Polarons in the Cubic Generalized Fr\"ohlich Model: Spontaneous Symmetry Breaking

TL;DR

This paper numerically investigates polarons in a cubic generalized Fr"ohlich model, revealing spontaneous symmetry breaking and highlighting the limitations of previous Gaussian Ansatz approaches, with implications for understanding polaronic states in degenerate systems.

Contribution

It provides a detailed numerical analysis of polarons in the cubic generalized Fr"ohlich model, uncovering symmetry breaking and comparing methods to improve modeling accuracy.

Findings

Polaron solutions exhibit spontaneous symmetry breaking from cubic to lower symmetry groups.

The Gaussian Ansatz approach is inadequate for degenerate band systems.

The phase diagram of symmetry groups differs from simple effective mass analysis.

Abstract

Within the variational polaron equation framework, the Fr\"ohlich model for cubic systems with three-fold degenerate electronic bands is numerically solved in the strong coupling regime, for a wide range of its input parameters. By comparing the results to the previously reported ones obtained with the Gaussian Ansatz approach, the inadequacy of the latter is uncovered, especially when degenerate bands are present in a system. Moreover, the symmetry groups of polaronic solutions in the cubic generalized Fr\"ohlich model without spin-orbit coupling are investigated: we provide and discuss a phase diagram of symmetry groups of ground-state polarons, showing spontaneous symmetry breaking. While the cubic symmetry of the three-band degenerate model Hamiltonian corresponds to the full octahedral group $O_h$, lowest-energy polarons possess either $D_{4h}$ or $D_{3d}$ point groups. This phase diagram bears some similarities but differs nevertheless from the one that is obtained by the straight analysis of the band effective masses. The obtained results will provide a firm ground for further exploration of the generalized Fr\"ohlich model and will likely be applicable beyond the model's inherent approximations.