Many-Body Self-Interaction and Polarons

Stefano Falletta, Alfredo Pasquarello
2022
Article

Résumé

We address the many-body self-interaction in relation to polarons in density functional theory. Our study provides (i) a unified theoretical framework encompassing many-body and one-body forms of self-interaction and (ii) an efficient semilocal scheme for charge localization. Our theoretical formulation establishes a quantitative connection between the many-body and one-body forms of self-interaction in terms of electron screening, thereby conferring superiority to the concept of many-body self-interaction. Our semilocal methodology involves the use of a weak localized potential and applies equally to electron and hole polarons. We find that polarons free from many-body self-interaction have formation energies that are robust with respect to the functional adopted.

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https://infoscience.epfl.ch/record/297111?ln=fr

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We develop a unified theoretical framework encompassing one-body and many-body forms of self-interaction. We find an analytic expression for both the one-body and the many-body self-interaction energies, and quantitatively connect the two expressions through the dielectric constant. The two forms of self-interaction are found to coincide in the absence of electron screening. This analysis confers superiority to the notion of many-body self-interaction over the notion of one-body self-interaction. Next, we develop a semilocal density functional scheme that addresses the many-body self-interaction of polarons, thereby overcoming the limitations of standard density functional theory. Polaron localization is achieved through the addition of a weak local potential in the Kohn-Sham Hamiltonian that enforces the piece-wise linearity of the total energy upon partial electron occupation. Our method equivalently applies to electron and hole polarons and does not require any constraint on the wave functions during the self-consistent optimization. The implementation of this scheme does not produce any computational overhead compared to standard semilocal calculations and achieves fast convergence. This approach results in polaron properties, including the atomic geometry, the electron density, and the formation energy, which are close to those achieved with a hybrid functional that similarly satisfies the piece-wise linearity condition. This suggests that addressing the many-body self-interaction results in a polaron description that is robust with respect to the functional adopted. We illustrate our approach through applications to the electron polaron in BiVO4 , the hole polaron in MgO, and the hole trapped at the Al impurity in α-SiO2.

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Ab Initio Electron-Phonon Interactions in Correlated Electron Systems

Matteo Cococcioni, Andrea Floris, Nicola Marzari, Iurii Timrov

Electron-phonon (e-ph) interactions are pervasive in condensed matter, governing phenomena such as transport, superconductivity, charge-density waves, polarons, and metal-insulator transitions. First-principles approaches enable accurate calculations of e-ph interactions in a wide range of solids. However, they remain an open challenge in correlated electron systems (CES), where density functional theory often fails to describe the ground state. Therefore reliable e-ph calculations remain out of reach for many transition metal oxides, high-temperature superconductors, Mott insulators, planetary materials, and multiferroics. Here we show first-principles calculations of e-ph interactions in CES, using the framework of Hubbard-corrected density functional theory (DFT + U) and its linear response extension (DFPT + U), which can describe the electronic structure and lattice dynamics of many CES. We showcase the accuracy of this approach for a prototypical Mott system, CoO, carrying out a detailed investigation of its e-ph interactions and electron spectral functions. While standard DFPT gives unphysically divergent and short-ranged e-ph interactions, DFPT + U is shown to remove the divergences and properly account for the long-range Frohlich interaction, allowing us to model polaron effects in a Mott insulator. Our work establishes a broadly applicable and affordable approach for quantitative studies of e-ph interactions in CES, a novel theoretical tool to interpret experiments in this broad class of materials.

AMER PHYSICAL SOC2021

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