Large cylindrical polaron in orthorhombic SnSe: A theoretical study

Due to its phenomenal thermoelectric properties, SnSe has received increased interest, triggering systematic studies of both electronic and vibrational properties and the associated coupling. Recent experimental work claims that orthorhombic SnSe sustains a one-dimensional large polaron with a dimension of about 2 nm. In search of its theoretical signature, we first establish the level of precision that can be reached in describing the electronic structure of SnSe by means of ab initio density functional and many-body perturbation theories. As the characterization of band extrema by means of effective masses plays a crucial role in determining polaron properties, we signal the existence of a broad variation of such quantity among the various ab initio methodologies employed and in the available experimental data. The impact of electron-phonon coupling is then analyzed by employing the recently developed generalized Fröhlich model as well as the nonadiabatic Allen-Heine-Cardona formalism, and their relative accuracy is rationalized. We found that, although the vast majority of band extrema in SnSe cannot sustain a large one-dimensional polaron with a radius as small as 2 nm, there is one case in which another type of polaron emerges, indeed one-dimensional, but with an unusual oscillating electronic density of an approximate real space period of ∼3 nm that evokes a stack of disks. Such type of polaron is obtained from two theoretical treatments: a fixed Gaussian ansatz for the polaron wave function and a variational approach, both within the Fröhlich formalism. We hypothesize that such cylindrical polaron might be found in other materials with extended, shallow double-well band extrema.