frequency $\omega= T(a)$ (for the triangular lattice, $m_{0xy}=1/3a^{2}T(a)$). Finally, the bipolaron in a hexagonal lattice with out-of-plane hopping $T'=T(a)/3$ has also a light in-plane inverse mass, $m_{xy}^{**}\thickapprox 4.5
m_{0xy}$ but a small size, $R_{bp}\thickapprox 2.6a$ for experimentally achievable values of the phonon frequency $\omega=T(a)=200$meV and EPI, $\lambda=0.36$. Out-of-plane $m_{z}^{**}\thickapprox70m_{0z}$ is Holstein like, where $m_{0z}=1/2d^2T'$, ($d$ is the inter-plane spacing). When bipolarons are small and pairs do not overlap, the pairs can form a BEC at $T_{BEC}=3.31(2n_B/a^2\sqrt{3}d)^{2/3}/(m_{xy}^{2/3}m_z^{1/3})$. If we choose realistic values for the lattice constants of 0.4 nm in the plane and 0.8 nm out of the plane, and allow the density of bosons to be $n_B$=0.12 per lattice site, which easily avoids overlap of pairs, then $T_{BEC}\thickapprox$ 300K.

Summary
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For a very strong electron-phonon coupling in the Holstein model with the zero-range EPI, polarons become self-trapped on a single lattice site and bipolarons are on-site singlets. The on-site bipolaron mass appears only in the second order of polaron hopping [@aleran], so that on-site bipolarons are very heavy. This estimate led some authors to the conclusion that *high-temperature* bipolaronic superconductivity is impossible .

However we have found that small but relatively light bipolarons could exist within the realistic range 