LAUSR

We study the Bose–Einstein condensation in a tight-binding model with a hopping rate enhanced only on a surface. We show that this model exhibits two different critical phenomena depending on whether the hopping rate on the surface $$t_s$$ts exceeds the critical value 5t / 4, where t is the hopping rate in the bulk. For $$t_s/t<5/4$$ts/t<5/4, normal Bose–Einstein condensation occurs, while the Bose–Einstein condensation for $$t_s/t\ge 5/4$$ts/t≥5/4 is characterized by the spatial localization of the macroscopic number of particles at the surface. By exactly calculating the surface free energy, we show that for $$t_s/t<5/4$$ts/t<5/4, the singularity of the surface free energy stems from diverging the correlation length in the bulk, while for $$t_s/t\ge 5/4$$ts/t≥5/4, it is induced by the coupling effects between the bulk and surface.