The electron-phonon interaction plays a crucial role in many fields of physics and chemistry. Nevertheless, its actual calculation by means of modern many-body perturbation theory is weakened by the use of model Hamiltonians that are based on parameters difficult to extract from the experiments. Such shortcoming can be bypassed by using density-functional theory to evaluate the electron-phonon scattering amplitudes, phonon frequencies and electronic bare energies. In this work, we discuss how a consistent many-body diagrammatic expansion can be constructed on top of density-functional theory. In that context, the role played by screening and self-consistency when all the components of the electron-nucleus and nucleus-nucleus interactions are taken into account is paramount. A way to avoid over-screening is notably presented. Finally, we derive cancellations rules as well as internal consistency constraints in order to draw a clear, sound and practical scheme to merge many-body perturbation and density-functional theory.
A full quantum mechanical theory for the spontaneous emission from excitons simultaneously coupled to electronic excitations and anharmonic phonons in solid is developed. Origin of detailed structures, such as zero-phonon line splitting, Fano lineshape near one phonon sideband, strong second-order phonon Stokes line, asymmetric phonon anti-Stokes lines, and two-electron satellites as well as their phonon replicas recently revealed in the low-temperature photoluminescence of ZnO, has been identified by quantitative calculations from the theory.
Lattice vibrations in CH$_3$NH$_3$PbI$_3$ are strongly interacting, with double well instabilities present at the Brillouin zone boundary. Analysis within a first-principles lattice dynamics framework reveals anharmonic potentials with short phonon quasi-particle lifetimes and mean-free paths. The phonon behaviour is distinct from the inorganic semiconductors GaAs and CdTe where three-phonon interaction strengths are three orders of magnitude smaller. The implications for the applications of hybrid halide perovskites arising from thermal conductivity, band-gap deformation, and charge-carrier s…
We develop a theory for the electron-phonon interaction effects on the electronic properties of graphene. We analytically calculate the electron self-energy, spectral function and band velocity renormalization due to phonon-mediated electron-electron interaction. We find that phonon-mediated electron-electron coupling has a large effect on the graphene band structure renormalization, and our analytic theory successfully captures the essential features of the observed graphene electron spectra in the ARPES experiments, predicting a kink at $\sim 200\mathrm{meV}$ below the Fermi level and a redu…
Based on a new self-energy for atom-phonon interaction, preceding Comment argues about the insufficiency of the mathematical techniques within the Independent Boson Model (IBM) to study physisorption in graphene membranes. In this Reply, we show that the new self-energy reported in the Comment is a perturbative expansion approximated for a 2-phonon process, severely divergent for membrane sizes larger than 100 nm and within its current mathematical form, ill-suited for investigating the physics of physisorption in graphene micromembranes. Additionally, we provide with further evidence of the a…
A method is proposed for the inclusion of electron correlation in the calculation of the temperature dependence of band structures arising from electron-phonon coupling. It relies on an efficient exploration of the vibrational phase space along the recently introduced thermal lines. Using the $G_0W_0$ approximation, the temperature dependence of the direct gaps of diamond, silicon, lithium fluoride, magnesium oxide, and titanium dioxide is calculated. Within the proposed formalism, a single calculation at each temperature of interest is sufficient to obtain results of the same accuracy as in a…
We probe the accuracy limit of {\it ab initio} calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive calculations of electron and hole mobilities require many-body quasiparticle corrections to band structures and electron-phonon matrix elements, the inclusion of spin-orbit coupling, and an extremely fine sampling of inelastic scattering processes in momentum space. By considering all these factors we obtain excellent agreement with experiment, and we identify…
Many-Body Correlation Effects in Fröhlich Electron-Phonon Coupling
University of Southern California（南加州大学）；Tamkang University（淡江大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. In this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this …
We theoretically study various aspects of the electron-surface optical phonon interaction effects in graphene on a substrate made of polar materials. We calculate the electron self-energy in the presence of the surface phonon-mediated electron-electron interaction focusing on how the linear chiral graphene dispersion is renormalized by the surface phonons. The electron self-energy as well as the quasiparticle spectral function in graphene are calculated, taking into account electron-polar optical phonon interaction by using a many body perturbative formalism. The scattering rate of free electr…
The interaction of electrons with crystal lattice vibrations (phonons) and collective charge-density fluctuations (plasmons) influences profoundly the spectral properties of solids revealed by photoemission spectroscopy experiments. Photoemission satellites, for instance, are a prototypical example of quantum emergent behavior that may result from the strong coupling of electronic states to plasmons and phonons. The existence of these spectral features has been verified over energy scales spanning several orders of magnitude (from 50 meV to 15-20 eV) and for a broad class of compounds such as …
For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and extreme non-adiabatic limit. Not only the values of the coupling parameters in the two limits, but also the expressions of the corresponding terms in the Hamiltonian differ. Depending on the distance between the dimer ions, some of the two-body couplings are comparable, or even larger than the one-body ones.
Carbon, a basic versatile element in our universe, exhibits rich varieties of allotropic phases, most of which possess promising nontrivial topological fermions. In this work, we identify a distinct topological phonon phase in a realistic carbon allotrope with a body-centered cubic structure, termed bcc-C$_{8}$. We show by symmetry arguments and effective model analysis that there are three intersecting phonon nodal rings perpendicular to each other in different planes. The intersecting phonon nodal rings are protected by time-reversal and inversion symmetries, which quantize the corresponding…
We study the electron-phonon coupling in the C60 fullerene within the first-principles GW approach, focusing on the lowest unoccupied t1u three-fold electronic state which is relevant for the superconducting transition in electron doped fullerides. It is shown that the strength of the coupling is significantly enhanced as compared to standard density functional theory calculations with (semi)local functionals, with a 48% increase of the electron-phonon potential Vep. The calculated GW value for the contribution from the Hg modes of 93 meV comes within 4% of the most recent experimental values.…
We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the phonon-mediated self-energy is composed by two distinct terms. One term is the Fan-Migdal self-energy and describes dynamic electron-phonon processes, the other term is a new contribution to the self-energy originating from the static displacements of the atomic nuclei in the polaronic ground state. The lowest-order approximation to the present theory yields the s…
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.
Phonon-assisted luminescence is a key property of defect centers in semiconductors, and can be measured to perform the readout of the information stored in a quantum bit, or to detect temperature variations. The investigation of phonon-assisted luminescence usually employs phenomenological models, such as that of Huang and Rhys, with restrictive assumptions that can fail to be predictive. In this work, we predict luminescence and study exciton-phonon couplings within a rigorous many-body perturbation theory framework, an analysis that has never been performed for defect centers. In particular,…
Many-body localization (MBL) has attracted significant attention due to its immunity to thermalization, role in logarithmic entanglement entropy growth, and opportunities to reach exotic quantum orders. However, experimental realization of MBL in solid-state systems has remained challenging. Here we report evidence of a possible phonon MBL phase in disordered GaAs/AlAs superlattices. Through grazing-incidence inelastic X-ray scattering, we observe a strong deviation of the phonon population from equilibrium in samples doped with ErAs nanodots at low temperature, signaling a departure from ther…
Using ab initio methods, we have studied the electron-phonon interaction in compressed, body-centered cubic (bcc) yttrium, which is predicted to be stable at 280 GPa [Melsen et al, Phys. Rev. B 48, 15574 (1993)]. We find that compressed, bcc yttrium has a large electron-phonon coupling with lambda=1.8, leading to a superconducting transition temperature T_c ~ 30 K or above. Our results indicate that the large electron-phonon coupling is due to the lattice hardening.
We present results of lattice dynamics calculations of the $P-V$ equation of state and the pressure dependence of the Raman-active $E_{2g}$ lattice phonon for $p-$H$_2$ and $o-$D$_2$ in a wide pressure range up to $\sim$2 Mbar using our recently developed semi-empirical many-body potential, and density-functional theory. Comparison with existing body of experimental and theoretical results showed that the employed many-body potential is a reliable basis for high-precision calculations for phases I, II, and III of solid hydrogens.
The indirect carrier-phonon vertex function is evaluated for cubic zirconia by employing the many-body perturbation theory on top of the frozen phonon model. The phonon-induced carrier velocity and spectral renormalization are represented at each individual lattice vibronic mode. Our results show that for the indirect electron-phonon scattering, optical phonons make up the dominant contribution. It is observed that, despite the phonon-phonon interaction, there is a substantial polaronic character for all the activated lattice optical vibrations which is in accordance with the previous experime…
We present first-principles calculations of the optical response of monolayer molybdenum disulfide employing the GW-Bethe Salpeter equation (GW-BSE) approach including self-energy, excitonic, and electron-phonon effects. We show that monolayer MoS2 possesses a large and diverse number of strongly bound excitonic states with novel k-space characteristics that were not previously seen experimentally or theoretically. The absorption spectrum is shown to be dominated by excitonic states with binding energy close to $1$~eV and by strong electron-phonon broadening in the visible to ultra-violet rang…
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…
In this paper the phonon self energy produced by anharmonicity is calculated using second order many body perturbation theory for all bcc, fcc and hcp transition metals. The symmetry properties of the phonon interactions are used to obtain an expression for the self energy as a sum over irreducible triplets, very similar to integration in the irreducible part of the Brillouin zone for one particle properties. The results obtained for transition metals shows that the lifetime is on the order of 10^10 s. Moreover the Peierls approximation for the imaginary part of the self energy is shown to be …
We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect of the electric field. This total-energy functional is expanded in small atomic displacements within the framework of density-functional perturbation theory. The linear response of field-polarized Bloch functions to atomic displacements is obtained by minimizing the second-order derivatives of the total-energy functional. In the general case of nonzero phon…
Ruddlesden-Popper (RP) phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) are evolved as new promising class of chalcogenide perovskites in the field of optoelectronics, especially in solar cells. However, detailed studies regarding its optical, excitonic, polaronic and transport properties are hitherto unknown. Here, we have explored the excitonic and polaronic effect in RP phases of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) using several first-principles based state-of-the-art methodologies under the framework of Many Body Perturbation Theory.…
With the ever-increasing sophistication of codes, the verification of the implementation of advanced theoretical formalisms becomes critical. In particular, cross comparison between different codes provides a strong hint in favor of the correctness of the implementations, and a measure of the (hopefully small) possible numerical differences. We lead a rigorous and careful study of the quantities that enter in the calculation of the zero-point motion renormalization of the direct band gap of diamond due to electron-phonon coupling, starting from the total energy, and going through the computati…
Carrier doping by the electric field effect has emerged recently as an ideal route for monitoring many-body physics in two-dimensional (2D) materials where the Fermi level is tuned in a way that -- indirectly -- the strength of the interactions can also be scanned. The possibility of systematic doping in combination with high resolution photoemission has allowed to uncover a genuinely many-body electron spectrum in single-layer MoS2 transition metal dichalcogenide, resolving three clear quasi-particle states, where only one state should be expected if the electron-phonon interaction vanished. …
In this paper we investigate from first principles the effect of the electron-phonon interaction in two paradigmatic nanostructures: trans-polyacetylene and polyethylene. We found that the strong electron-phonon interaction leads to the appearance of complex structures in the frequency dependent electronic self-energy. Those structures rule out any quasi-particle picture, and make the adiabatic and static approximations commonly used in the well-established Heine Allen Cardona (HAC) approach inadequate. We propose, instead, a fully ab-initio dynamical formulation of the problem within the Many…
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 tim…
Recent experimental data on the optical conductivity of niobium doped SrTiO$_{3}$ are interpreted in terms of a gas of large polarons with effective coupling constant $α_{eff}\approx2$. The {theoretical approach takes into account} many-body effects, the electron-phonon interaction with multiple LO-phonon branches, and the degeneracy and the anisotropy of the Ti t$_{2g}$ conduction band. {Based on the Fröhlich interaction, the many-body large-polaron theory} provides an interpretation for the essential characteristics, except -- interestingly -- for the unexpectedly large intensity of a peak a…
The electrical resistivity, thermoelectric power and electronic thermal conductivity of simple (isotropic) metals are studied in a uniform way. Starting from results of a variational solution of the Boltzmann equation, a generalized Matthiessen rule is used in order to superpose the inelastic (or not) electron-phonon and elastic electron-impurity scattering cross sections ("matrix elements"). The temperature dependence relative to these processes is given through simple functions and physical parameters over the usually investigated range of temperature for each transport coefficient. The cohe…
Amplification of light through stimulated emission or nonlinear optical interactions has had a transformative impact on modern science and technology. The amplification of other bosonic excitations, like phonons in solids, is likely to open up new remarkable physical phenomena. Here, we report on an experimental demonstration of optical phonon amplification. A coherent mid-infrared optical field is used to drive large amplitude oscillations of the Si-C stretching mode in silicon carbide. Upon nonlinear phonon excitation, a second probe pulse experiences parametric optical gain at all wavelengt…
In model Hamiltonians, like Fröhlich's, the electron-phonon interaction is assumed to be screened from the beginning. The same occurs when this interaction is obtained by using the state-of-the-art density functional perturbation theory as starting point. In this work I formally demonstrate that these approaches are affected by a severe over-screening error. By using an out-of-equilibrium Many-Body technique I discuss how to merge the many-body approach with density-functional perturbation theory in order to correct the over-screening error. A symmetric statically screened phonon self-energy i…
The concept of quasiparticles in solid-state physics is an extremely powerful way to describe complex many-body phenomena in terms of single particle excitations. Introducing a simple particle such as electron, e, hole, h, or a phonon, p, deforms a many-body system through interaction with other particles. We say the added particle is dressed or renormalized by a self-energy cloud that describes the response of the many-body system forming a new entity, the quasiparticle. With ultrafast laser techniques we can impulsively generate bare particles and observe their dressing by the many-body inte…
We present a self-consistent analysis of the photoemission spectral function A(k, w) of graphene monolayers grown epitaxially on SiC(0001). New information derived from spectral intensity anomalies (in addition to linewidths and peak positions) confirms that sizeable kinks in the electronic dispersion at the Dirac energy ED and near the Fermi level EF arise from many-body interactions, not single-particle effects such as substrate bonding or extra bands. The relative electron-phonon scattering rate from phonons at different energy scales evolves with doping. The electron-phonon coupling streng…
Here we present a theoretical analysis of inelastic effects on thermoelectric properties of molecular-scale junction in both linear and nonlinear response regimes. Considered device is composed of molecular quantum dot (with discrete energy levels) asymmetrically connected to metallic electrodes (treated within the wide-band approximation) via potential barriers, where molecular vibrations are modeled as dispersionless phonon excitations. Nonperturbative computational scheme, used in this work, is based on Green's function theory within the framework of polaron transformation (GFT-PT) which ma…
The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe$_2$ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, $\Re\left[χ_0(\mathbf{q})\right]$, from those due to the electron-phonon coupling vertex, $g_{\mathbf{q}}$, by following the response of semi-metallic (normal phase) 1T-TiSe$_2$ to the selective photo-doping of carriers into the electron pocket …
The interplay between electron-electron interaction and electron-phonon coupling has been one of the key issues in graphene as it can provide information on the origin of enhanced electron-phonon coupling in graphene by foreign atoms. In ytterbium-decorated graphene on SiC substrate, electron-phonon coupling exhibits strong enhancement compared to that of as-grown graphene. Based on angle-resolved photoemission study, the presence of ytterbium is also found to result in the decrease of Fermi velocity, revealing the enhancement of electron-electron interaction within the Fermi liquid theory. Ou…
