Facile ab initio approach for self-localized polarons from canonical transformations

Abstract

Electronic states in a crystal can localize due to strong electron-phonon (e-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wave function using ab initio e-ph interactions. Comparison of the calculated polaron and band-edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime.

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

“…The diagonal part of λ mn vanishes, and thus exp(−λ mm ) = 1 for all sites m. In ionic materials, usually the off-diagonal part of exp(−λ mn ) is orders of magnitude smaller than unity (typically of order 10 −2 to 10 −10 at 300 K), as we verify explicitly with numerical calculations here and in Ref. [1]. In this case, polaron hopping is negligible, and we have exp(−λ mn ) ≈ δ mn .…”

“…Starting from the Hamiltonian matrix E mn , we calculate the polaron band structure using a standard tight-binding approach. Due to its simple workflow, the canonical-transformation method enables rapid calculations of small-polaron energies in a wide range of materials [1], and is particularly promising for high-throughput and data-driven studies of small polarons.…”

“…The conventional approach employs DFT calculations on supercells with excess charge or defects added explicitly [12][13][14][15]. Yet, recent work has developed a different family of firstprinciples methods aimed at computing polarons using only a unit cell of the material with ab initio e-ph calculations [1][2][3]. The goal of these approaches is two-fold: reducing computational cost by avoiding calculations on large supercells with many atoms, and formulating rigorous polaron calculations by combining many-body techniques with first-principles theories.…”

“…Within this recent body of work, we formulated an efficient approach based on the canonical transformation formalism [1]; this method can compute the small-polaron formation energy in a localized Wannier basis starting from a trial polaron wave function. Its computational cost is a minimal overhead to a DFT calculation on a unit cell, enabling investigations of small polarons in a wide range of materials with minimal computational effort [1]. A different approach, proposed by Sio et al [2,3], uses a Landau-Pekar-type energy functional to obtain coupled equations for the polaron wave function and its associated atomic displacements.…”

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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].

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