We report a deficiency of luminous Lyman break galaxies (LBGs) with a large rest-frame equivalent width (EW_rest) of Lyman-alpha emission at z~5-6. Combining our spectroscopic sample of LBGs at z~5 and those from the literature, we found that luminous LBGs at z~5-6 generally show weak Lyman-alpha emissions, while faint LBGs show a wide range of Lyman-alpha EW_rest and tend to have strong (EW_rest >20A) Lyman-alpha emissions; i.e., there is a deficiency of strong Lyman-alpha emission in luminous LBGs. There seems to be a threshold UV luminosity for the deficiency; it is M_1400 = -21.5 ~ -21.0 mag, which is close to or somewhat brighter than the M* of the UV luminosity function at z~5 and 6. Since the large EW_rest of Lyman-alpha emission can be seen among the faint LBGs, the fraction of Lyman-alpha emitters in LBGs may change rather abruptly with the UV luminosity. If the weakness of Lyman-alpha emission is due to dust absorption, the deficiency suggests that luminous LBGs at z=5-6 tend to be in dusty and more chemically evolved environments and started star formation earlier than faint ones, though other causes cannot be ruled out.
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