We present a combined angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations study of the electronic structure of LaAgSb$_2$ in the entire first Brillouin zone. We observe a Dirac-cone-like structure in the vicinity of the Fermi level formed by the crossing of two linear energy bands, as well as the nested segments of Fermi surface pocket emerging from the cone. Our ARPES results show the close relationship of the Dirac cone to the charge-density-wave ordering, providing consistent explanations for exotic behaviors in this material.
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