  The determination of the brown dwarf binary fraction may contribute to the
understanding of the substellar formation mechanisms. Unresolved brown dwarf
binaries may be revealed through their peculiar spectra or the discrepancy
between optical and near-infrared spectral type classification.
  We obtained medium-resolution spectra of 22 brown dwarfs with these
characteristics using the X-Shooter spectrograph at the VLT.
  We aimed to identify brown dwarf binary candidates, and to test if the
BT-Settl 2014 atmospheric models reproduce their observed spectra.
  To find binaries spanning the L-T boundary, we used spectral indices and
compared the spectra of the selected candidates to single spectra and synthetic
binary spectra. We used synthetic binary spectra with components of same
spectral type to determine as well the sensitivity of the method to this class
of binaries.
  We identified three candidates to be combination of L plus T brown dwarfs. We
are not able to identify binaries with components of similar spectral type. In
our sample, we measured minimum binary fraction of $9.1^{+9.9}_{-3.0}$.
  From the best fit of the BT-Settl models 2014 to the observed spectra, we
derived the atmospheric parameters for the single objects. The BT-Settl models
were able to reproduce the majority of the SEDs from our objects, and the
variation of the equivalent width of the RbI (794.8 nm) and CsI (852.0 nm)
lines with the spectral type. Nonetheless, these models did not reproduce the
evolution of the equivalent widths of the NaI (818.3 nm and 819.5 nm) and KI
(1253 nm) lines with the spectral type.
