Comparing the canonical-transformation and energy-functional approaches for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. Various theoretical treatments of small polarons have been proposed. We recently developed an ab initio approach based on canonical transformations that can efficiently compute the formation and energetics of small polarons with quantitative accuracy [1]. A different, energy-functional approach has also been proposed in the literature [2]. In this talk, we compare these two methods using a unified formalism, which allows us to shed light on the physical effects included or neglected in these two approaches. We show that our canonical transformation formalism can properly include lattice vibrational effects while using a fixed polaron wave function. Conversely, we show that the energy-functional approach neglects lattice vibrations and treats the electrons and phonons as decoupled; it attempts to describe the polaron wave function but misses the physics of polaron self-localization and band narrowing. We will conclude our talk by presenting extensions of the canonical transformation approach to compute the polaron wave function as well as charge transport in the polaron hopping regime.

[1] N.-E. Lee, H.-Y. Chen, J.-J. Zhou, and M. Bernardi, Phys. Rev. Materials. 5, 063805 (2021)

[2] W. H. Sio, C. Verdi, S. Ponce, and F. Giustino, Phys. Rev. B 99, 235139 (2019).