This study shows that a terahertz (THz) wave can be generated from the (001) surface of cleaved Bi$_{textrm{2}}$Se$_{textrm{3}}$ and Cu-doped Bi$_{textrm{2}}$Se$_{textrm{3}}$ single crystals using 800 nm femtosecond pulses. The generated THz power is strongly dependent on the carrier concentration of the crystals. An examination of the dependence reveals the two-channel free carrier absorption to which Dirac fermions are indispensable. Dirac fermions in Bi$_{textrm{2}}$Se$_{textrm{3}}$ are significantly better absorbers of THz radiation than bulk carriers at room temperature. Moreover, the characteristics of THz emission confirm the existence of a recently proposed surface phonon branch that is normalized by Dirac fermions.
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