Electron-phonon physics from first principles using the EPW code
Hyungjun Lee, Samuel Poncé, Kyle Bushick, Samad Hajinazar, Jon Lafuente-Bartolome, Joshua Leveillee, Chao Lian, Francesco Macheda, Hari Paudyal, Weng Hong Sio, … 展开作者
Hyungjun Lee, Samuel Poncé, Kyle Bushick, Samad Hajinazar, Jon Lafuente-Bartolome, Joshua Leveillee, Chao Lian, Francesco Macheda, Hari Paudyal, Weng Hong Sio, Marios Zacharias, Xiao Zhang, Nicola Bonini, Emmanouil Kioupakis, Elena R. Margine, Feliciano Giustino
EPW is an open-source software for $\textit{ab initio}$ calculations of electron-phonon interactions and related materials properties. The code combines density functional perturbation theory and maximally-localized Wannier functions to efficiently compute electron-phonon coupling matrix elements on ultra-fine Brillouin zone grids. This data is employed for predictive calculations of temperature-dependent properties and phonon-assisted quantum processes in bulk solids and low-dimensional materials. Here, we report on significant new developments in the code that occurred during the period 2016-2022, namely: a transport module for the calculation of charge carrier mobility and conductivity under electric and magnetic fields within the $\textit{ab initio}$ Boltzmann transport equation; a superconductivity module for the calculation of critical temperature and gap structure in phonon-mediated superconductors within the $\textit{ab initio}$ anisotropic multi-band Eliashberg theory; an optics module for calculations of phonon-assisted indirect transitions; a module for the calculation of small and large polarons without supercells using the $\textit{ab initio}$ polaron equations; and a module for calculating electron-phonon couplings, band structure renormalization, and temperature-dependent optical spectra using the special displacement method. For each capability, we outline the methodology and implementation, and provide example calculations. We describe recent code refactoring to prepare EPW for exascale architectures, we discuss efficient parallelization strategies, and report on extreme parallel scaling tests.
The EPW (Electron-Phonon coupling using Wannier functions) software is a Fortran90 code that uses density-functional perturbation theory and maximally localized Wannier functions for computing electron-phonon couplings and related properties in solids accurately and efficiently. The EPW v4 program can be used to compute electron and phonon self-energies, linewidths, electron-phonon scattering rates, electron-phonon coupling strengths, transport spectral functions, electronic velocities, resistivity, anisotropic superconducting gaps and spectral functions within the Migdal-Eliashberg theory. Th…
EPW (Electron-Phonon coupling using Wannier functions) is a program written in FORTRAN90 for calculating the electron-phonon coupling in periodic systems using density-functional perturbation theory and maximally-localized Wannier functions. EPW can calculate electron-phonon interaction self-energies, electron-phonon spectral functions, and total as well as mode-resolved electron-phonon coupling strengths. The calculation of the electron-phonon coupling requires a very accurate sampling of electron-phonon scattering processes throughout the Brillouin zone, hence reliable calculations can be pr…
Motivated by the recent experimental discovery of strongly surface-plane-dependent superconductivity at surfaces of KTaO$_3$ single crystals, we calculate the electron-phonon coupling strength, $λ$, of doped KTaO$_3$ along the reciprocal-space high-symmetry directions. Using the Wannier-function approach implemented in the EPW package, we calculate $λ$ across the experimentally covered doping range and compare its mode-resolved distribution along the [001], [110] and [111] reciprocal-space directions. We find that the electron-phonon coupling is strongest in the optical modes around the $Γ$ po…
We have studied the influence of magnetic order on the optical phonons of the geometrically frustrated spinel ZnCr$_2$O$_4$ from first-principles. By mapping the first-principles phonon calculations onto a Heisenberg-like model, we developed a method to calculate exchange derivatives and subsequently the spin-phonon couping parameter from first-principles. All calculations were performed within LSDA+U.
Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized. Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.
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.
Lattice thermal conductivities of two SiO$_2$ polymorphs, i.e., $α$-quartz (low) and $α$-cristobalite (low), were studied using first-principles anharmonic phonon calculation and linearized phonon Boltzmann transport equation. Although $α$-quartz and $α$-cristobalite have similar phonon densities of states, phonon frequency dependencies of phonon group velocities and lifetimes are dissimilar, which results in largely different anisotropies of the lattice thermal conductivities. For $α$-quartz and $α$-cristobalite, distributions of the phonon lifetimes effective to determine the lattice thermal…
First principles calculation supports the occurence of a phonon anomaly along [211] in Ni$_2$FeGa that was observed experimentally for the first time as structural modulations along [211] direction. Fermi surface scans have been performed in both austenite and martensite phase to observe the possible Fermi nesting features in the system. The magnitude of observed Fermi surface nesting vectors in (211) plane exactly match the phonon anomaly wavevectors along [211] direction. Electron-phonon calculations in the austenite phase shows that there is significant electron-phonon coupling in the syste…
Phonon energies at finite temperatures shift away from their harmonic values due to anharmonicity. In this paper, we have realized the rigorous calculation of phonon energy shifts of silicon by three and four-phonon scattering from first principles. The anharmonic fourth-order force constants are calculated by considering up to the fifth nearest neighbors. The results agree reasonably well with available data from inelastic neutron scattering throughout the Brillouin zone. Surprisingly, the frequency shifts of optical phonon modes near the $Γ$ point are sensitive to the cutoff radius of the fo…
We study the magnetically-induced phonon splitting in cubic ACr$_2$O$_4$ (A=Mg, Zn, Cd, Hg) spinels from first principles, and demonstrate that the sign of the splitting, which is experimentally observed to be opposite in CdCr$_2$O$_4$ compared to ZnCr$_2$O$_4$ and MgCr$_2$O$_4$, is determined solely by the particular magnetic ordering pattern observed in these compounds. We further show that this interaction between magnetism and phonon frequencies can be fully described by the previously proposed spin-phonon coupling model that includes only the nearest neighbor exchange. Finally, using this…
We have studied the dielectric properties of the ferromagnetic spinel CdCr$_2$S$_4$ from first principles. Zone-center phonons and Born effective charges were calculated by frozen-phonon and Berry phase techniques within LSDA+U. We find that all infrared-active phonons are quite stable within the cubic space group. The calculated static dielectric constant agrees well with previous measurements. These results suggest that the recently observed anomalous dielectric behavior in CdCr$_2$S$_4$ is not due to the softening of a polar mode. We suggest further experiments to clarify this point.
We develop a method for calculating the electron-phonon vertex in polar semiconductors and insulators from first principles. The present formalism generalizes the Fröhlich vertex to the case of anisotropic materials and multiple phonon branches, and can be used either as a post-processing correction to standard electron-phonon calculations, or in conjunction with {\it ab initio} interpolation based on maximally localized Wannier functions. We demonstrate this formalism by investigating the electron-phonon interactions in anatase TiO$_2$, and show that the polar vertex significantly reduces the…
Longitudinal-optical (LO) mode phonon branches of KCl and NaCl were measured using inelastic X-ray scattering (IXS) at 300 K and calculated by the first-principles phonon calculation with the stochastic self-consistent harmonic approximation. Spectral shapes of the IXS measurements and calculated spectral functions agreed well. We analyzed the calculated spectral functions that provide higher resolutions of the spectra than the IXS measurements. Due to strong anharmonicity, the spectral functions of these phonon branches have several peaks and the LO modes along $Γ$--L paths are disconnected.
Separating electron and phonon thermal conductivity components is imperative for understanding the principle thermal transport mechanisms in metals and highly desirable in many applications. In this work, we predict the mode-dependent electron and phonon thermal conductivities of 18 different metals at room-temperature from first-principles. Our first-principles predictions, in general, agree well with experimental data. We find that the phonon thermal conductivity is in the range of 2 - 18 $W/mK$, which accounts for 1% - 40% of the total thermal conductivity. It is also found that the phonon …
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 …
Electron-phonon interaction has been well known to create major resistance to electron transport in metals and semiconductors, whereas less studies were directed to its effect on the phonon transport, especially in semiconductors. We calculate the phonon lifetimes due to scattering with electrons (or holes), combine them with the intrinsic lifetimes due to the anharmonic phonon-phonon interaction, all from first-principles, and evaluate the effect of the electron-phonon interaction on the lattice thermal conductivity of silicon. Unexpectedly, we find a significant reduction of the lattice ther…
Inelastic scattering experiments are key methods for mapping the full dispersion of fundamental excitations of solids in the ground as well as non-equilibrium states. A quantitative analysis of inelastic scattering in terms of phonon excitations requires identifying the role of multi-phonon processes. Here, we develop an efficient first-principles methodology for calculating the all-phonon quantum mechanical structure factor of solids. We demonstrate our method by obtaining excellent agreement between measurements and calculations of the diffuse scattering patterns of black phosphorus, showing…
$Ab-initio$ probabilities of phonon-assisted intervalley scattering of electrons in the conduction bands of ternary chalcopyrite compounds $ZnSiP_2$ and $ZnGeP_2$ between the central $Γ$ minima and the lowest lateral minima (valleys) at $T$ and $N$ points have been calculated using the density functional theory. The equilibrium parameters of crystal structures, spectra of electrons and phonons are calculated self-consistently and are in fairly good agreement with the experiment and available theoretical calculations. The electron-phonon coupling constants with short-wave (inter-valley) phonons…
We report first-principles calculations of the phonon dispersion spectrum, thermal expansion, and heat capacity of uranium dioxide. The so-called direct method, based on the quasiharmonic approximation, is used to calculate the phonon frequencies within a density functional framework for the electronic structure. The phonon dispersions calculated at the theoretical equilibrium volume agree well with experimental dispersions. The computed phonon density of states (DOS) compare reasonably well with measurement data, as do also the calculated frequencies of the Raman and infrared active modes inc…
This study presents the first-principles phonon calculations to understand the experimental thermal expansion ($α(T)$) and lattice thermal conductivity ($κ_{L}$) of CoSi at high temperature region. Phonon dispersion is computed using finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of $α(T)$ is done under quasi-harmonic approximation. The $κ_{L}$ is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. Calculated $α(T)$ in the temperature range $…
This article reviews the theory of electron-phonon interactions in solids from the point of view of ab-initio calculations. While the electron-phonon interaction has been studied for almost a century, predictive non-empirical calculations have become feasible only during the past two decades. Today it is possible to calculate from first principles many materials properties related to the electron-phonon interaction, including the critical temperature of conventional superconductors, the carrier mobility in semiconductors, the temperature dependence of optical spectra in direct and indirect-gap…
Renormalization of the electronic band gap due to electron-phonon coupling in the tetrahedral semiconductors diamond, silicon and cubic silicon carbide is studied from first principles. There is a marked difference between the coupling of the vibrational state to the valence band maximum and to the conduction band minimum. The strength of phonon coupling to the valence band maximum is similar between the three systems and is dominated by vibrations that change the bond length. The coupling strength to the conduction band minimum differs significantly in diamond, silicon carbide and silicon. In…
The phonon-assisted interband optical absorption spectrum of silicon is calculated at the quasiparticle level entirely from first principles. We make use of the Wannier interpolation formalism to determine the quasiparticle energies, as well as the optical transition and electron-phonon coupling matrix elements, on fine grids in the Brillouin zone. The calculated spectrum near the onset of indirect absorption is in very good agreement with experimental measurements for a range of temperatures. Moreover, our method can accurately determine the optical absorption spectrum of silicon in the visib…
The lattice dynamic properties and spin-phonon coupling in DyMn$_2$O$_5$ are studied by using the density-functional theory. The calculated phonon frequencies are in very good agreement with experiments. We then compare the phonon modes calculated from different spin configurations. The results show that the phonon frequencies change substantially in different spin configurations, suggesting that the spin-phonon coupling in this material is very strong. Especially, the short range spin ordering has drastic effects on the highest Raman and IR phonon modes that might be responsible for the obser…
Ferromagnetic \nmg has unique magnetoelastic properties. These are investigated by detailed computational studies of the phonon dispersion curves for the non-modulated cubic \Ltw and tetragonal structures. For the \Ltw\ structure, a complete softening of the transverse acoustic mode has been found around the wave vector $\mathbf{q}=[1/3,1/3,0](2 π/a)$. The softening of this \TA{2} phonon mode leads to the premartensitic modulated super-structure observed experimentally. Further phonon anomalies, related to other structural transformations in \nmg, have also been found and examined. These anoma…
Two-dimensional transition metal dichalcogenides (TMDCs) are finding promising electronic and optical applications due to their unique properties. In this letter, we systematically study the phonon transport and thermal conductivity of eight semiconducting single-layer TMDCs, MX2 (M=Mo, W, Zr and Hf, X=S and Se), by using the first-principles-driven phonon Boltzmann transport equation approach. The validity of the single-mode relaxation time approximation to predict the thermal conductivity of TMDCs is assessed by comparing the results with the iterative solution of the phonon Boltzmann transp…
We calculate the lattice dielectric function of strongly anharmonic rutile $\mathrm{TiO}_2$ from ab initio anharmonic lattice dynamics methods. Since an accurate calculation of the $Γ$ point phonons is essential for determining optical properties, we employ the modified self-consistent approach, including third-order anharmonicity as well as fourth-order anharmonicity. The resulting optical phonon frequencies and linewidths at the $Γ$ point much better agree with experimental measurements than those from a perturbative approach. We show that the four-phonon scattering process contributes as mu…
Understanding and predicting lattice dynamics in strongly anharmonic crystals is one of the long-standing challenges in condensed matter physics. Here we propose a first-principles method that gives accurate quasiparticle (QP) peaks of the phonon spectrum with strong anharmonic broadening. On top of the conventional first-order self-consistent phonon (SC1) dynamical matrix, the proposed method incorporates frequency renormalization effects by the bubble self-energy within the QP approximation. We apply the developed methodology to the strongly anharmonic $α$-CsPbBr$_3$ that displays phonon ins…
ZrW2O8 exhibits isotropic negative thermal expansions over its entire temperature range of stability, yet so far its physical properties and mechanism have not been fully addressed. In this article, the electronic structure, elastic, thermal, optical and phonon properties of α-ZrW2O8 are systematically investigated from first principles. The agreements between the generalized gradient approximation (GGA) calculation and experiments are found to be quite satisfactory. The calculation results can be useful in relevant material designs, e.g., when ZrW2O8 is employed to adjust the thermal expansio…
We present a simple and efficient approximation to the electron-phonon scattering rate suitable for high-throughput screening of candidate materials for thermoelectric devices, based on electronic transport. The method is applied to calculate the electronic transport coefficients of half-Heusler compounds, showing agreement with experimental data. By directly computing electrical and the electronic part of the thermal conductivities, we find deviations from the Wiedemann-Franz law in these compounds at high temperatures and low carrier concentrations.
The phonon and thermodynamic properties of rare-earth-aluminum intermetallics AlRE (RE=Y, Gd, Pr, Yb) with B2-type structure are investigated by performing density functional theory and density functional perturbation theory within the quasiharmonic approximation. The phonon spectra and phonon density of states, including the phonon partial density of states and total density of states, have been discussed. Our results demonstrate that the density of states is mostly composed of Al states at the high frequency. The temperature dependence of various quantities such as the thermal expansions, th…
Using a first-principles cluster expansion, we shed light on the solid-state phase diagram and structure of the recently discovered high-performance thermoelectrics, Pb-Ag-Sb-Te alloys. The observed nanoscale inhomogeneities are shown to be coherent precipitates of ordered (Ag)m(Sb)n(Te)m+n phases, such as AgSbTe2, all immiscible with rocksalt PbTe. The solubility is high for PbTe in AgSbTe2 and low for (Ag,Sb)Te in PbTe (8% vs. 0.6% at 850 K). The differences in the phonon spectra of PbTe and AgSbTe2 confirm that the inhomogeneities enhance the thermoelectric performance.
Phonon transport of recently-fabricated $\mathrm{Na_2He}$ at high pressure is investigated from a combination of first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). The calculated room-temperature lattice thermal conductivity is 149.19 $\mathrm{W m^{-1} K^{-1}}$, which is very close to one of Si. It is found that low-frequency optical modes comprise 16\% of the lattice thermal conductivity, while high-frequency optical modes have negligible contribution. The high lattice thermal conductivity is due to large grou…
We investigate the role of rattling guest atoms on the lattice thermal-conductivity of a type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ by first-principles lattice dynamics. Comparing phonon properties of filled and empty clathrates, we show that rattlers cause 10-fold reductions in the relaxation time of phonons by increasing the phonon-phonon scattering probability. Contrary to the resonant scattering scenario, the reduction in the relaxation time occurs in a wide frequency range, which is crucial for explaining unusually low thermal-conductivities of clathrates. We also find that the impact of…
We obtained the spin-wave spectrum based on a first-principles method of exchange constants, calculated the phonon spectrum by the first-principles phonon calculation method, and extracted the broadening of the magnon spectrum, $Δω$, induced by magnon-phonon interactions in gadolinium iron garnet (GdIG). Using the obtained exchange constants, we reproduce the experimental Curie temperature and the compensation temperature from spin models using Metropolis Monte Carlo (MC) simulations. In the lower-frequency regime, the fitted positions of the magnon-phonon dispersion crossing points are consis…
First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Theory of Quantum Systems and Complex Systems, Universiteit Antwerpen（安特卫普大学量子系统与复杂系统理论）；Faculty of Physics, Computational Materials Physics, University of Vienna（维也纳大学物理学院计算材料物理系）；Department of Physics and Astronomy “Augusto Righi”, Alma Mater Studiorum - Università di Bologna（博洛尼亚大学阿ugusto Righi物理与天文学系）
First-principles calculations are employed to investigate the phonon transport of BiCuOSe. Our calculations reproduce the lattice thermal conductivity of BiCuOSe. The calculated gruneisen parameter is 2.4~2.6 at room temperature, a fairly large value indicating a strong anharmonicity in BiCuOSe, which leads to its ultralow lattice thermal conductivity. The contribution to total thermal conductivity from high-frequency optical phonons, which are mostly contributed by the vibrations of O atoms, is larger than 1/3, remarkably different from the usual picture with very little contribution from hig…
The paper presents the first-principle calculation of the electron-phonon coupling and the temperature dependence of the intrinsic electrical resistivity of the zirconium-hydrogen system with various hydrogen concentrations. The nature of the anomalous decrease in the electrical resistivity of the Zr-H system with the increase of hydrogen concentration (at the high concentrations of H/Zr$>$1.5) was studied. It was found that the hydrogen concentration, where the resistivity starts to decrease, is very close to the critical concentration of the $δ-\varepsilon$ phase transition. It was shown tha…
Spin-orbit interaction is an important vehicle for spin relaxation. At finite temperature lattice vibrations modulate the spin-orbit interaction and thus generate a mechanism for spin-phonon coupling, which needs to be incorporated in any quantitative analysis of spin transport. Starting from a density functional theory \textit{ab initio} electronic structure, we calculate spin-phonon matrix elements over the basis of maximally localized Wannier functions. Such coupling terms form an effective Hamiltonian to be used to extract thermodynamic quantities, within a multiscale approach particularly…
It is generally assumed in the thermoelectric community that the lattice thermal conductivity of a given material is independent of the electronic properties. This perspective is however questionable since the electron-phonon coupling could have certain effects on both the carrier and phonon transport, which in turn will affect the thermoelectric properties. Using SiGe compound as a prototypical example, we give an accurate prediction of the carrier relaxation time by considering scattering from all the phonon modes, as opposed to the simple deformation potential theory. It is found that the c…
Cyanide based framework compounds are known to show large negative thermal expansion behaviour. Here we report the phonon and anomalous lattice behavior of two metal cyanide framework compounds i.e. KMnAg3(CN)6 and KNiAu3(CN)6. We have studied the role of van der Waals dispersion and magnetic interactions on structural stability of these compounds. The behavior of these compounds under isotropic compression shows the presence of negative linear compressibility. The calculated phonon spectra, validated by inelastic neutron scattering measurements and elastic constants are used to study the nega…
We present an \textit{ab initio} framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density-functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO$_{3}$ and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistorti…
The perovskite BaSnO$_3$ provides a promising platform for the realization of an earth abundant $n$-type transparent conductor. Its optical properties are dominated by a dispersive conduction band of Sn $5s$ states, and by a flatter valence band of O $2p$ states, with an overall indirect gap of about $2.9$ eV. Using first-principles methods, we study the optical properties of BaSnO$_3$ and show that both electron-phonon interactions and exact exchange, included using a hybrid functional, are necessary to obtain a qualitatively correct description of optical absorption in this material. In part…
