Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

Abstract

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons[1]. A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature [2,3]. In this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

arXiv comment14 pages, 3 figures

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Cited by in corpus (5)

• Variational Lang-Firsov approach plus Møller-Plesset perturbation theory with applications to ab initio polariton chemistry
• Data-driven compression of electron-phonon interactions
• Computational protocol to evaluate electron-phonon interactions within density matrix perturbation theory
• Variational Polaron Equations Applied to the Anisotropic Fröhlich Model
• Comparison between first-principles supercell calculations of polarons and the ab initio polaron equations