The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model

TL;DR

This study investigates how next-nearest neighbour hopping influences the polaron effective mass in the Holstein model across one, two, and three dimensions, using exact calculations and perturbative methods.

Contribution

It introduces a modified Trugman method and a heuristic scaling to analyze the impact of NNN hopping on polaron properties in various dimensions.

Findings

Including NNN hopping increases the polaron effective mass.

The heuristic scaling maps NNN Holstein model to the original model.

Modified bandwidth considerations are crucial for accurate results.

Abstract

Allowing a single electron to hop to next-nearest neighbours (NNN) in addition to the closest atomic sites in the Holstein model, a modified Trugman method is applied to exactly calculate the effect on the polaronic effective mass in one, two, and three dimensions, building on the previous study of the one-dimensional NNN Holstein model. We also present perturbative calculations and a heuristic scaling factor for the coupling strength and ion frequency to nearly map the NNN Holstein model back onto the original Holstein model. When account is taken of the modified electronic bandwidth near the electron energy, we find that including NNN hopping effectively increases the polaron effective mass.