A self-consistent many-body theory of polarons is presented. This unifies weak- and strong-coupling approaches to the electron-phonon interaction from first principles, opening the door toward a full characterization of polaronic effects in materials at all coupling strengths.
This article reviews recent theoretical developments in the ab initio study of polarons in materials. The polaron is an emergent quasiparticle that arises from the interaction between electrons and phonons in solids, and consists of an electron or a hole accompanied by a distortion of the crystal lattice. Recent advances in experiments, theory, and computation have made it possible to investigate these quasiparticles with unprecedented detail, reigniting the interest in this classic problem of condensed matter physics. Recent theoretical and computational advances include ab initio calculations of polaron spectral functions, wavefunctions, lattice distortions, and transport and optical properties. These developments provide new insight into polaron physics, but they have evolved somewhat independently from the earlier effective Hamiltonian approaches that laid the foundation of the field. This article aims to bridge these complementary perspectives by placing them within a single unified conceptual framework. To this end, we start by reviewing effective Hamiltonians of historical significance in polaron theory, ab initio techniques based on density functional theory, and many-body first-principles approaches to polarons. After this survey, we outline a general field-theoretic framework that bridges between these diverse approaches to polaron physics. For completeness, we also review recent progress in the study of exciton polarons and self-trapped excitons and their relations to polarons. Beyond the methodology, we discuss recent applications to several classes of materials that attracted attention in the context of polaron physics.
Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.
In this work, we demonstrate that accurate ground-state wave functions may be constructed for polarons in a fully ab initio setting across the wide range of couplings associated with both the large and small polaron limits. We present a single general unitary transformation approach which encompasses an ab initio version of the Lee-Low-Pines theory at weak coupling and the coherent-state Landau-Pekar framework at strong coupling, while interpolating between these limits in general cases. We show that perturbation theory around these limits may be performed in a facile manner to assess the accuracy of the approach, as well as provide an independent route to the ab initio properties of polarons. We test these ideas on the case of LiF, where the electron polaron is expected to be large and relatively weakly coupled, while the hole polaron is expected to be a strongly coupled small polaron.
In this work we demonstrate that accurate ground state wave functions may be constructed for polarons in a fully ab initio setting across the wide range of couplings associated with both the large and small polaron limits. We present a single general unitary transformation approach which encompasses an ab initio version of the Lee-Low-Pines theory at weak coupling and the coherent state Landau-Pekar framework at strong coupling while interpolating between these limits in general cases. We show that perturbation theory around these limits may be performed in a facile manner to assess the accuracy of the approach, as well as provide an independent route to the ab initio properties of polarons. We test these ideas on the case of LiF, where the electron-polaron is expected to be large and relatively weakly coupled, while the hole-polaron is expected to be a strongly coupled small polaron.
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.