  We present a search for low-mass brown dwarfs in the Pleiades open cluster.
The identification of Pleiades members fainter and cooler than those currently
known allows us to constrain evolutionary models for L dwarfs and to extend the
study of the cluster mass function to lower masses. We conducted a 1.8 deg^2
near-infrared J-band survey at the 3.5m Calar Alto Telescope, with completeness
J~19.0. The detected sources were correlated with those of previously available
optical I-band images (completeness I~22). Using a J versus I-J
colour-magnitude diagram, we identified 18 faint red L-type candidates, with
magnitudes 17.4<J<19.7 and colours I-J>3.2. If Pleiades members, their masses
would span ~0.040-0.020 M_Sol. We performed follow-up HKs-band imaging to
further confirm their cluster membership by photometry and proper motion. Out
of 11 IJ candidates with proper motion measurements, we find six cluster
members, two non-members and three whose membership is uncertain and depends on
the intrinsic velocity dispersion of Pleiades brown dwarfs. This dispersion (>4
mas yr^-1) is at least four times that of cluster stars with masses >1 M_Sol.
Five of the seven other IJ candidates are discarded because their J-Ks colours
are bluer than those of confirmed members. The J versus I-J sequence of the
L-type candidates at J>18 is not as red as theoretical models predict; it
rather follows the field L-dwarf sequence translated to the cluster distance.
This sequence overlapping, also observed in the J versus J-H and J-K diagrams,
suggests that Pleiades and field L dwarfs may have similar spectral energy
distributions and luminosities, and thus possibly similar radii. Also, we find
alpha=0.5+-0.2 for a power-law approximation dN/dM propor. M^-alpha of the
survey mass spectrum in the mass range 0.5-0.026 M_Sol.
