The polaron paradigm: a dual coupling effective band model

TL;DR

This paper investigates a combined polaron model with both diagonal and non-diagonal couplings, revealing a transition line that alters polaron properties and challenges the traditional self-trapping concept.

Contribution

It introduces a dual coupling polaron model and characterizes a transition line affecting ground state momentum and band shape, expanding understanding of polaron dynamics.

Findings

Transition line depends on adiabaticity parameter

Destabilization of Holstein polaron at transition

No self-trapping transition observed

Abstract

Non-diagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally-coupled paradigm of smoothly-varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and non-diagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the $k=0$ effective mass diverges, now becomes a transition line in the coupling constant plane - the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No 'self-trapping transition' exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.