Bose-Einstein condensation in tight-binding bands

We present a theoretical study of the condensation of bosons in tight-binding bands corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. We have analyzed noninteracting bosons, weakly interacting bosons using the Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for the number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body-centered cubic lattice have the highest Bose condensation temperature. The growth of the condensate fraction of noninteracting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes the bosons to form a Bose-Mott-Hubbard insulator for integer filling.

Figure 1

The variation of the condensate fraction with temperature for bosons in a sc lattice for $n=0.8$ (top), $n=0.6$ (middle), and $n=0.4$ (bottom). In this and later figures, $W$ is the half-bandwidth.

Figure 2

The same as in Fig. 1 for bosons in a bcc lattice for $n=0.8$ (top), $n=0.6$ (middle), and $n=0.4$ (bottom).

Figure 3

The same as in Fig. 1 for bosons in a fcc lattice for $n=0.8$ (top), $n=0.6$ (middle), and $n=0.4$ (bottom).

Figure 4

The variation of the condensate fraction (for $n=0.6$) for bcc (top), fcc (middle), and sc (bottom) lattices. The dots are plots of $1-{(T∕T_c)}^{3∕2}$.

Figure 5

The variation of the Bose condensation temperature (of noninteracting or weakly interacting bosons) with $n$ for bcc (top), fcc (middle), and sc (bottom) lattices.

Figure 6

The variation of the condensate fraction (for $T=0$ and $n=0.4$) with $U∕W$ for bcc (top), fcc (middle), and sc (bottom) lattices.

Figure 7

Condensate fraction (for $n=0.4$) vs temperature for various values of $U∕W$ (shown on the curves) and for the sc lattice.

Figure 8

Bose condensation temperature (of strongly interacting bosons) vs $n$ for bcc (top), fcc (middle), and sc (bottom) lattices. The dots represent noninteracting bosons in a bcc lattice.