The end points in the dispersion of Holstein polarons

TL;DR

This paper studies the existence of end points in the dispersion of Holstein polarons across different dimensions, revealing their presence in 3D and layered systems, but not in 1D or pure 2D models, using the Momentum Average approximation.

Contribution

It demonstrates that end points are generic in 3D Holstein models and appear in layered systems, extending understanding of polaron spectral features across dimensions.

Findings

End points are absent in 1D Holstein polarons.

End points are generic in 3D Holstein polarons.

Layered systems exhibit 3D-like end point behavior.

Abstract

We investigate the existence of end points in the dispersion of Holstein polarons in various dimensions, using the Momentum Average approximation which has proved to be very accurate for this model. An end point separates momenta for which the lowest-energy state is a discrete level, i.e., an infinitely-lived polaron, from those where the lowest-energy feature is a continuum in which the "polaron'" is signalled by a resonance with a finite lifetime. While such end points are known to not appear in 1D, we show here that they are generic in 3D if the particle-boson coupling is not too strong. The 2D case is "critical": a pure 2D Holstein model has no end points, like the 1D case. However, any amount of interlayer hopping leads to 3D-like behavior. As a result, such end points are expected to appear in the spectra of layered, quasi-2D systems described by Holstein models. Generalizations to other models are also briefly discussed.