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We mainly aim to search for the lithium depletion boundary (LDB) among thesub-stellar population of the open star cluster Coma Berenices. We carried outa search for brown dwarf (BD) candidates using colour-magnitude diagramscombining optical and infrared photometry from the latest public releases ofthe following large-scale surveys: UKIRT/UKIDSS, Pan-STARRS, SDSS, and AllWISE.We checked astrometric consistency with cluster membership using $Gaia$ DR2. Acouple dozen new candidate BDs located inside the tidal radius of Coma Ber arereported, but none of these are significantly fainter and cooler thanpreviously known members. A search for Li in three new and five previouslyknown BD candidate cluster members was performed via spectroscopic observationsusing the OSIRIS instrument at the 10.4-m GTC. No LiI resonance doublet at6707.8 A was detected in any of eight Coma Ber targets in the magnitude rangeJ=15--19 and G=20--23 observed with the GTC. Spectral types and radialvelocities were derived from the GTC spectra. These values confirm the clustermembership of four L2--L2.5 dwarfs, two of which are new in the literature. Thelarge Li depletion factors found among the four bona fide BD members in ComaBer implies that the LDB must be located at spectral type later than L2.5 inthis cluster. Using the latest evolutionary models for BDs, a lower limit of550 Myr on the cluster age is set. This constraint has been combined with otherdating methods to obtain an updated age estimate of 780$\pm$230 Myr for theComa Ber open cluster. Identification of significantly cooler sub-stellarcluster members in Coma Ber awaits the advent of the Euclid wide survey, whichshould reach a depth of about J=23; this superb sensitivity will make itpossible to determine the precise location of the sub-stellar LDB in thiscluster and to carry out a complete census of its sub-stellar population.

Search for the sub-stellar lithium depletion boundary in the open star cluster Coma Berenices