Theory of ab initio downfolding with arbitrary range electron-phonon coupling

TL;DR

This paper develops a comprehensive ab initio downfolding method that includes all electron-phonon interactions of any range, revealing significant effects on electron-electron interactions and superconductivity in materials like MgO and GeTe.

Contribution

It introduces a novel theory for ab initio downfolding that accounts for both short- and long-range electron-phonon couplings simultaneously, compatible with existing methods.

Findings

Phonons reduce on-site electron repulsion significantly in MgO and GeTe.

Long-range electron-phonon interactions are crucial in determining material properties.

Attractive interactions suggest potential for superconductivity in GeTe.

Abstract

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.