Ab initio downfolding for electron-phonon coupled systems: constrained density-functional perturbation theory (cDFPT)

TL;DR

This paper introduces cDFPT, an ab initio method to accurately derive low-energy electron-phonon Hamiltonians by including high-energy electron screening effects, applicable to various phonon-related phenomena.

Contribution

The paper develops and demonstrates cDFPT, a modified DFPT approach that incorporates screening effects for realistic low-energy Hamiltonian construction in electron-phonon systems.

Findings

Successfully applied to fullerene superconductors

Provides a realistic Hamiltonian including high-energy electron screening

Enables study of phonons in strongly correlated materials

Abstract

We formulate an ab initio downfolding scheme for electron-phonon coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme, which we call constrained density-functional perturbation theory (cDFPT), can be implemented by slightly modifying the conventional DFPT, which is one of the standard methods to calculate phonon properties from first principles. Our scheme can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity and multiferroicity. We believe that the cDFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to the fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.