Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model

TL;DR

This paper investigates the behavior of a single polaron in the SSH model, revealing a sharp transition at a critical coupling strength that affects the polaron's momentum and other properties, with implications for experimental observations.

Contribution

It demonstrates that in the SSH model, the polaron exhibits a sharp transition at a critical coupling, unlike the smooth crossover seen in models with only momentum-dependent coupling.

Findings

Polaron ground state momentum changes abruptly at the critical coupling.

All properties except the phonon number are singular at the transition.

The results have implications for ARPES and conductivity experiments.

Abstract

We study a single polaron in the Su-Schrieffer-Heeger (SSH) model using four different techniques (three numerical and one analytical). Polarons show a smooth crossover from weak to strong coupling, as a function of the electron-phonon coupling strength $\lambda$, in all models where this coupling depends only on phonon momentum $q$. In the SSH model the coupling also depends on the electron momentum $k$; we find it has a sharp transition, at a critical coupling strength $\lambda_c$, between states with zero and nonzero momentum of the ground state. All other properties of the polaron are also singular at $\lambda = \lambda_c$, except the average number of phonons in the polaronic cloud. This result is representative of all polarons with coupling depending on $k$ and $q$, and will have important experimental consequences (eg., in ARPES and conductivity experiments).