Two-dimensional localized vibrational modes around a polaron with the next-nearest-neighbor hopping interactions

Abstract

We have calculated the vibrational modes around a polaron to test the effects of the next-nearest-neighbor hopping ineractions on the localized modes within a framework of the two-dimensional mode. The results show that: (1) For a negative polaron, eleven localized modes have been found, compared with ten modes obtained on a previous work without non-nearest neighbor hopping. (2) For a positive polaron, two additional localized modes occur. (3) The localization of localized modes are strengthened and their frequencies move after turning on the next-nearest-neighbor hopping interactions.