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

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