Electron-phonon coupling has been a central topic in condensed matter physics for decades, and firstprinciples methods have demonstrated remarkable success in quantitatively capturing its role in a wide variety of physical phenomena and materials. Conventional calculations of electron-phonon coupling typically assume that phonons have infinite lifetimes, but phonons can exhibit finite lifetimes due to anharmonic phonon-phonon interactions. In this work, we derive an expression for the electron-phonon coupling scattering rates including the effects of anharmonic three-phonon interactions, which lead to phonon dephasing and finite phonon lifetimes. We also describe a first-principles implementation of this anharmonic electron-phonon coupling which can be seamlessly integrated within existing workflows for the evaluation of electron-phonon and phonon-phonon coupling interactions. Finally, we present calculations of electron-phonon scattering rates including phonon dephasing in a range of materials, and discuss the different microscopic mechanisms by which anharmonic phonons influence electron-phonon coupling. This study establishes the importance of finite phonon lifetimes in the evaluation of electron-phonon coupling, and provides a platform to explore these effects in a wide range of materials and phenomena.
Electron-phonon coupling has been a central topic in condensed matter physics for decades, and firstprinciples methods have demonstrated remarkable success in quantitatively capturing its role in a wide variety of physical phenomena and materials. Conventional calculations of electron-phonon coupling typically assume that phonons have infinite lifetimes, but phonons can exhibit finite lifetimes due to anharmonic phonon-phonon interactions. In this work, we derive an expression for the electron-phonon coupling scattering rates including the effects of anharmonic three-phonon interactions, which lead to phonon dephasing and finite phonon lifetimes. We also describe a first-principles implementation of this anharmonic electron-phonon coupling which can be seamlessly integrated within existing workflows for the evaluation of electron-phonon and phonon-phonon coupling interactions. Finally, we present calculations of electron-phonon scattering rates including phonon dephasing in a range of materials, and discuss the different microscopic mechanisms by which anharmonic phonons influence electron-phonon coupling. This study establishes the importance of finite phonon lifetimes in the evaluation of electron-phonon coupling, and provides a platform to explore these effects in a wide range of materials and phenomena.
Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.
Ab initio downfolding describes the electronic structure of materials within a low-energy subspace, often around the Fermi level. Typically starting from mean-field calculations, this framework allows for the calculation of one- and two-electron interactions, and the parametrization of a many-body Hamiltonian representing the active space of interest. The subsequent solution of such Hamiltonians can provide insights into the physics of strongly-correlated materials. While phonons can substantially screen electron-electron interactions, electron-phonon coupling has been commonly ignored within ab initio downfolding, and when considered this is done only for short-range interactions. Here we propose a theory of ab initio downfolding that accounts for all mechanisms of electron-phonon coupling on equal footing, regardless of the range of the interactions. Our practical computational implementation is readily compatible with current downfolding approaches. We apply our approach to polar materials MgO and GeTe, and we reveal the importance of both short-range and long-range electron-phonon coupling in determining the magnitude of electron-electron interactions. Our results show that in the static limit, phonons reduce the on-site repulsion between electrons by 40% for MgO, and by 79% for GeTe. Our framework also predicts that overall attractive nearest-neighbor interactions arise between electrons in GeTe, consistent with superconductivity in this material.
Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.
Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo (DiagMC) data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109 (2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.
While different expressions of homogeneous linear electronic dipole moment time correlation functions and their respective absorption lineshapes of anharmonic systems were derived and discussed at length in part I [Toutounji, M. J. Phys. Chem. B 2010, in press] of this study, the electronic dephasing (zero-phonon line width), caused by pseudolocal phonons, and vibrational relaxation time scales were treated equally, hence, unphysical. In this study electronic dephasing and vibrational structure are correctly accounted for in harmonic and anharmonic multimode systems. Model calculations are presented. Anharmonic hole-burned spectra are calculated using linear anharmonic absorption lineshapes. An analytical expression of hole-burned absorption line shape in terms of the linear dipole moment time correlation function, leading to a hole-burned absorption line shape expressed in time-domain, is reported. An elementary method is utilized to treat nonlinear spectra in anharmonic molecules. The link between a hole-burned spectrum and a 2-pulse photon echo profile is established by combining the theoretical framework of Mukamel and that of Hays-Small, thereby calculating photon echo signals of anharmonic systems. Model photon echo calculations of a solvable harmonic model and an anharmonic system are reported. Applications to Al-phthaolcyanine tetrasulphonate (APT) in hyperquenched glassy ethanol and special pair bacterial reaction center are presented and discussed in detail.
Electron-phonon interactions play a central role in the behaviour of matter in the condensed phase. Physicists’ interest in this subject can be traced back to the early days of quantum mechanics, when key concepts like vibration quanta in the theory of specific heat or the Born-Oppenheimer approximation in molecular electronic structure, to mention a few, were first introduced. The controlled manufacturing of nanoscale systems has ushered a renewed interest in the basic aspects of electron-phonon interactions since the spatial confinement in nano-structures can enhance the effect of specific vibrational modes, leading to concrete manifestations of interesting concepts such as, local temperature and heating. It is also expected that in an another area of physics, namely ultracold-atoms, the study of the interaction between itinerant fermions and phonon-like excitations can be successfully undertaken due to the possibility of controlled and accurate manipulation of experimental setups and selective inclusion of physical effects. This thesis investigates some elementary aspects of the electron-phonon interactions in small open and closed 1D chains. Using an exact numerical method, the time-behaviour of 1) quantum rings in magnetic fields, and 2) parabolically trapped systems has been addressed when electron-phonon and/or electron-electron interaction are present. A first outcome of this thesis is the implementation ex-novo of a computer code to describe the non-equilibrium dynamics of these aforementioned model systems. Using such numerical capability, we performed several numerical simulations. As a second outcome of our work, we have obtained a set of results which illustrates the complex interplay among fermion-fermion and fermion-phonon interactions in the presence of magnetic time-varying fields, and how such interplay depends on the i) non/adiabatic and ii) non/resonant character of the external perturbation. Our work only touches the very superficial aspects of these very interesting topics, and we hope it will provide inspiration for further investigations.