The effects of next to nearest neighbor hopping on Bose-Einstein condensation in cubic lattices

TL;DR

This study investigates how next to nearest neighbor hopping energy influences Bose-Einstein condensation in cubic lattices, revealing lattice-dependent effects on condensation temperature and condensate depletion.

Contribution

It provides new insights into the impact of next to nearest neighbor hopping on Bose-Einstein condensation in different cubic lattice structures using Bogoliubov theory.

Findings

Condensation temperature increases with $t'$ in simple cubic lattices.

Condensation temperature decreases with $t'$ in bcc and fcc lattices.

Interaction-induced condensate depletion varies with lattice type.

Abstract

In this paper, we present results of our calculations on the effects of next to nearest neighbor boson hopping ($t^{\prime}$) energy on Bose-Einstein condensation in cubic lattices. We consider both non-interacting and repulsively interacting bosons moving in the lowest Bloch band. The interacting bosons are studied making use of the Bogoliubov method. We find that the bose condensation temperature is enhanced with increasing $t^{\prime}$ for bosons in a simple cubic (sc) lattice and decreases for bosons in body-centered cubic (bcc) and face-centered cubic (fcc) lattices. We also find that interaction induced depletion of the condensate is reduced for bosons in a sc lattice while is enhanced for bosons in bcc and fcc lattices.