well as the defect-limited resistivity at low temperature. Our interpolation approach opens doors for atomistic calculations of charge carrier dynamics in the presence of defects.

cond-mat.mtrl-sci↗

arXiv2019

Ab Initio Calculations of Exciton Radiative Lifetimes in Bulk Crystals, Nanostructures and Molecules

Excitons are bound electron-hole pairs that dominate the optical response of semiconductors and insulators, especially in materials where the Coulomb interaction is weakly screened. Light absorption (including excitonic effects) has been studied extensively using first-principles calculations, but methods for computing radiative recombination and light emission are still being developed. Here we show a unified ab initio approach to compute exciton radiative recombination in materials ranging from bulk crystals to nanostructures and molecules. We derive the rate of exciton radiative recombination in bulk crystals, isolated systems, and in one- and two-dimensional materials, using Fermi's golden rule within the Bethe-Salpeter equation approach. We present benchmark calculations of radiative lifetimes in a GaAs crystal and in gas-phase organic molecules. Our work provides a general method for studying exciton recombination and light emission in bulk, nanostructured and molecular materials from first principles.

cond-mat.mtrl-sci↗

arXiv2019

Elliott-Yafet Spin-Phonon Relaxation Times from First Principles

We present a first-principles approach for computing the phonon-limited $T_1$ spin relaxation time due to the Elliot-Yafet mechanism. Our scheme combines fully-relativistic spin-flip electron-phonon interactions with an approach to compute the effective spin of band electrons in materials with inversion symmetry. We apply our method to silicon and diamond, for which we compute the temperature dependence of the spin relaxation times and analyze the contributions to spin relaxation from different phonons and valley processes. The computed spin relaxation times in silicon are in excellent agreement with experiment in the 50$-$300 K temperature range. In diamond, we predict intrinsic spin relaxation times of 540 $μ$s at 77 K and 2.3 $μ$s at 300 K. Our work enables precise predictions of spin-phonon relaxation times in a wide range of materials, providing microscopic insight into spin relaxation and guiding the development of spin-based quantum technologies.

cond-mat.mtrl-sci↗

arXiv2019

Next-to-Leading Order Ab Initio Electron-Phonon Scattering

Electron-phonon (e-ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading order e-ph interactions, and compute from first principles the associated two-phonon e-ph scattering rates. The derivation involves Matsubara sums of the relevant two-loop Feynman diagrams, and the numerical calculations are challenging since they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using random grids and Monte Carlo integration, together with a self-consistent update of the intermediate state lifetimes, we compute and converge the two-phonon scattering rates, using GaAs as a case study. For the longitudinal optical phonon in GaAs, we find that the two-phonon scattering rates are as large as nearly half the value of the leading-order rates. The energy and temperature dependence of the two-phonon processes are analyzed. We show that including the two-phonon processes is important to accurately predicting the electron mobility in GaAs.

cond-mat.mes-hall↗

arXiv2019

Efficient Ab Initio Calculations of Electron-Defect Scattering and Defect-Limited Carrier Mobility

Electron-defect ($e$-d) interactions govern charge carrier dynamics at low temperature, where they limit the carrier mobility and give rise to phenomena of broad relevance in condensed matter physics. Ab initio calculations of $e$-d interactions are still in their infancy, mainly because they require large supercells and computationally expensive workflows. Here we develop an efficient ab initio approach for computing elastic $e$-d interactions, their associated $e$-d relaxation times (RTs), and the low-temperature defect-limited carrier mobility. The method is applied to silicon with simple neutral defects, such as vacancies and interstitials. Contrary to conventional wisdom, the computed $e$-d RTs depend strongly on carrier energy and defect type, and the defect-limited mobility is temperature dependent. These results highlight the shortcomings of widely employed heuristic models of $e$-d interactions in materials. Our method opens new avenues for studying $e$-d scattering and low-temperature charge transport from first principles.

cond-mat.mtrl-sci↗

arXiv2018

Electron-Phonon Scattering in the Presence of Soft Modes and Electron Mobility in SrTiO$_{3}$ Perovskite from First Principles

Structural phase transitions and soft phonon modes pose a longstanding challenge to computing electron-phonon (e-ph) interactions in strongly anharmonic crystals. Here we develop a first-principles approach to compute e-ph scattering and charge transport in materials with anharmonic lattice dynamics. Our approach employs renormalized phonons to compute the temperature-dependent e-ph coupling for all phonon modes, including the soft modes associated with ferroelectricity and phase transitions. We show that the electron mobility in cubic SrTiO$_{3}$ is controlled by scattering with longitudinal optical phonons at room temperature and with ferroelectric soft phonons below 200~K. Our calculations can accurately predict the temperature dependence of the electron mobility in SrTiO$_{3}$ between 150$-$300~K, and reveal the microscopic origin of its roughly $T^{-3}$ trend. Our approach enables first-principles calculations of e-ph interactions and charge transport in broad classes of crystals with phase transitions and strongly anharmonic phonons.

cond-mat.mtrl-sci↗

arXiv2018

Exploiting Recurrent Neural Networks and Leap Motion Controller for Sign Language and Semaphoric Gesture Recognition

In human interactions, hands are a powerful way of expressing information that, in some cases, can be used as a valid substitute for voice, as it happens in Sign Language. Hand gesture recognition has always been an interesting topic in the areas of computer vision and multimedia. These gestures can be represented as sets of feature vectors that change over time. Recurrent Neural Networks (RNNs) are suited to analyse this type of sets thanks to their ability to model the long term contextual information of temporal sequences. In this paper, a RNN is trained by using as features the angles formed by the finger bones of human hands. The selected features, acquired by a Leap Motion Controller (LMC) sensor, have been chosen because the majority of human gestures produce joint movements that generate truly characteristic corners. A challenging subset composed by a large number of gestures defined by the American Sign Language (ASL) is used to test the proposed solution and the effectiveness of the selected angles. Moreover, the proposed method has been compared to other state of the art works on the SHREC dataset, thus demonstrating its superiority in hand gesture recognition accuracy.

cs.CV↗

arXiv2018

Ab Initio Electron-Phonon Interactions Using Atomic Orbital Wavefunctions

The interaction between electrons and lattice vibrations determines key physical properties of materials, including their electrical and heat transport, excited electron dynamics, phase transitions, and superconductivity. We present a new ab initio method that employs atomic orbital (AO) wavefunctions to compute the electron-phonon (e-ph) interactions in materials and interpolate the e-ph coupling matrix elements to fine Brillouin zone grids. We detail the numerical implementation of such AO-based e-ph calculations, and benchmark them against direct density functional theory calculations and Wannier function (WF) interpolation. The key advantages of AOs over WFs for e-ph calculations are outlined. Since AOs are fixed basis functions associated with the atoms, they circumvent the need to generate a material-specific localized basis set with a trial-and-error approach, as is needed in WFs. Therefore, AOs are ideal to compute e-ph interactions in chemically and structurally complex materials for which WFs are challenging to generate, and are also promising for high-throughput materials discovery. While our results focus on AOs, the formalism we present generalizes e-ph calculations to arbitrary localized basis sets, with WFs recovered as a special case.

cond-mat.mtrl-sci↗

arXiv2018

Charge Transport in Organic Molecular Semiconductors from First Principles: The Band-Like Hole Mobility in Naphthalene Crystal

Predicting charge transport in organic molecular crystals is notoriously challenging. Carrier mobility calculations in organic semiconductors are dominated by quantum chemistry methods based on charge hopping, which are laborious and only moderately accurate. We compute from first principles the electron-phonon scattering and the phonon-limited hole mobility of naphthalene crystal in the framework of ab initio band theory. Our calculations combine GW electronic bandstructures, ab initio electron-phonon scattering, and the Boltzmann transport equation. The calculated hole mobility is in very good agreement with experiment between 100$-$300 K, and we can predict its temperature dependence with high accuracy. We show that scattering between inter-molecular phonons and holes regulates the mobility, though intra-molecular phonons possess the strongest coupling with holes. We revisit the common belief that only rigid molecular motions affect carrier dynamics in organic molecular crystals. Our work provides a quantitative and rigorous framework to compute charge transport in organic crystals, and is a first step toward reconciling band theory and carrier hopping computational methods.

cond-mat.mtrl-sci↗

arXiv2018

Theory and Ab Initio Computation of the Anisotropic Light Emission in Monolayer Transition Metal Dichalcogenides

Monolayer transition metal dichalcogenides (TMDCs) are direct gap semiconductors with unique potential for ultrathin light emitters. Yet, their photoluminescence (PL) is not completely understood. We compute the radiative recombination rate in monolayer TMDCs as a function of photon emission direction and polarization, and obtain polar plots of the PL for different excitation scenarios using the ab initio Bethe-Salpeter equation. We show that excitons in a quantum superposition state of the K and K' inequivalent valleys emit light anisotropically upon recombination. Our results can explain the PL anisotropy and polarization dependence measured in recent experiments, and predict new light emission regimes. When averaged over emission angle and exciton momentum, our new treatment recovers the temperature dependent radiative lifetimes we previously derived. Our work provides a first-principles approach to study light emission in two-dimensional materials.

cond-mat.mtrl-sci↗

arXiv2017

Ultrafast Hot Carrier Dynamics in GaN and its Impact on the Efficiency Droop

GaN is a key material for lighting technology. Yet, the carrier transport and ultrafast dynamics that are central in GaN light emitting devices are not completely understood. We present first-principles calculations of carrier dynamics in GaN, focusing on electron-phonon (e-ph) scattering and the cooling and nanoscale dynamics of hot carriers. We find that e-ph scattering is significantly faster for holes compared to electrons, and that for hot carriers with an initial 0.5$-$1 eV excess energy, holes take a significantly shorter time ($\sim$0.1 ps) to relax to the band edge compared to electrons, which take $\sim$1 ps. The asymmetry in the hot carrier dynamics is shown to originate from the valence band degeneracy, the heavier effective mass of holes compared to electrons, and the details of the coupling to different phonon modes in the valence and conduction bands. We show that the slow cooling of hot electrons and their long ballistic mean free paths (over 3 nm) are a possible cause of efficiency droop in GaN light emitting diodes. Taken together, our work sheds light on the ultrafast dynamics of hot carriers in GaN and the nanoscale origin of efficiency droop.

cond-mat.mtrl-sci↗

arXiv2016

Ab initio Electron Mobility and Polar Phonon Scattering in GaAs

In polar semiconductors and oxides, the long-range nature of the electron-phonon (\textit{e}-ph) interaction is a bottleneck to compute charge transport from first principles. Here, we develop an efficient ab initio scheme to compute and converge the \textit{e}-ph relaxation times (RTs) and electron mobility in polar materials. We apply our approach to GaAs, where using the Boltzmann equation with state-dependent RTs, we compute mobilities in excellent agreement with experiment at 250$-$500~K. The $e$-ph RTs and the phonon contributions to intravalley and intervalley $e$-ph scattering are also analyzed. Our work enables efficient ab initio computations of transport and carrier dynamics in polar materials.

cond-mat.mtrl-sci↗

arXiv2016

First-principles dynamics of electrons and phonons

First-principles calculations combining density functional theory and many-body perturbation theory can provide microscopic insight into the dynamics of electrons and phonons in materials. We review this theoretical and computational framework, focusing on perturbative treatments of scattering, dynamics and transport of coupled electrons and phonons. We discuss application of these first-principles calculations to electronics, lighting, spectroscopy and renewable energy.

cond-mat.mtrl-sci↗