The gapless energy band spectra make the structures based on graphene and graphenebilayer with the population inversion to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer, the indirect interband radiative transitions accompanied by scattering of carriers by disorder can provide a substantial negative contribution to the THz conductivity (together with the direct interbandtransitions). In the graphene bilayer on high-κ substrates with point charged defects, thesetransitions substantially compensate the losses due to the intraband (Drude) absorption. We also demonstrate that the indirect interband contribution to the THz conductivity in a graphenebilayer with the extended defects (such as the charged impurity clusters) can surpass by several times the fundamental limit associated with the direct interband transitions, and the Drude conductivity as well. These predictions can affect the strategy of the graphene-based THz laser implementation.
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