Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Abstract

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 selfconsistent, 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 strongcoupling 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.

Screening and Antiscreening in Fullerene-Like Cages: Dipole-Field Amplification with Ionic Nanocages

“…We observe here the analogy with ionic crystals, where strong electron-phonon coupling can be associated to the rise of polarons [32], which involve a major interplay between charge localization and structural distortions.…”

First-principles study of the bandgap renormalization and optical property of β-LiGaO2

“…[50,51] A self-consistent many-body theory of electron-phonon couplings was developed, which unifies the calculations of phonon-induced band structure renormalization and polaron localization. [52,53] The localization effect on the band structure renormalization of β -LiGaO 2 is worth investigating in future work. Moreover, recent developments of polaron calculations [50][51][52][53] make possible the exploration of polaronic effects on the exciton property.…”

“…[52,53] The localization effect on the band structure renormalization of β -LiGaO 2 is worth investigating in future work. Moreover, recent developments of polaron calculations [50][51][52][53] make possible the exploration of polaronic effects on the exciton property.…”

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

“…Among others, Sio et al [14,15] developed a first-principles theory of polarons, later reformulated using a variational principle [16]. More recently, Lafuente-Bartolome et al proposed a self-consistent many-body Green's function theory which simultaneously addresses phonon-induced band structure renormalization and small polaron formation [17,18]. From another perspective, Houtput and Tempere [19] derived anharmonic corrections to the Fröhlich Hamiltonian, and Kandolf et al [20] and Macheda et al [21] investigated the Fröhlich interaction in doped solids.…”